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We review recent suggestions to quantum simulate scalar electrodynamics (the lattice Abelian Higgs model) in $1+1$ dimensions with rectangular arrays of Rydberg atoms. We show that platforms made publicly available recently allow empirical explorations of the critical behavior of quantum simulators. We discuss recent progress regarding the phase diagram of two-leg ladders, effective Hamiltonian approaches and the construction of hybrid quantum algorithms targeting hadronization in collider physics event generators., Comment: 7 pages, 2 figures, presented at the 40th International Symposium on Lattice Field Theory (Lattice 2023)

We consider multileg ladders of Rydberg atoms which have been proposed as quantum simulators for the compact Abelian Higgs model (CAHM) in 1+1 dimensions [Y. Meurice, Phys. Rev. D 104, 094513 (2021)] and modified versions of theses simulators such as triangular prisms. Starting with the physical Hamiltonian for the analog simulator, we construct translation-invariant effective Hamiltonians by integrating over the simulator high-energy states produced by the blockade mechanism when some of the atoms are sufficiently close to each others. Remarkably, for all the simulators considered, the effective Hamiltonians have the three types of terms present for the CAHM (Electric field, matter charge and currents energies) but, in addition, terms quartic in the electric field. For the two leg ladder, these additional terms cannot be removed by fine-tuning the adjustable parameters of currently available devices. For positive detuning, the new terms create highly-degenerate vacua resulting in a very interesting phase diagram. Using numerical methods, we demonstrate the close correspondence between the physical simulator and the effective description for the ground state energy and real-time evolution. We discuss the phase diagram at fixed geometry with variable Rabi frequency and detuning and show that a rich variety of phases can be reached with potential interest in the context of QCD at finite density. We illustrate how the effective description can be used to design simulators with desirable properties from the point of view of constructing hybrid event generators., Comment: 32 pages, 16 figures, references added, expanded section III with one new figure

We discuss recent progress in Tensor Lattice Field Theory and economical, symmetry preserving, truncations suitable for quantum computations or simulations. We focus on spin and gauge models with continuous Abelian symmetries such as the Abelian Higgs model and emphasize noise-robust implementations of Gauss's law. We discuss recent progress concerning the comparison between field digitizations and character expansions, symmetry breaking in tensor language, wave-packet preparation and possible new implementations of Abelian models using Rydberg atoms., Comment: Contribution to Lattice 2021, PoS(LATTICE2021)608 (submitted)

We study a fully connected quantum spin model resonantly coupled to a small environment of non-interacting spins, and investigate how initial state properties are remembered at long times. We find memory of initial state properties, in addition to the total energy, that are not conserved by the dynamics. This memory occurs in the middle of the spectrum where an eigenstate quantum phase transition (ESQPT) occurs as a function of energy. The memory effect at that energy in the spectrum is robust to system-environment coupling until the coupling changes the energy of the ESQPT. This work demonstrates the effect of ESQPT memory as independent of integrability and suggests a wider generality of this mechanism for preventing thermalization at ESQPTs., Comment: 8 pages, 8 Figures

The O(2) model in Euclidean space-time is the zero-gauge-coupling limit of the compact scalar quantum electrodynamics. We obtain a dual representation of it called the charge representation. We study the quantum phase transition in the charge representation with a truncation to ``spin $S$," where the quantum numbers have an absolute value less than or equal to $S$. The charge representation preserves the gapless-to-gapped phase transition even for the smallest spin truncation $S = 1$. The phase transition for $S = 1$ is an infinite-order Gaussian transition with the same critical exponents $\delta$ and $\eta$ as the Berezinskii-Kosterlitz-Thouless (BKT) transition, while there are true BKT transitions for $S \ge 2$. The essential singularity in the correlation length for $S = 1$ is different from that for $S \ge 2$. The exponential convergence of the phase-transition point is studied in both Lagrangian and Hamiltonian formulations. We discuss the effects of replacing the truncated $\hat{U}^{\pm} = \exp(\pm i \hat{\theta})$ operators by the spin ladder operators $\hat{S}^{\pm}$ in the Hamiltonian. The marginal operators vanish at the Gaussian transition point for $S = 1$, which allows us to extract the $\eta$ exponent with high accuracy.

A few years ago Avetissian {\it et al.} \cite{Avetissian2014,Avetissian2015} discovered that the exponential growth rate of the stimulated annihilation photons from a singlet positronium Bose-Einstein condensate should be proportional to the square root of the positronium number density, not to the number density itself. In order to elucidate this surprising result obtained via a field-theoretical analysis, we point out that the basic physics involved is the same as that of resonant subharmonic transitions between two quantum oscillators. Using this model, we show that nonlinearities of the type discovered by Avetissian {\it et al.} are not unique to positronium and in fact will be encountered in a wide range of systems that can be modeled as nonlinearly coupled quantum oscillators., Comment: 5 pages and 1 figure

The second-harmonic generation process of a focused laser beam inside a nonlinear crystal is described by the Boyd-Kleinman theory. Calculating the actual conversion efficiency and upconverted power requires the solution of a double integral that is analytically intractable. We provide an expression that predicts the exact gain coefficient within an error margin of less than 2% over several orders of magnitude of the confocal parameter and as a function of the walk-off parameter. Our result allows for readily tuning the beam parameters to optimize the performance of the upconversion process and improve optical system designs., Comment: 7 pages, 3 figures

Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a two-dimensional lattice populated by another species of fermions, and where all bare interactions are contact interactions. By focusing on the one-dimensional fermions, we map this problem onto a model of fermions with non-local interactions on a chain. The effective interaction is mediated by the two-dimensional fermions and is both attractive and retarded, the form of which can be varied by changing the density of the two-dimensional fermions. By using the functional renormalization group in the weak-coupling and adiabatic limit, we show that the one-dimensional fermions can be controlled to be in various density-wave, or spin-singlet or triplet superconducting phases., Comment: 7 pages, 6 figures

Finite size scaling for a first order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field in order to study the finite size behavior on a $L \times L \times L$ simple cubic lattice for the first order "spin-flop" transition between the Ising-like antiferromagnetic state and the canted, XY-like state. Our theory predicts that for large linear dimension $L$ the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor $q$ that characterizes the relative degeneracy of the ordered phases. Our theory yields $q=\pi$, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first order phase transitions., Comment: 20 pages, 21 figures

We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a $2^{nd}$ order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied with careful pinning., Comment: 10 pages, 12 figures

We show that the Polyakov loop of the two-dimensional lattice Abelian Higgs model can be calculated using the tensor renormalization group approach. We check the accuracy of the results using standard Monte Carlo simulations. We show that the energy gap produced by the insertion of the Polyakov loop obeys universal finite-size scaling which persists in the time continuum limit. We briefly discuss the relevance of these results for quantum simulations., Comment: 10 pages, 11 figures, 1 table

We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable on optical lattices as quantum simulators for CFT models., Comment: Talk presented at Lattice 2016 by Y. Meurice, POS 325, 7 pages, 4 figures

We present a gauge-invariant effective action for the Abelian-Higgs model in 1+1 dimensions. It is constructed by integrating out the gauge field and then using the hopping parameter expansion. The latter is tested with Monte Carlo simulations for small values of the scalar self-coupling. In the opposite limit, at infinitely large self-coupling, the Higgs mode is frozen and the partition function can be written in terms of local tensors and the tensor renormalization group blocking can be applied. The numerical implementation requires truncations and the time continuum limit of the blocked transfer matrix can be obtained numerically. At zero gauge coupling and with a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large onsite repulsion. The procedure is extended to finite gauge coupling and we derive a spin-1 approximation of the Hamiltonian which involves terms corresponding to transitions among the two species in the Bose-Hubbard model. An optical lattice implementation involving a ladder structure is proposed., Comment: 7 pages, 3 figures, talk presented at the XXXIII International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japan

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this difficulty, allowing exploration of higher parameter phase space by keeping track of the joint density of states., Comment: Proceedings of CCP2014 will appear in Journal of Physics: Conference Series (JPCS), published by the IOP

We present a gauge-invariant effective action for the Abelian Higgs model (scalar electrodynamics) with a chemical potential $\mu$ on a 1+1 dimensional lattice. This formulation provides an expansion in the hopping parameter $\kappa$ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling $\beta_{pl}$ and small values of the scalar self-coupling $\lambda$. In the opposite limit of infinitely large $\lambda$, the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Their numerical implementation requires truncations but there is no sign problem for arbitrary values of $\mu$. We show that the time continuum limit of the blocked transfer matrix can be obtained numerically and, in the limit of infinite $\beta_{pl}$ and with a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large onsite repulsion. We extend this procedure for finite $\beta_{pl}$ and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure., Comment: 10 pages, 9 figures

We discuss the U(1)-Higgs model in two dimensions in the strongly coupled regime. If we neglect the plaquette interactions, we generate an effective theory where link variables are integrated out, producing 4-field operators. Plaquette interactions can be restored order by order as in recent calculations with staggered fermions. In the case of a SU(2) gauge theory with fermions, this strong coupling expansion can be related to the strong coupling expansion of Fermi-Hubbard models possibly implementable on optical lattice. We would like to provide a similar construction relating the U(1)-Higgs model to some Bose-Hubbard model. As a first step in this direction, we discuss a recent proposal to implement the O(2) model on optical lattices using a 87Rb and 41K Bose-Bose mixture of cold atoms., Comment: 7 pages, poster presented at the XXXII International Symposium on Lattice Field Theory, June 23-28, 2014, Columbia University, New York City, NY

We study density wave instabilities in a doubly-degenerate Fermi-Fermi mixture with $SU(2)\times SU(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, two conventional ($s$-wave) number density waves are formed with a $\pi$-phase difference between them to minimize the inter-species repulsion. Upon moving one species away from half-filling, an unconventional density wave with $d_{xy}$-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the $d_{xy}$-density wave phase based on a four-patch model. We find a robust and general mechanism for $d_{xy}$-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to phase-space discrepancy for different inter-species Umklapp couplings. Using a phase space argument for leading corrections in the one-loop renormalization group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intra-species Umklapp couplings and that this triggers the $d_{xy}$-density-wave instability., Comment: revised long version; 8 pages, 7 figures

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal breaking (p_x + ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (p_x +ip_y)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while d_{xy}-pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.

The search for realistic one-dimensional (1D) models that exhibit dominant superconducting (SC) fluctuations effects has a long history. In these 1D systems, the effects of commensurate band fillings--strongest at half-filling--and electronic repulsions typically lead to a finite charge gap and the favoring of insulating density wave ordering over superconductivity. Accordingly, recent proposals suggesting a gapless metallic state in the Holstein-Hubbard (HH) model, possibly superconducting, have generated considerable interest and controversy, with the most recent work demonstrating that the putative dominant superconducting state likely does not exist. In this paper we study a model with non-local electron-phonon interactions, in addition to electron-electron interactions, this model unambiguously possesses dominant superconducting fluctuations at half filling in a large region of parameter space. Using both the numerical multi-scale functional renormalization group for the full model and an analytic conventional renormalization group for a bosonized version of the model, we demonstrate the existence of dominant superconducting (SC) fluctuations. These dominant SC fluctuations arise because the spin-charge coupling at high energy is weakened by the non-local electron-phonon interaction and the charge gap is destroyed by the resultant suppression of the Umklapp process. The existence of the dominant SC pairing instability in this half-filled 1D system suggests that non-local boson-mediated interactions may be important in the superconductivity observed in the organic superconductors., Comment: 8 pages, 4 figures

The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. Different effective interactions and novel correlated quantum many-body phases may be engineered in these systems, with the different phases being tunable via external parameters. In this article we investigate a two-species Fermi atom mixture: one species of atom exists in two hyperfine states and is confined to move in a two-leg ladder, interacting with an on-site interaction, and the other moves freely in a two dimensional square lattice that contains the two-leg ladder. The two species of atoms interact via an on-site interaction on the ladder. In the limit of weak inter-species interactions, the two-dimensional gas can be integrated out, leading to an effective long-range mediated interaction in the ladder, generated by to the on-site inter-species interaction. We show that the form of the mediated interaction can be controlled by the density of the two-dimensional gas and that it enhances the charge density wave instability in the two-leg ladder after the renormalization group transformation. Parameterizing the phase diagram with various experimentally controllable quantities, we discuss the possible tuning of the macroscopic quantum many-body phases of the two-leg ladder in this mixed-dimensional fermionic cold atom system., Comment: 4 pages and 3 figures

The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models. This opens the possibility of letting nature take care of sign problems and real time evolution in carefully prepared situations. Up to now, experimentalists have succeeded to implement several types of Hubbard models considered by condensed matter theorists. In this proceeding, we discuss the possibility of extending this effort to lattice gauge theory. We report recent efforts to establish the strong coupling equivalence between the Fermi Hubbard model and SU(2) pure gauge theory in 2+1 dimensions by standard determinantal methods developed by Robert Sugar and collaborators. We discuss the possibility of using dipolar molecules and external fields to build models where the equivalence holds beyond the leading order in the strong coupling expansion., Comment: 6 pages, 3 figures,poster presented at the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases., Comment: 5 pages, 3 figures

We study a two species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive interaction. Such a model can be realized in a cold atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable inter-species interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities for the minority species, we find that several correlated phases emerge as the ground state, including a spin density wave state, a charge density wave state with stripe structure, and various p-wave BCS pairing states for both species. We study this system using a functional renormalization group method, determine its phase diagram at weak coupling, discuss the origin and characteristics of each phase, and provide estimates for the critical temperatures., Comment: 5 pages, 4 figures, figures updated

Recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides opportunity to engineer Hubbard-like models with long range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum". Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques., Comment: 5 pages, 3 figures, supplementary material also included; to appear in Phys. Rev. Lett. (in press)

We present exact analytical calculations of scanning tunneling currents in locally disordered graphene using a multimode description of the microscope tip. Analytical expressions for the local density of states (LDOS) are given for energies beyond the Dirac cone approximation. We show that the LDOS at the $A$ and $B$ sublattices of graphene are out of phase by $\pi$ implying that the averaged LDOS, as one moves away from the impurity, shows no trace of the $2q_F$ (with $q_F$ the Fermi momentum) Friedel modulation. This means that a STM experiment lacking atomic resolution at the sublattice level will not be able of detecting the presence of the Friedel oscillations [this seems to be the case in the experiments reported in Phys. Rev. Lett. {\bf 101}, 206802 (2008)]. The momentum maps of the LDOS for different types of impurities are given. In the case of the vacancy, $2q_F$ features are seen in these maps. In all momentum space maps, $K$ and $K+K^\prime$ features are seen. The $K+K^\prime$ features are different from what is seen around zero momentum. An interpretation for these features is given. The calculations reported here are valid for chemical substitution impurities, such as boron and nitrogen atoms, as well as for vacancies. It is shown that the density of states close to the impurity is very sensitive to type of disorder: diagonal, non-diagonal, or vacancies. In the case of weakly coupled (to the carbon atoms) impurities, the local density of states presents strong resonances at finite energies, which leads to steps in the scanning tunneling currents and to suppression of the Fano factor., Comment: 21 pages. Figures 6 and 7 are correctly displayed in this new version

We study the local density of states at and around a substituting impurity and use these results to compute current versus bias characteristic curves of Scanning Tunneling Microscopy (STM) experiments done on the surface of graphene. This allow us to detect the presence of substituting impurities on graphene. The case of vacancies is also analyzed. We find that the shape and magnitude of the STM characteristic curves depend on the position of the tip and on the nature of the defect, with the strength of the binging between the impurity and the carbon atoms playing an important role. Also the nature of the last atom of the tip has an influence on the shape of the characteristic curve., Comment: Accepted in PRB

Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) are shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using adaptive windows. Instead of defining fixed energy windows (or windows in the energy-magnetization plane for the Potts model), the boundary positions depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows. Adaptive windows extend significantly the range of system sizes that may be studied reliably using WLS.

The superconducting instability of the Fermi liquid state is investigated by considering anisotropic electron-boson couplings. Both electron-electron interactions and anisotropic electron-boson couplings are treated with a renormalization-group method that takes into account retardation effects. Considering a non-interacting circular Fermi surface, we find analytical solutions for the flow equations and derive a set of generalized Eliashberg equations. Electron-boson couplings with different momentum dependences are studied, and we find superconducting instabilities of the metallic state with competition between order parameters of different symmetries. Numerical solutions for some couplings are given to illustrate the frequency dependence of the vertices at different coupling regimes., Comment: 9 pages, 7 figures. Final version as published in Phys. Rev. B

We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface., Comment: 7 pages, 3 figures

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave (BCDW), also known as a ``bond order wave'' (BOW), near $U = 2V$ and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately., Comment: 4 pages, 4 figures, minor changes, final version

When high quality bismuth or graphite crystals are placed in a magnetic field directed along the c-axis (trigonal axis for bismuth) and the temperature is lowered, the resistance increases as it does in an insulator but then saturates. We show that the combination of unusual features specific to semimetals, i.e., low carrier density, small effective mass, high purity, and an equal number of electrons and holes (compensation), gives rise to a unique ordering and spacing of three characteristic energy scales, which not only is specific to semimetals but which concomitantly provides a wide window for the observation of apparent field induced metal-insulator behavior. Using magnetotransport and Hall measurements, the details of this unusual behavior are captured with a conventional multi-band model, thus confirming the occupation by semimetals of a unique niche between conventional metals and semiconductors., Comment: 4 pages, 4 figs, data and discussion on bismuth added, final published version

We have studied magnetic ordering in ferro/antiferromagnetic (F/AF) bilayers using Monte Carlo simulations of classical Heisenberg spins. For both flat and stepped interfaces we observed order in the AF above the Neel temperature, with the AF spins aligning collinearly with the F moments. In the case of the stepped interface there is a transition from collinear to perpendicular alignment of the F and AF spins at a lower temperature., Comment: Latex, 2 pages, 2 figures (proceedings of ICM2003)

A d-wave superconductor with isolated strong non-magnetic impurities should exhibit an upturn in the penetration depth at low temperatures. Here we calculate how an external magnetic field supresses this effect., Comment: 2 pages, 1 figure, to appear in Physica C (proceedings for the M2S-RIO Conference, May 25-30, Rio de Janeiro, Brazil)

Monte-Carlo simulations and ground-state calculations have been used to map out the phase diagram of a system of classical spins, on a simple cubic lattice, where nearest-neighbor pairs of spins are coupled via competing antiferromagnetic superexchange and ferromagnetic double-exchange interactions. For a certain range of parameters, this model is relevant for some magnetic materials, such as doped manganites, which exhibit the remarkable colossal magnetoresistance effect. The phase diagram includes two regions in which the two sublattice magnetizations differ in magnitude. Spin-dynamics simulations have been used to compute the time- and space-displaced spin-spin correlation functions, and their Fourier transforms, which yield the dynamic structure factor $S(q,\omega)$ for this system. Effects of the double-exchange interaction on the dispersion curves are shown., Comment: Latex, 3 pages, 3 figures

Using a recently implemented integration method [Krech et. al.] based on an iterative second-order Suzuki-Trotter decomposition scheme, we have performed spin dynamics simulations to study the critical dynamics of the BCC Heisenberg antiferromagnet with uniaxial anisotropy. This technique allowed us to probe the narrow asymptotic critical region of the model and estimate the dynamic critical exponent $z=2.25 \pm 0.08$. Comparisons with competing theories and experimental results are presented., Comment: Latex, 3 pages, 5 figures

Monte Carlo simulations have been used to study phase transitions on coupled anisotropic ferro/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. We consider films of different thicknesses, with fully compensated exchange across the FM/AFM interface. We find indications of a phase transition on each film, occuring at different temperatures. It appears that both transition temperatures depend on the film thickness., Comment: Revtex, 4 pages, 4 figures

Monte Carlo and spin dynamics simulations have been used to study the dynamic critical behavior of RbMnF$_3$, treated as a classical Heisenberg antiferromagnet on a simple cubic lattice. In an attempt to understand the difference in the value of the dynamic critical exponent $z$ between experiment and theory, we have used larger lattice sizes than in our previous simulations to better probe the asymptotic critical region in momentum. We estimate $z=1.49\pm 0.03$, in good agreement with the renormalization-group theory and dynamic scaling predictions. In addition, the central peak in the dynamic structure factor at $T_c$, seen in experiments and previous simulations, but absent in the renomalization-group and mode-coupling theories, is shown to be solely in the longitudinal component., Comment: Revtex, 6 pages, 7 figures

Monte Carlo simulations have been used to study magnetic ordering in coupled anisotropic ferro/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. We consider films with flat interfaces that are fully uncompensated as well as rough interfaces that are compensated on average. For both types of interfaces above the ``N\'eel temperature'' we observed order in the AFM with the AFM spins aligning collinearly with the FM moments. In the case of rough interfaces there is a transition from collinear to perpendicular alignment of the FM and AFM spins at a lower temperature., Comment: Revtex, 4 pages, 4 figures

The current response of a d-wave superconductor containing a single impurity is calculated and shown to be singular in the low-temperature limit, leading in the case of strong scattering to a 1/T term in the penetration depth $\lambda(T)$ similar to that induced by Andreev surface bound states. For a small number of such impurities, we argue this low-$T$ upturn could be observable in cuprate superconductors., Comment: 4 pages, 2 .eps figures. Minor changes to match the published version

Effects of the electron-electron interaction on tunneling into a metal in ultra-high magnetic field (ultra-quantum limit) are studied. The range of the interaction is found to have a decisive effect both on the nature of the field-induced instability of the ground state and on the properties of the system at energies above the corresponding gap. For a short-range repulsive interaction, tunneling is dominated by the renormalization of the coupling constant, which leads eventually to the charge-density wave instability. For a long-range interaction, there exists an intermediate energy range in which the conductance obeys a power-law scaling form, similar to that of a 1D Luttinger liquid. The exponent is magnetic-field dependent, and more surprisingly, may be positive or negative, i. e., interactions may either suppress or enhance the tunneling conductance compared to its non-interacting value. At energies near the gap, scaling breaks down and tunneling is again dominated by the instability, which in this case is an (anisotropic) Wigner crystal instability., Comment: 4 pages, 2 .eps figures