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The lack of both nesting and a van Hove singularity at half filling, together with the presence of Dirac cones makes the honeycomb lattice a special laboratory to explore strongly correlated phenomena. For instance, at zero temperature the repulsive [attractive] Hubbard model only undergoes a transition to an antiferromagnetic [$s$-wave superconducting degenerate with charge density wave (SC-CDW)] for sufficiently strong on-site coupling, $U/t\gtrsim 3.85$ [$U/t\lesssim -3.85$]; in between these, the system is a semi-metal, by virtue of the Dirac cones. The addition of an additional interaction, $V>0$ or $V<0$, between fermions in nearest neighbor orbitals should break the SC-CDW degeneracy giving rise to a phase diagram quite distinct from the one for the square lattice. Here we perform determinant quantum Monte Carlo simulations to investigate the whole phase diagram, covering the four combinations of signs of $U$ and $V$; the use of complex Hubbard-Stratonovich fields renders the region $|V|\leq |U|/3$ free from the `minus sign problem'. We calculate structure factors associated with different orderings, which, together with the double occupancy and the average sign allows us to map out the whole phase diagram. We have found that the SM phase forms a zone from which ordered phases are excluded, preventing the stabilization of a $d$-wave SC phase, i.e., only $s$-wave pairing is allowed.

We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory, and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with $\nu$ decreasing with lattice dimensionality, $d$, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.

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

We theoretically investigate the effects of criticality and multifractal states in a one-dimensional Aubry-Andre-Harper model coupled to electromagnetic cavities. We focus on two specific cases where the phonon frequencies are $\omega_{0}=1$ and $\omega_{0}=2$, respectively. Phase transitions are analyzed using both the average and minimum inverse participation ratio to identify metallic, fractal, and insulating states. We provide numerical evidence to show that the presence of the optical cavity induces a critical, intermediate phase in between the extended and localized phases, hence drastically modifying the traditional transport phase diagram of the Aubry-Andre-Harper model, in which critical states can only exist at the well-defined metal-insulator critical point. We also investigate the probability distribution of the inverse participation ratio and conduct a multifractal analysis to characterize the nature of the critical phase, in which we show that extended, localized, and fractal eigenstates coexist. Altogether our findings reveal the pivotal role that the coupling to electromagnetic cavities plays in tailoring critical transport phenomena at the microscopic level of the eigenstates., Comment: 10 pages, 10 Figures

We study four spins on a ring coupled through competing Heisenberg interactions between nearest neighbors, $J$, and next-nearest neighbors, $J_2\equiv\alpha J>0$. The spectrum is obtained in a simple way by using the rules for addition of 4 angular momenta. This allows us to follow the evolution of the ground state with $\alpha$, characterized by level crossings and by analyses of spin-spin correlation functions. Further insight is obtained by examining the entanglement between different parts of the system: we observe that the entanglement entropy is strongly dependent on how the system is partitioned., Comment: 10 pages, 5 figures

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

The extended Hubbard model (EHM) describes fermions on a lattice coupled through on-site, $U$, and first-neighbor, $V$, interactions. In the context of high-$T_c$ cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U$-$V$ plane in which the boundaries involving antiferromagnetic, charge-ordered, $s$- and $d$-wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram, $T_c(U,V)$, featuring critical temperatures for the CDW and $s$-wave superconducting phases.

We investigate how magnetic impurities may affect a system exhibiting charge-density wave (CDW) in its ground state. We consider a disordered Hubbard-Holstein model with a homogeneous electron-phonon interaction, but with a (randomly chosen) fraction of sites displaying a non-zero Coulomb repulsion, $U$, and perform state-of-the-art finite-temperature quantum Monte Carlo simulations. For a single magnetic impurity, charge-charge correlations hamper the spin-spin ones around the repulsive site, thus requiring a strong enough value of $U$ to create non-negligible antiferromagnetic (AFM) correlations. As the number of magnetic impurities increases, these AFM correlations become deleterious to CDW order and its features. First, the critical temperature is drastically reduced, and seems to vanish around 40$\%$ of impurities (for fixed $U/\lambda=2$), which we correlate with the classical percolation threshold. We also notice that just a small amount of disorder suffices to create a \textit{bad insulating} state, with the suppression of both Peierls and spin gaps, even within the charge-ordered phase. Finally, we have also found that pairing correlations are enhanced at large doping, driven by the competition between CDW and AFM tendencies.

The nature of metal-insulator and magnetic transitions is still a subject under intense debate in condensed matter physics. Amongst the many possible mechanisms, the interplay between electronic correlations and spin-orbit couplings is an issue of a great deal of interest, in particular when dealing with quasi-2D compounds. In view of this, here we use a Hartree-Fock approach to investigate how the Rashba spin-orbit coupling, $V_\text{SO}$, affects the magnetic ordering provided by a Hubbard interaction, $U$, on a square lattice. At half-filling, we have found a sequence of transitions for increasing $V_\text{SO}$: from a Mott insulator to a metallic antiferromagnet, and then to a paramagnetic Rashba metal. Also, our results indicate that the Rashba coupling favors magnetic striped phases in the doped regime. By analyzing spectral properties, we associate the rearrangement of the magnetic ordering with the emerging chirality created by the spin-orbit coupling. Our findings provide insights towards clarifying the competition between these tendencies.

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

In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures $T_c(q)$, for $q = 3, 4$ and $5$, results show that non-linear methods as UMAP and TDA are less dependent on finite size effects, while still being able to distinguish between first and second order phase transitions. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions., Comment: Added computation of critical exponents; exposition improved

The nature of superconductivity in heavy-fermion materials is a subject under intense debate, and controlling this many-body state is central for its eventual understanding. Here, we examine how proximity effects may change this phenomenon, by investigating the effects of an additional metallic layer on the top of a Kondo-lattice, and allowing for pairing in the former. We analyze a bilayer Kondo Lattice Model with an on-site Hubbard interaction, $-U$, on the additional layer, using a mean-field approach. For $U=0$, we notice a drastic change in the density-of-states due to multiple-orbital singlet resonating combinations. It destroys the well-known Kondo insulator at half filling, leading to a metallic ground state, which, in turn, enhances antiferromagnetism through the polarization of the conduction electrons. For $U\neq 0$, a superconducting Kondo state sets in at zero temperature, with the occurrence of unconventional pairing amplitudes involving $f$-electrons. We establish that this remarkable feature is only possible due to the proximity effects of the additional layer. At finite temperatures we find that the critical superconducting temperature, $T_c$, decreases with the interlayer hybridization. We have also established that a zero temperature superconducting amplitude tracks $T_c$, which reminisces the BCS proportionality between the superconducting gap and $T_c$., Comment: 11 pages, 10 figures

The Kondo and Periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling $J$ or hybridization $V$ between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small $J$ or $V$, limit, the moments survive, and the conduction electrons mediate an effective interaction which can trigger long range, often antiferromagnetic, order. In the case of the Kondo model, where the moments are described by local spins, Nozi\`eres considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting `exhaustion' problem, and how the `coherence temperature' where a heavy Fermi liquid forms is related to the Kondo temperature. In this paper, we study a version of the Periodic Anderson model in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low temperature Quantum Monte Carlo simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical $V$ for the singlet-antiferromagnetic transition., Comment: 10 figures and 9 pages. Accepted for publication in Physical Review B

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.

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

We study the Kondo Lattice Model (KLM) on a square lattice through a Hartree-Fock approximation in which the local spins are treated semi-classically, in the sense that their average values are modulated by a magnetic wavevector $\mathbf{Q}$ while they couple with the conduction electrons through fermion operators. In this way, we obtain a ground state phase diagram in which spiral magnetic phases (in which the wavevector depends on the coupling constants and on the density) interpolate between the low-density ferromagnetic phase and the antiferromagnetic phase at half filling; within small regions of the phase diagram commensurate magnetic phases can coexist with Kondo screening. We have also obtained `Doniach-like' diagrams, showing the effect of temperature on the ground state phases, and established that for some ranges of the model parameters (the exchange coupling and conduction electron density) the magnetic wavevector changes with temperature, either continuously or abruptly (e.g., from spiral to ferromagnetic)., Comment: 13 pages, 15 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 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

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 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

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 perform a theoretical study, using {\it ab initio} total energy density-functional calculations, of the effects of disorder on the $Mn-Mn$ exchange interactions for $Ga_{1-x}Mn_xAs$ diluted semiconductors. For a 128 atoms supercell, we consider a variety of configurations with 2, 3 and 4 Mn atoms, which correspond to concentrations of 3.1%, 4.7%, and 6.3%, respectively. In this way, the disorder is intrinsically considered in the calculations. Using a Heisenberg Hamiltonian to map the magnetic excitations, and {\it ab initio} total energy calculations, we obtain the effective $\JMn$, from first ($n=1$) all the way up to sixth ($n=6$) neighbors. Calculated results show a clear dependence in the magnitudes of the $\JMn$ with the Mn concentration $x$. Also, configurational disorder and/or clustering effects lead to large dispersions in the Mn-Mn exchange interactions, in the case of fixed Mn concentration. Moreover, theoretical results for the ground-state total energies for several configurations indicate the importance of a proper consideration of disorder in treating temperature and annealing effects.

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