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The attractive Hubbard model has become a model readily realizable with ultracold atoms on optical lattices. However, the superconducting (superfluid) critical temperatures, $T_c$'s, are still somewhat smaller than the lowest temperatures achieved in experiments. Here we consider two possible routes, generically called layering, to increase $T_c$: a bilayer and a simple cubic lattice, both with tunable hopping, $t_z$, between attractive Hubbard planes. We have performed minus-sign--free determinant quantum Monte Carlo simulations to calculate response functions such as pairing correlation functions, uniform spin susceptibility, and double occupancy, through which we map out some physical properties. We have found that by a judicious choice of fillings and intensity of on-site attraction, a bilayer can exhibit $T_c$'s between 1.5 and 1.7 times those of the single layer; for the simple-cubic lattice the enhancement can be 30\% larger than the maximum for the single layer. We also check the accuracy of both a BCS-like estimate for $T_c$ in the attractive Hubbard model, as well as of an upper bound for $T_c$ based on the superfluid density., Comment: 12 pages, 17 figures

Cold atom systems provide a rich platform to realize strongly interacting condensed matter systems, and recent progress in fluorescence imaging technique has enabled identification of nontrivial doublon, singlon, and holon correlation functions. We show that these correlators can be used to identify the conditions under which local moments form in an interacting electronic system. Toward this end, we report a Determinantal Quantum Monte Carlo (DQMC) study of such correlation functions in the two-dimensional repulsive Fermi Hubbard model on a square lattice as a function of doping, interaction strength and temperature. We find definite signatures of the crossover from small U(band regime) to large U(correlated insulator regime). Our key findings are: (1) An opening of a charge gap in the thermodynamic density of states is accompanied by the appearance of temperature insensitive points in the equation of state at finite doping, which can be used to distinguish the band regime in cold atom experiments. (2) Nearest neighbor doublon holon correlations track the opening of charge gap; these compete with density correlations to generate moment moment correlations that show different behavior in the metallic and correlated insulator regime. (3) Non local correlation functions can be used to distinguish between the two regimes, both at and away from half filling. Our results allow comparisons of different correlation functions with recent experimental findings and guide further experimental investigations., Comment: 17 pages, 10 figures

The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical mean field theory (DMFT), including cluster-DMFT, one usually obtains the Green's function in imaginary-time $G(\tau)$. The process of inverting a Laplace transform to obtain the spectral function $A(\omega)$ in real-frequency is an ill-posed problem and forms the core of the analytic continuation problem. In this Letter, we propose to use a completely unsupervised autoencoder-type neural network to solve the analytic continuation problem. We introduce an encoder-decoder approach that, together with only minor physical assumptions, can extract a high-quality frequency response from the imaginary time domain. With a deeply tunable architecture, this method can, in principle, locate sharp features of spectral functions that might normally be lost using already well-established methods, such as maximum entropy (MaxEnt) methods. We demonstrate the strength of the autoencoder approach by applying it to QMC results of $G(\tau)$ for a single-band Hubbard model. The proposed method is general and can also be applied to other ill-posed inverse problems., Comment: 7 pages, 5 figures, supplement

The topological properties of the Su-Schrieffer-Heeger (SSH) model in the presence of nearest-neighbor interaction are investigated by means of a topological marker, generalized from a noninteracting one by utilizing the single-particle Green's function of the many-body ground state. We find that despite the marker not being perfectly quantized in the presence of interactions, it always remains finite in the topologically nontrivial phase while converging to zero in the trivial phase when approaching the thermodynamic limit, and hence correctly judges the topological phases in the presence of interactions. The marker also correctly captures the interaction-driven, second-order phase transitions between a topological phase and a Landau-ordered phase, which is a charge density wave order in our model with a local order parameter, as confirmed by the calculation of entanglement entropy and the many-body Zak phase. Our work thus points to the possibility of generalizing topological markers to interacting systems through Green's function, which may be feasible for topological insulators in any dimension and symmetry class., Comment: 10 pages, 10 figures, Accepted to Physical Review B

The interest in the physical properties of kagome lattices has risen considerably. In addition to the synthesis of new materials, the possibility of realizing ultracold atoms on an optical kagome lattice (KL) raises interesting issues. For instance, by considering the Hubbard model on an anisotropic KL, with a hopping $t^\prime$ along one of the directions, one is able to interpolate between the Lieb lattice ($t^\prime=0$) and the isotropic KL ($t^\prime=t$). The ground state of the former is a ferrimagnetic insulator for any on-site repulsion, $U$, while the latter displays a transition between a paramagnetic metal and a Mott insulator. One may thus consider $t^\prime$ as a parameter controlling the degree of magnetic frustration in the system. By means of extensive quantum Monte Carlo simulations, we have examined magnetic and transport properties as $t^\prime$ varies between these limits in order to set up a phase diagram in the $(U/t, t^\prime/t)$ parameter space. As an auxiliary response, analysis of the average sign of the fermionic determinant provides consistent predictions for critical points in the phase diagram. We observe a metal-insulator transition occurring at some critical point $U_c^\text{M}(t^\prime)$, which increases monotonically with $ t^\prime $, from the unfrustrated lattice limit. In addition, we have found that the boundary between the ferrimagnetic insulator and the Mott insulator rises sharply with $t^\prime$., Comment: 8 pages, 7 figures

We obtain the Seebeck coefficient or thermopower $S$, which determines the conversion efficiency from thermal to electrical energy, for the two-dimensional Hubbard model on different geometries (square, triangular, and honeycomb lattices) for different electronic densities and interaction strengths. Using Determinantal Quantum Monte Carlo (DQMC) we find the following key results: (a) the bi-partiteness of the lattice affects the doping dependence of $S$; (b) strong electronic correlations can greatly enhance $S$ and produce non-trivial sign changes as a function of doping especially in the vicinity of the Mott insulating phase; (c) $S(T)$ near half filling can show non-monotonic behavior as a function of temperature. We emphasize the role of strong interaction effects in engineering better devices for energy storage and applications, as captured by our calculations of the power factor $PF=S^2 \sigma$ where $\sigma$ is the dc conductivity., Comment: 10 pages, 8 figures

Heavy fermion materials are compounds in which localized $f$-orbitals hybridize with delocalized $d$ ones, leading to quasiparticles with large renormalized masses. The presence of strongly correlated $f$-electrons at the Fermi level may also lead to long-range order, such as magnetism, or unconventional superconductivity. From a theoretical point of view, the ``standard model'' for heavy fermion compounds is the Periodic Anderson Model (PAM). Despite being extensively scrutinized, its thermodynamic properties in three-dimensional lattices have not been carefully addressed by unbiased methodologies. Here we investigate the 3D PAM employing state-of-the-art finite temperature auxiliary field quantum Monte Carlo simulations. We present the behavior of the kinetic energy, the entropy, the specific heat, and the double occupancy as functions of the temperature and the hybridization strength. From these quantities, and by the analysis of the spin-spin correlation functions, we investigate the occurrence of magnetic phase transitions at finite temperatures, and determine the phase diagram of the model, including the behavior of the N\'eel temperature as a function of the external parameters., Comment: 9 pages, 9 figures

Over the past decades, magnetic frustration has been under intense debate due to its unusual properties. For instance, frustration in the kagome lattice suppresses long range spin correlations and it is expected to be a candidate for a spin liquid system. Therefore, with the advent of experiments with ultra-cold atoms, the interest for frustrated geometries has increased. Given this, in the present work we investigate the repulsive Hubbard model on the kagome lattice by unbiased quantum Monte Carlo simulations. We examine its thermodynamic properties, as well as the magnetic and transport response of the system at finite temperatures and different values of the repulsive interaction. From these results, we discuss the possible occurrence of adiabatic cooling, a quite important feature in ultra-cold systems, and the presence of a metal-to-insulator transition at a finite interaction strength. Our findings may guide future experiments in ultra-cold fermionic atoms on the kagome lattice., Comment: 8 pages, 11 figures

Recent experiments with ultracold fermionic atoms in optical lattices have provided a tuneable and clean realization of the attractive Hubbard model (AHM). In view of this, several physical properties may be thoroughly studied across the crossover between weak (Bardeen-Cooper-Schrieffer, BCS) and strong (Bose-Einstein condensation, BEC) couplings. Here we report on extensive determinant Quantum Monte Carlo (DQMC) studies of the AHM on a square lattice, from which several different quantities have been calculated and should be useful as a roadmap to experiments. We have obtained a detailed phase diagram for the critical superconducting temperature, $T_c$, in terms of the band filling, $\ave{n}$, and interaction strength, $U$, from which we pinpoint a somewhat wide region $|U|/t \approx 5 \pm 1$ ($t$ is the hopping amplitude) and $\ave{n} \approx 0.79 \pm 0.09$ leading to a maximum $T_c \approx 0.16 t$. Two additional temperature scales, namely pairing, $T_p$, and degeneracy, $T_d$, have been highlighted: the former sets the scale for pair formation (believed to be closely related to the scale for the gap of spin excitations in cuprates), while the latter sets the scale for dominant quantum effects. Our DQMC data for the distribution of doubly occupied sites, for the momentum distribution function, and for the quasiparticle weight show distinctive features on both sides of the BCS-BEC crossover, being also suggestive of an underlying crossover between Fermi- and non-Fermi liquid behaviors., Comment: 9 pages, 12 figures

The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using Determinant Quantum Monte Carlo, a simple realization of anisotropy in the 3D Hubbard model in which the tunneling between planes, $t_\perp$, is unequal to the intraplane tunneling $t$. This model interpolates between the three-dimensional isotropic ($t_\perp = t$) and two-dimensional ($t_\perp =0$) systems. We show that at fixed interaction strength to tunneling ratio ($U/t$), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the N\'eel temperature $T_{\rm N\acute{e}el}$ is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal $U/t$. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly-occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D., Comment: 13 pages, 13 figures

One of the fundamental questions about the high temperature cuprate superconductors is the size of the Fermi surface (FS) underlying the superconducting state. By analyzing the single particle spectral function for the Fermi Hubbard model as a function of repulsion $U$ and chemical potential $\mu$, we find that the Fermi surface in the normal state reconstructs from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the "Luttinger Breaking" (LB) phase, as the Mott insulator is approached. This transition into a non-Fermi liquid phase that violates the Luttinger count, is a continuous phase transition at a critical density in the absence of any other broken symmetry. We obtain the Fermi surface contour from the spectral weight $A_{\vec{k}}(\omega=0)$ and from an analysis of the poles and zeros of the retarded Green's function $G_{\vec{k}}^{ret}(E=0)$, calculated using determinantal quantum Monte Carlo and analytic continuation methods.We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy and angle resolved photoemission spectroscopy.

We investigate the emergence of a myriad of phases in the strong coupling regime of the dipolar Hubbard model in two dimensions. By using a combination of numerically unbiased methods in finite systems with analytical perturbative arguments, we show the versatility that trapped dipolar atoms possess in displaying a wide variety of many-body phases, which can be tuned simply by changing the collective orientation of the atomic dipoles. We further investigate the stability of these phases to thermal fluctuations in the strong coupling regime, highlighting that they can be accessed with current techniques employed in cold atoms experiments on optical lattices. Interestingly, both quantum and thermal phase transitions are signalled by peaks or discontinuities in local moment-local moment correlations, which have been recently measured in some of these experiments, so that they can be used as probes for the onset of different phases.

We use numerically unbiased methods to show that the one-dimensional Hubbard model with periodically distributed on-site interactions already contains the minimal ingredients to display the phenomenon of magnetoresistance; i.e., by applying an external magnetic field, a dramatic enhancement on the charge transport is achieved. We reach this conclusion based on the computation of the Drude weight and of the single-particle density of states, applying twisted boundary condition averaging to reduce finite-size effects. The known picture that describes the giant magnetoresistance, by interpreting the scattering amplitudes of parallel or antiparallel polarized currents with local magnetizations, is obtained without having to resort to different entities; itinerant and localized charges are indistinguishable., Comment: 6+4 pages 5+5 figures, as published

We study magnetic, transport and thermodynamic properties of the half-filled two-dimensional ($2D$) Hubbard model with layered distributed repulsive interactions using unbiased finite temperature quantum Monte Carlo simulations. Antiferromagnetic long-ranged correlations at $T=0$ are confirmed by means of the magnetic structure factor and the onset of short-ranged ones is at a minimum temperature which can be obtained by peaks in susceptibility and specific heat following an RPA prediction. We also show that transport is affected in the large interaction limit and is enhanced in the non-repulsive layers suggesting a change of dimensionality induced by increased interactions. Lastly, we show that by adiabatically switching the interactions in layered distributed patterns reduces the overall temperature of the system with a potential application in cooling protocols in cold atoms systems., Comment: 14 pages, 19 figures. Published version

Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model, a minimal model that has been realized with cold atoms in optical lattices. Here we report on site-resolved measurements of the Fermi-Hubbard model in a spin-imbalanced atomic gas, allowing us to explore the response of the system to large effective magnetic fields. We observe short-range canted antiferromagnetism at half-filling with stronger spin correlations in the direction orthogonal to the magnetization, in contrast with the spin-balanced case where identical correlations are measured for any projection of the pseudospin. The rotational anisotropy of the spin correlators is found to increase with polarization and with distance between the spins. Away from half-filling, the polarization of the gas exhibits non-monotonic behavior with doping for strong interactions, resembling the behavior of the magnetic susceptibility in the cuprates. We compare our measurements to predictions from Determinantal Quantum Monte Carlo (DQMC) and Numerical Linked Cluster Expansion (NLCE) algorithms and find good agreement. Calculations on the doped system are near the limits of these techniques, illustrating the value of cold atom quantum simulations for studying strongly-correlated materials.

The noninteracting electronic structures of tight binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a \emph{uniform} on-site Hubbard interaction $U$ is turned on, Lieb proved rigorously that at half filling ($\rho=1$) the ground state has a non-zero spin. In this paper we consider a `CuO$_2$ lattice (also known as `Lieb lattice', or as a decorated square lattice), in which `$d$-orbitals' occupy the vertices of the squares, while `$p$-orbitals' lie halfway between two $d$-orbitals. We use exact Determinant Quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of $U$ and temperature. We study both the homogeneous (H) case, $U_d= U_p$, originally considered by Lieb, and the inhomogeneous (IH) case, $U_d\neq U_p$. For the H case at half filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all $U$. For the IH system at half filling, we argue that the case $U_p\neq U_d$ falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases $U_p=0,U_d=U$ and $U_p=U, U_d=0$. We found that the different environments of $d$ and $p$ sites lead to a ferromagnetic insulator when $U_d=0$; by contrast, $U_p=0$ leads to to a metal without any magnetic ordering. In addition, we have also established that at density $\rho=1/3$, strong antiferromagnetic correlations set in, caused by the presence of one fermion on each $d$ site., Comment: 10 pages, 14 figures

Strong electron correlations lie at the origin of transformative phenomena such as colossal magneto-resistance and high-temperature superconductivity. Already near room temperature, doped copper oxide materials display remarkable features such as a pseudo-gap and a "strange metal" phase with unusual transport properties. The essence of this physics is believed to be captured by the Fermi-Hubbard model of repulsively interacting, itinerant fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. Correlations between singly charged sites are negative at large doping, revealing the Pauli and correlation hole\textemdash a suppressed probability of finding two fermions near each other. However, as the doping is reduced below a critical value, correlations between such local magnetic moments become positive, signaling strong bunching of doublons and holes. Excellent agreement with numerical linked-cluster expansion (NLCE) and determinantal quantum Monte Carlo (DQMC) calculations is found. Positive non-local moment correlations directly imply potential energy fluctuations due to doublon-hole pairs, which should play an important role for transport in the Fermi-Hubbard model.

Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a non-disordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Ne\'el temperature of the three-dimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust., Comment: 5 figures, supplement with 5 figures

We investigate the harmonic-trap control of size and shape of Mott regions in the Fermi Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50-80 samples, drastically reduce finite-size effects in some ground state properties; calculations in the grand canonical ensemble together with a local-density approximation (LDA) allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state, to a Mott core, and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A `phase diagram' in terms of an effective density and the on-site repulsion is proposed, as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative) display detectable signatures of the core-ring transition. Some spin correlation functions are also calculated, and predict the existence N\'eel ordering within Mott cores and rings., Comment: 5 pages, 6 figures

We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in-situ imaging to extract the central density of the gas, and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interactions reveal that the temperature of the gas is of the order of, or below, the tunneling energy scale. Our results hold great promise for the exploration of many-body phenomena with ultracold atoms, where the local compressibility can be a useful tool to detect signatures of different phases or phase boundaries at specific values of the filling.

Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-$T_c$ superconductivity. The Hubbard model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realise the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram. Realisation of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realisation of the 3D Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques. We reach these low temperatures using a unique compensated optical lattice technique, in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinantal quantum Monte Carlo and numerical linked-cluster expansion calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for achieving and characterising other novel quantum states of matter, such as the pseudogap regime of the 2D Hubbard model.

We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. We examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. For the homogeneous case, this process is found to be more efficient at finite doping than at half filling. That, in turn, leads to an efficient adiabatic cooling in the presence of a trap which, starting with even relatively high entropies, can drive the system to have a Mott insulating phase with substantial antiferromagnetic correlations., Comment: 11 pages, 11 figures, 1 table, as published

We study transport properties of the half-filled two-dimensional (2D) Hubbard model with spatially varying interactions, where a pattern of interacting and non-interacting sites is formed. We use Determinantal Quantum Monte Carlo method to calculate the double occupation, effective hopping and Drude weight. These data point to two phase transitions, driven by fermionic correlations. The first is the expected metal to a Mott insulating state. The second one, is an exotic transition from a Mott insulating state to a highly anisotropic metal, that takes place at large values of the fermion-fermion interaction. This second transition occurs when the layers formed by the spatially varying interactions decouple due to the suppression of the hopping between interacting and non-interacting sites, leading to fermionic transport along the non-interacting ones.

We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice experiments., Comment: 5 pages, 4 figures

We have examined the behavior of the compressibility, the dc-conductivity, the single-particle gap, and the Drude weight as probes of the density-driven metal-insulator transition in the Hubbard model on a square lattice. These quantities have been obtained through determinantal quantum Monte Carlo simulations at finite temperatures on lattices up to 16 X 16 sites. While the compressibility, the dc-conductivity, and the gap are known to suffer from `closed-shell' effects due to the presence of artificial gaps in the spectrum (caused by the finiteness of the lattices), we have established that the former tracks the average sign of the fermionic determinant (), and that a shortcut often used to calculate the conductivity may neglect important corrections. Our systematic analyses also show that, by contrast, the Drude weight is not too sensitive to finite-size effects, being much more reliable as a probe to the insulating state. We have also investigated the influence of the discrete imaginary-time interval (\Delta\tau) on , on the average density (\rho), and on the double occupancy (d): we have found that and \rho are more strongly dependent on \Delta \tau away from closed-shell configurations, but d follows the \Delta\tau^2 dependence in both closed- and open-shell cases., Comment: 11 pages and 16 figures. To appear in Phys Rev B

A major challenge in realizing antiferromagnetic (AF) and superfluid phases in optical lattices is the ability to cool fermions. We determine the equation of state for the 3D repulsive Fermi-Hubbard model as a function of the chemical potential, temperature and repulsion using unbiased determinantal quantum Monte Carlo methods, and we then use the local density approximation to model a harmonic trap. We show that increasing repulsion leads to cooling, but only in a trap, due to the redistribution of entropy from the center to the metallic wings. Thus, even when the average entropy per particle is larger than that required for antiferromagnetism in the homogeneous system, the trap enables the formation of an AF Mott phase., Comment: 4 pages; 5 figures; also see supplementary material in 2 pages with 1 figure

One of the major challenges in realizing antiferromagnetic and superfluid phases in optical lattices is the ability to cool fermions. We determine constraints on the entropy for observing these phases in two-dimensional Hubbard models. We investigate antiferromagnetic correlations in the repulsive model at half filling and superfluidity of s-wave pairs in the attractive case away from half filling using determinantal quantum Monte Carlo simulations that are free of the fermion sign problem. We find that an entropy per particle ~log(2) is sufficient to observe the charge gap in the repulsive Hubbard model or the pairing pseudogap in the attractive case. Observing antiferromagnetic correlations or superfluidity in 2D systems requires a further reduction in entropy by a factor of three or more. In contrast to higher dimensions, we find that adiabatic cooling is not useful to achieve the required low temperatures. We also show that double occupancy measurements are useful for thermometry for temperatures greater than the nearest-neighbor hopping., Comment: 4 pages, 4 figures

The temperature dependence of the static magnetic susceptibility of exchange-disordered antiferromagnetic Heisenberg spin-1/2 finite chains with an odd number of spins is investigated as a function of size and type of disorder in the exchange coupling. Two models for the exchange disorder distribution are considered. At sufficiently low temperatures each chain behaves like an isolated spin-1/2 particle. As the size of the chains increases, this analogy is lost and the chains evolve into the thermodynamic limit behavior. The present study provides a simple criterion, based on susceptibility measurements, to establish when odd-sized chains effectively simulate a single spin-1/2 particle., Comment: 8 pages, 3 figures

We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction $f$ of sites, while keeping a finite $U$ on the remaining ones. Through Quantum Monte Carlo (QMC) simulations for several values of $f$ and $U$, and for system sizes ranging from $8\times 8$ to $16\times 16$, we have calculated the configurational averages of the equal-time pair structure factor $P_s$, and, for a more restricted set of variables, the helicity modulus, $\rho_s$, as functions of temperature. Two finite-size scaling {\it ansatze} for $P_s$ have been used, one for zero-temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration, $f_c$, which increases with $U$, at least up to U=4 (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of $f$ shows a maximum near $f\sim 0.07$, for $2\lesssim U\lesssim 6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of $f$, for $U=3,$ 4 and 6: they also show maxima near $f\sim 0.07$, with the highest $T_c$ increasing with $U$ in this range. We argue that, overall, the observed behavior results from both the breakdown of CDW-superconductivity degeneracy and the fact that free sites tend to "push" electrons towards attractive sites, the latter effect being more drastic at weak couplings., Comment: 9 two-column pages, 14 figures, RevTeX

We study height and roughness distributions of films grown with discrete Kardar-Parisi-Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square windows of sizes $8\leq r\leq 128$ gliding through a much larger surface. Results for models with weak finite-size corrections indicate that the absolute value of the skewness and the value of the kurtosis of height distributions converge to $0.2\leq |S|\leq 0.3$ and $0\leq Q\leq 0.5$, respectively. Despite the low accuracy of these results, they give additional support to a recent claim of KPZ scaling in oligomer films. However, there are significant finite-size effects in the scaled height distributions of models with large local slopes, such as ballistic deposition, which suggests that comparison of height distributions must not be used to rule out KPZ scaling. On the other hand, roughness distributions of the same models show good data collapse, with negligible dependence on time and window size. The estimates of skewness and kurtosis for roughness distributions are $1.7\leq S\leq 2$ and $3\leq Q\leq 7$. A stretched exponential tail was found, which seems to be a particular feature of KPZ systems in 2+1 dimensions. Moreover, the KPZ roughness distributions cannot be fitted by those of $1/f^{\alpha}$ noise. This study suggests that the roughness distribution is the best option to test KPZ scaling in the growth regime, and provides quantitative data for future comparison with other models or experiments., Comment: 14 pages, 6 figures, final version

We discuss the interplay between electronic correlations and an underlying superlattice structure in determining the period of charge density waves (CDW's), by considering a one-dimensional Hubbard model with a repeated (non-random) pattern of repulsive (U>0) and free (U=0) sites. Density matrix renormalization group diagonalization of finite systems (up to 120 sites) is used to calculate the charge-density correlation function and structure factor in the ground state. The modulation period can still be predicted through effective Fermi wavevectors, k_F*, and densities, and we have found that it is much more sensitive to electron (or hole) doping, both because of the narrow range of densities needed to go from q*=0 to \pi, but also due to sharp 2k_F*-4k_F* transitions; these features render CDW's more versatile for actual applications in heterostructures than in homogeneous systems., Comment: 4 pages, 5 figures, to appear in Phys Rev B

The low-temperature behavior of the static magnetic susceptibility $\chi(T)$ of exchange-disordered antiferromagnetic spin chains is investigated. It is shown that for a relatively small and even number of spins in the chain, two exchange distributions which are expected to occur in nanochains of P donors in silicon lead to qualitatively distinct behaviors of the low-temperature susceptibility. As a consequence, magnetic measurements might be useful to characterize whether a given sample meets the requirements compatible with Kane's original proposalfor the exchange gates in a silicon-based quantum computer hardware. We also explore the dependence of $\chi(T)$ on the number of spins in the chain as it increases towards the thermodynamic limit, where any degree or distribution of disorder leads to the same low-temperature scaling behavior. We identify a crossover regime where the two distributions of disorder may not be clearly differentiated, but the characteristic scaling of the thermodynamic limit has not yet been reached.

We study the effect of U=0 impurities on the superconducting and thermodynamic properties of the attractive Hubbard model on a square lattice. Removal of the interaction on a critical fraction of $f_{\rm crit} \approx 0.30$ of the sites results in the destruction of off-diagonal long range order in the ground state. This critical fraction is roughly independent of filling in the range $0.75 < \rho < 1.00$, although our data suggest that $f_{\rm crit}$ might be somewhat larger below half-filling than at $\rho=1$. We also find that the two peak structure in the specific heat is present at $f$ both below and above the value which destroys long range pairing order. It is expected that the high $T$ peak associated with local pair formation should be robust, but apparently local pairing fluctuations are sufficient to generate a low temperature peak.

We investigate ground state and finite temperature properties of the half-filled Hubbard model on a honeycomb lattice using quantum monte carlo and series expansion techniques. Unlike the square lattice, for which magnetic order exists at T=0 for any non-zero $U$, the honeycomb lattice is known to have a semi-metal phase at small $U$ and an antiferromagnetic one at large $U$. We investigate the phase transition at T=0 by studying the magnetic structure$and compressibility using quantum monte carlo simulations and by calculating the sublattice magnetization, uniform susceptibility, spin-wave and single hole %single-particle dispersion using series expansions around the ordered phase. Our results are consistent with a single continuous transition at $U_c/t$ in the range 4-5. Finite temperature signatures of this phase transition are seen in the behavior of the specific heat, $C(T)$, which changes from a two-peaked structure for $U>U_c$ to a one-peaked structure for $U < U_c$. Furthermore, the $U$ dependence of the low temperature coefficient of $C(T)$ exhibits an anomaly at $U \approx U_c$., Comment: 11 pages, 19 figures

The critical temperature for the attractive Hubbard model on a square lattice is determined from the analysis of two independent quantities, the helicity modulus, $\rho_s$, and the pairing correlation function, $P_s$. These quantities have been calculated through Quantum Monte Carlo simulations for lattices up to $18\times 18$, and for several densities, in the intermediate-coupling regime. Imposing the universal-jump condition for an accurately calculated $\rho_s$, together with thorough finite-size scaling analyses (in the spirit of the phenomenological renormalization group) of $P_s$, suggests that $T_c$ is considerably higher than hitherto assumed., Comment: 5 pages, 6 figures. Accepted for publication in Phys. Rev. B

We propose a superlattice model to describe superconductivity in layered materials, such as the borocarbide families with the chemical formul\ae\ $RT_2$B$_2$C and $RT$BC, with $R$ being (essentially) a rare earth, and $T$ a transition metal. We assume a single band in which electrons feel a local attractive interaction (negative Hubbard-$U$) on sites representing the $T$B layers, while U=0 on sites representing the $R$C layers; the multi-band structure is taken into account minimally through a band offset $\epsilon$. The one-dimensional model is studied numerically through the calculation of the charge gap, the Drude weight, and of the pairing correlation function. A comparison with the available information on the nature of the electronic ground state (metallic or superconducting) indicates that the model provides a systematic parametrization of the whole borocarbide family., Comment: 4 figures

We consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard-U couplings arranged in a repeated pattern of repulsive (i.e., U>0) and free (U=0) sites. Density Matrix Renormalization Group (DMRG) diagonalization of finite systems is used to calculate the local moment and the magnetic structure factor in the ground state. We have found four regimes for magnetic behavior: uniform local moments forming a spin-density wave (SDW), `floppy' local moments with short-ranged correlations, local moments on repulsive sites forming long-period SDW's superimposed with short-ranged correlations, and local moments on repulsive sites solely with long-period SDW's; the boundaries between these regimes depend on the range of electronic densities, rho, and on the SL aspect ratio. Above a critical electronic density, rho_{uparrow downarrow}, the SDW period oscillates both with rho and with the spacer thickness. The former oscillation allows one to reproduce all SDW wave vectors within a small range of electronic densities, unlike the homogeneous system. The latter oscillation is related to the exchange oscillation observed in magnetic multilayers. A crossover between regimes of `thin' to `thick' layers has also been observed., Comment: 9 two-column pages, 10 figures

We study a simple model for $f$-electron systems, the three-dimensional periodic Anderson model, in which localized $f$ states hybridize with neighboring $d$ states. The $f$ states have a strong on-site repulsion which suppresses the double occupancy and can lead to the formation of a Mott-Hubbard insulator. When the hybridization between the $f$ and $d$ states increases, the effects of these strong electron correlations gradually diminish, giving rise to interesting phenomena on the way. We use the exact quantum Monte-Carlo, approximate diagrammatic fluctuation-exchange approximation, and mean-field Hartree-Fock methods to calculate the local moment, entropy, antiferromagnetic structure factor, singlet-correlator, and internal energy as a function of the $f-d$ hybridization for various dopings. Finally, we discuss the relevance of this work to the volume-collapse phenomenon experimentally observed in f-electron systems., Comment: 12 pages, 8 figures

We study the formation of charge density waves (CDW's) in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive (U>0) and free (U=0) sites. By means of Lanczos diagonalizations for the ground state, we calculate the charge structure factor. Our results show that while the superlattice structure affects the modulation of the charge density waves, the periodicity can still be predicted through an effective density. We also show that, for a fixed repulsive layer thickness, the periodicity of the CDW is an oscillatory function of the free layer thickness., Comment: 4 pages, 4 figures

Local moment formation driven by the on--site repulsion $U$ is one of the most fundamental features in the Hubbard model. At the simplest level, the temperature dependence of the local moment is expected to have a single structure at $T \sim U$, reflecting the suppression of the double occupancy. In this paper we show new low temperature Quantum Monte Carlo data which emphasize that the local moment also has a signature at a lower energy scale which previously had been thought to characterize only the temperatures below which moments on {\it different} sites begin to correlate locally. We discuss implications of these results for the structure of the specific heat, and connections to quasiparticle resonance and pseudogap formation in the density of states., Comment: 13 pages, 19 figures

Charge density waves in the Hubbard chain are studied by means of finite-temperature Quantum Monte Carlo simulations and Lanczos diagonalizations for the ground state. We present results both for the charge susceptibilities and for the charge structure factor at densities \rho=1/6 and 1/3; for \rho=1/2 (quarter filled) we only present results for the charge structure factor. The data are consistent with a 4k_F instability dominating over the 2k_F one, at least for sufficiently large values of the Coulomb repulsion, U. This can only be reconciled with the Luttinger liquid analyses if the amplitude of the 2k_F contribution vanishes above some U^*(\rho)., Comment: RevTeX, 4 two-column pages with 7 colour figures embedded in text

Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antiferromagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Our main findings are summarised as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero -field fixed point at a finite angle. Our best estimate of the slope at the origin is $(dT_c/dH)_{T=H=0} = 4.74 \pm 0.15$. For SPAF-3 we provided evidence that the zero-field correlation length diverges as $\xi(T \to 0, H=0) \simeq \exp (a/T^{x})$, with $x=1.08 \pm 0.13$, through analysis of the critical curve at $H \neq 0$ plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as: (a) H=0: $c=1, \eta=1/3$; (b) $H \neq 0: c=1/2, \eta=1/4$., Comment: RevTex, 7 pages, 4 eps figures, to be published in Phys. Rev. E

We study the Metal-Insulator transition in one-dimensional Hubbard superlattices (SL's), modelled by a repeated pattern of repulsive (i.e., positive on-site coupling) and free sites. The evolution of the local moment and of the charge gap (calculated from Lanczos diagonalization of chains up to 18 sites), together with a strong coupling analysis, show that the electron density at which the system is insulating increases with the size of the free layer, relative to the repulsive one. In the insulating state, the mechanism of interaction between fermions separated by a free layer is the analog of superexchange, and the charge gap display universal features., Comment: 4 pages, 3 colour figures; Phys Rev B 15 Sept (tent)