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Calculating the out-of-equilibrium dynamics of many-body quantum systems theoretically is a challenging problem. Essentially exact results can be obtained for the out-of-equilibrium correlations in the Bose-Hubbard model in one dimension, but higher dimensions require approximate methods. One such method is the two-particle irreducible strong coupling (2PISC) approach [M.R.C. Fitzpatrick and M.P. Kennett, Nucl. Phys. B 930, 1 (2018)]. Calculations of the single-particle correlations using this method yield values of the velocity for correlation spreading that match well with exact methods in one dimension and experiments in one and two dimensions. However, the 2PISC method is less accurate for determining the amplitude of correlations, especially in the regime where interactions are not very strong. Viewing the calculation of the single-particle correlations as an image correction problem, we train a neural network (NN) to take input from the 2PISC approach to reproduce the output of exact diagonalization calculations. We show that the predictions of the NN improve on 2PISC results for parameters outside the training region. Our approach is not specific to the Bose-Hubbard model and may find application to the out-of-equilibrium dynamics of other quantum many-body systems., Comment: 12 pages, 16 figures

We study the out-of-equilibrium dynamics of the Bose-Hubbard model for two-component bosons using a strong-coupling approach within the closed-time-path formalism and develop an effective theory for the action of this problem. We obtain equations of motion for the superfluid order parameters of both boson species for both the superfluid and Mott-insulating phases and study these in the low-frequency, long-wavelength limit during a quantum quench for various initial conditions. We find that an additional degree of freedom for bosons leads to a richer phase diagram and out-of-equilibrium dynamics than the single-component situation., Comment: 28 pages, 10 figures

There has been considerable interest in the disordered Bose Hubbard model (BHM) in recent years, particularly in the context of thermalization and many-body localization. We develop a two-particle irreducible (2PI) strong-coupling approach to the disordered BHM that allows us to treat both equilibrium and out-of-equilibrium situations. We obtain equations of motion for spatio-temporal correlations and explore their equilibrium solutions. We study the equilibrium phase diagram as a function of disorder strength and discuss applications of the formalism to out-of-equilibrium situations. We also note that the disorder strengths where the emergence of non-ergodic dynamics was observed in a recent experiment [Choi $et \,al.$, Science $\bf{352}$, 1547 (2016)] appear to correspond to the Mott insulator -- Bose glass phase boundary., Comment: 20 pages, 6 figures

We study the collective excitations of fractional quantum Hall states in graphene. We focus on states which allow for chiral symmetry breaking (CSB) orders, specifically antiferromagnetism and charge density wave order. We investigate numerically how the collective excitation spectra depend on filling and the flux attachment scheme for two classes of variational states, the T\"{o}ke-Jain sequence and the Modak-Mandal-Sengupta sequence., Comment: 15 pages, 8 figures

We present an essentially exact numerical method for modelling flux qubit chains subject to charge and flux noise. We define an essentially exact method as one that introduces errors that are completely controlled such that they can be made arbitrarily small by tuning the simulation parameters. The method adopts the quasi-adiabatic path integral formalism to express the system's reduced density matrix as a time-discretized path integral, comprising a series of influence functionals that encode the non-Markovian dynamics of the system. We present a detailed derivation of the path integral expression for the system's reduced density matrix and describe in detail the tensor network algorithm used to evaluate the path integral expression. We have implemented our method in an open-sourced Python library called "spinbosonchain". When appropriate, we draw connections between concepts covered in this manuscript and the library's code., Comment: 106 pages, 0 figures

The charge degrees of freedom in several different organic charge transfer salts display slow or glassy dynamics. In order to gain insight into this behaviour, we obtain the low energy theory for an extended dimer Hubbard model, taking into account the occupations of sites on neighbouring dimers. We take a classical limit of the resulting effective model of coupled spins and dimers and study it using classical Monte Carlo simulations. We find that frustration induced by intra- and inter-dimer interactions leads to glassiness in the charge degress of freedom in the absence of ordering of the spin degrees of freedom. Our results may have relevance to experimental observations of relaxor ferroelectric behaviour in the dynamics of organic charge transfer salts., Comment: 20 pages, 13 figures

Lieb-Robinson and related bounds set an upper limit on the rate of spreading of information in non-relativistic quantum systems. Experimentally, they have been observed in the spreading of correlations in the Bose-Hubbard model after a quantum quench. Using a recently developed two particle irreducible (2PI) strong coupling approach to out-of-equilibrium dynamics in the Bose-Hubbard model we calculate both the group and phase velocities for the spreading of single-particle correlations in one, two and three dimensions as a function of interaction strength. Our results are in quantitative agreement with measurements of the velocities for the spreading of single particle correlations in both the one and two dimensional Bose-Hubbard model realized with ultra-cold atoms. They also agree with the claim that the phase velocity rather than the group velocity was observed in recent experiments in two dimensions. We demonstrate that there can be large differences between the phase and group velocities for the spreading of correlations and also explore the variation of the anisotropy in the velocity at which correlations spread across the phase diagram of the Bose-Hubbard model. Our results establish the 2PI strong coupling approach as a powerful tool to study out-of-equilibrium dynamics in the Bose-Hubbard model in dimensions greater than one., Comment: 5 pages, 6 figures, supplementary materials

The integer quantum Hall states at fillings $\nu = 0$ and $|\nu| = 1$ in monolayer graphene have drawn much attention as they are generated by electron-electron interactions. Here we explore aspects of the $\nu = 0$ and $|\nu| = 1$ quantum Hall states relevant for experimental samples. In particular, we study the effects of finite extent and finite temperature on the $\nu = 0$ state and finite temperature for the $\nu = 1$ state. For the $\nu = 0$ state we consider the situation in which the bulk is a canted antiferromagnet and use parameters consistent with measurements of the bulk gap to study the edge states in tilted magnetic fields in order to compare with experiment [A. F. Young et al., Nature 505, 528 (2014)]. When spatial modulation of the order parameters is taken into account, we find that for graphene placed on boron nitride, the gap at the edge closes for magnetic fields comparable to those in experiment, giving rise to edge conduction with $G \sim 2e^2/h$ while the bulk gap remains almost unchanged. We also study the transition into the ordered state at finite temperature and field. We determine the scaling of critical temperatures as a function of magnetic field, $B$, and distance to the zero field critical point and find sublinear scaling with magnetic field for weak and intermediate strength interactions, and $\sqrt{B}$ scaling at the coupling associated with the zero field quantum critical point. We also predict that critical temperatures for $\nu = 0$ states should be an order of magnitude higher than those for $|\nu| = 1$ states, consistent with the fact that the low temperature gap for $\nu = 0$ is roughly an order of magnitude larger than that for $|\nu| = 1$., Comment: 14 pages, 12 figures

We consider the effects of on-site and hopping disorder on zero modes in the Su-Schrieffer-Heeger model. In the absence of disorder a domain wall gives rise to two chiral fractionalized bound states, one at the edge and one bound to the domain wall. On-site disorder breaks the chiral symmetry, in contrast to hopping disorder. By using the polarization we find that on-site disorder has little effect on the chiral nature of the bound states for weak to moderate disorder. We explore the behaviour of these bound states for strong disorder, contrasting on-site and hopping disorder and connect our results to the localization properties of the bound states and to recent experiments., Comment: 5 pages, 6 figures

Incompressible even denominator fractional quantum Hall states at fillings $\nu = \pm \frac{1}{2}$ and $\nu = \pm \frac{1}{4}$ have been recently observed in monolayer graphene. We use a Chern-Simons description of multi-component fractional quantum Hall states in graphene to investigate the properties of these states and suggest variational wavefunctions that may describe them. We find that the experimentally observed even denominator fractions and standard odd fractions (such as $\nu=1/3, 2/5$, etc.) can be accommodated within the same flux attachment scheme and argue that they may arise from sublattice or chiral symmetry breaking orders (such as charge-density-wave and antiferromagnetism) of composite Dirac fermions, a phenomenon unifying integer and fractional quantum Hall physics for relativistic fermions. We also discuss possible experimental probes that can narrow down the candidate broken symmetry phases for the fractional quantum Hall states in the zeroth Landau level of monolayer graphene., Comment: 5 pages

We present the quantum critical theory of an interacting nodal Fermi-liquid of quasi-relativisitc pseudo-spin-3/2 fermions that have a non-interacting birefringent spectrum with two distinct Fermi velocities. When such quasiparticles interact with gapless bosonic degrees of freedom that mediate either the long-range Coulomb interaction or its short range component (responsible for spontaneous symmetry breaking), in the deep infrared or quantum critical regime in two dimensions the system is respectively described by a marginal- or a non-Fermi liquid of relativistic spin-1/2 fermions (possessing a unique velocity), and is always a marginal Fermi liquid in three dimensions. We consider a possible generalization of these scenarios to fermions with an arbitrary half-odd-integer spin, and conjecture that critical spin-1/2 excitations represent a superuniversal description of the entire family of interacting quasi-relativistic fermions., Comment: Published version in PRL: 4.5 Pages, 2 Figures (Supplementary: 6 Pages, Ancillary file)

We develop a formalism that allows the study of correlations in space and time in both the superfluid and Mott insulating phases of the Bose-Hubbard Model. Specifically, we obtain a two particle irreducible effective action within the contour-time formalism that allows for both equilibrium and out of equilibrium phenomena. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. To assess the accuracy of this formalism, we study the equilibrium solution of the equations of motion and compare our results to existing strong coupling methods as well as exact methods where possible. We discuss applications of this formalism to out of equilibrium situations., Comment: 41 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1606.04117

It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. Due to the multitude of ways to define these, the explicit identification of the optimally local pseudospins in specific systems is non-trivial. Given continuing intense interest in the role of disorder in strongly correlated systems, we consider the disordered Hubbard model. Focusing on a two-site system, we track the evolution of the optimally localized pseudospins as hopping and interactions are varied to move the system away from the trivially localized atomic limit, examining the explicit form of the pseudospins and exploring the broad distribution of non-optimal forms., Comment: 9 pages, 3 figures

We study the spreading of correlations in space and time after a quantum quench in the Bose Hubbard model. We derive equations of motion for the single-particle Green's function within the contour-time formalism, allowing us to study dynamics in the strong coupling regime. We discuss the numerical solutions of these equations and calculate the single-particle density matrix for quenches in the Mott phase. We demonstrate light-cone like spreading of correlations in the Mott phase in one, two, and three dimensions and calculate propagation velocities in each dimension., Comment: 16 pages, 9 figures

Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $\nu = 0$ and $\nu = \pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from interaction-induced chiral symmetry-breaking orders. We argue that when the chemical potential is at the Dirac point, weak on-site repulsion supports an easy-plane antiferromagnet state, which simultaneously gives rise to ferromagnetism oriented parallel to the magnetic field direction, whereas for $|\nu|=1$ easy-axis antiferromagnet and charge-density-wave orders coexist. We perform self-consistent calculations of the magnetic field dependence of the activation gap for the $\nu = 0$ and $|\nu| = 1$ states and obtain excellent agreement with recent experimental results. Implications of our study for fractional Hall states in monolayer graphene are highlighted., Comment: 5 pages, 3 figures + Supplementary Materials (3.5 pages, 2 figures): Published version, typos corrected, new references

Birefringent fermions arise as massless fermionic low energy excitations of a particular tight binding model for spinless fermions on a square lattice which have two "speeds of light" [M. P. Kennett, ${\it et \, al.}$, Phys. Rev. A ${\bf 83}$, 053636 (2011)]. We use mean field theory to study phases that can arise when there are nearest neighbour and next-nearest neighbour repulsive interactions in this model and demonstrate robustness of the birefringent semi-metal phase in the presence of weak interactions and identify transitions to staggered density and quantum anomalous Hall ordered phases. We consider the effect of coupling birefringent fermions to a magnetic field, and find analytic expressions for the corresponding Landau levels and demonstrate that their integer Quantum Hall effect displays additional plateaux beyond those observed for regular Dirac fermions, such as in graphene. We briefly discuss a tight-binding construction that leads to three dimensional birefringent fermions., Comment: 8 pages, 7 figures

The question of whether spatially inhomogeneous hopping in the two dimensional Hubbard model can lead to enhancement of superconductivity has been tackled by a number of authors in the context of the checkerboard Hubbard model (CHM). We address the effects of disorder on superconducting properties of the CHM by using exact diagonalization calculations for both potential and hopping disorder. We characterize the superconducting tendencies of the model by focusing on the pair binding energy, the spin gap, and d-wave pairing order parameter. We find that superconducting tendencies, particularly the pair binding energy, are more robust to disorder when there is inhomogeneous hopping than for the uniform Hubbard model. We also study all possible staggered potentials for an eight site CHM cluster and relate the behaviour of these configurations to the disordered system., Comment: 13 pages, 29 figures

We study the zero energy modes that arise in an unusual vortex configuration involving both the kinetic energy and an appropriate mass term in a model which exhibits birefringent Dirac fermions as its low energy excitations. We find the surprising feature that the ratio of the length scales associated with states centered on vortex and anti-vortex topological defects can be arbitrarily varied but that fractionalization of quantum numbers such as charge is unaffected. We discuss this situation from a symmetry point of view and present numerical results for a specific lattice model realization of this scenario., Comment: 7 pages, 6 figures

We study the real time dynamics of the Bose Hubbard model in the presence of time-dependent hopping allowing for a finite temperature initial state. We use the Schwinger-Keldysh technique to find the real-time strong coupling action for the problem at both zero and finite temperature. This action allows for the description of both the superfluid and Mott insulating phases. We use this action to obtain dynamical equations for the superfluid order parameter as hopping is tuned in real time so that the system crosses the superfluid phase boundary. We find that under a quench in the hopping, the system generically enters a metastable state in which the superfluid order parameter has an oscillatory time dependence with a finite magnitude, but disappears when averaged over a period. We relate our results to recent cold atom experiments., Comment: 22 pages, 7 figures

We generalize a proposal by Sorensen et al. [Phys. Rev. Lett. 94, 086803 (2005)] for creating an artificial magnetic field in a cold atom system on a square optical lattice. This leads us to an effective lattice model with tunable spatially periodic modulation of the artificial magnetic field and the hopping amplitude. When there is an average flux of half a flux quantum per plaquette the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different "speeds of light" which can be tuned to give a single Dirac cone and a flat band. These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain wall topological defects., Comment: 5 pages, 3 figures

The magnetic properties of a variety of materials with promise for technological applications have been described by models in which fermions are coupled to local moment spins. Monte Carlo studies of such models usually ignore electron-electron interactions, even though the energy scale corresponding to these interactions may be comparable to or larger than other relevant energy scales. In this work we add on-site interactions between fermions to the double exchange model which we study with a Monte Carlo scheme in which temporal fluctuations of local moment spins are fully accounted for and electron-electron interactions are treated at a mean field level. We show that when the number of fermions is considerably less than the number of local moments even moderate interactions can lead to significant enhancement of ferromagnetism and the Curie temperature., Comment: 4 + epsilon pages, 3 figures

Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resitance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave (CDW) order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We examine in detail a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau-level mixing plays an important role., Comment: 25 pages, 6 figures

Studies of interlayer transport in layered metals have generally made use of zero temperature conductivity expressions to analyze angle-dependent magnetoresistance oscillations (AMRO). However, recent high temperature AMRO experiments have been performed in a regime where the inclusion of finite temperature effects may be required for a quantitative description of the resistivity. We calculate the interlayer conductivity in a layered metal with anisotropic Fermi surface properties allowing for finite temperature effects. We find that resistance maxima are modified by thermal effects much more strongly than resistance minima. We also use our expressions to calculate the interlayer resistivity appropriate to recent AMRO experiments in an overdoped cuprate which led to the conclusion that there is an anisotropic, linear in temperature contribution to the scattering rate and find that this conclusion is robust., Comment: 8 pages, 4 figures

Studies of angle-dependent magnetoresistance oscillations (AMRO) in the interlayer conductivity of layered metals have generally considered semi-classical electron transport. We consider a quantum correction to the semi-classical conductivity that arises from what can be described as an interlayer Cooperon. This depends on both the disorder potential within a layer and the correlations of the disorder potential between layers. We compare our results with existing experimental data on organic charge transfer salts that are not explained within the standard semi-classical transport picture. In particular, our results may be applicable to effects that have been seen when the applied magnetic field is almost parallel to the conducting layers. We predict the presence of a peak in the resistivity as the field direction approaches the plane of the layers. The peak can occur even when there is weakly incoherent transport between layers., Comment: 11 pages, 6 figures

We study the zero temperature mean-field phase diagram of the Bose-Hubbard model in the presence of local coupling between the bosons and an external bath. We consider a coupling that conserves the on-site occupation number, preserving the robustness of the Mott and superfluid phases. We show that the coupling to the bath renormalizes the chemical potential and the interaction between the bosons and reduces the size of the superfluid regions between the insulating lobes. For strong enough coupling, a finite value of hopping is required to obtain superfluidity around the degeneracy points where Mott phases with different occupation numbers coexist. We discuss the role that such a bath coupling may play in experiments that probe the formation of the insulator-superfluid shell structure in systems of trapped atoms., Comment: 5 pages, 2 figures. Error found in v1, now corrected, leads to qualitative changes in results

Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of this "mobility" field has remained elusive due to the lack of coarse-graining procedures to obtain these models from a more microscopic point of view. Here we exhibit a scheme to map the dynamics of a two-dimensional soft disc glass former onto a kinetically constrained spin model, providing an attempt at bridging these two approaches., Comment: 6 pages, 5 figures, revised version

Many of the most interesting and technologically important electronic materials discovered in the past two decades have two common features: a layered crystal structure and strong interactions between electrons. Two of the most fundamental questions about such layered metals concern the origin of intralayer anisotropies and the coherence of interlayer charge transport. We show that angle dependent magnetoresistance oscillations (AMRO) are sensitive to anisotropies around an intralayer Fermi surface. Hence, AMRO can be a probe of intralayer anisotropies that is complementary to angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). However, AMRO are not very sensitive to the coherence of the interlayer transport. We illustrate this with comparisons to recent AMRO experiments on an overdoped cuprate., Comment: 7 pages, 3 figures

We introduce a lattice model for a classical doped two dimensional antiferromagnet which has no quenched disorder, yet displays slow dynamics similar to those observed in supercooled liquids. We calculate two-time spatial and spin correlations via Monte Carlo simulations and find that for sufficiently low temperatures, there is anomalous diffusion and stretched-exponential relaxation of spin correlations. The relaxation times associated with spin correlations and diffusion both diverge at low temperatures in a sub-Arrhenius fashion if the fit is done over a large temperature-window or an Arrhenius fashion if only low temperatures are considered. We find evidence of spatially heterogeneous dynamics, in which vacancies created by changes in occupation facilitate spin flips on neighbouring sites. We find violations of the Stokes-Einstein relation and Debye-Stokes-Einstein relation and show that the probability distributions of local spatial correlations indicate fast and slow populations of sites, and local spin correlations indicate a wide distribution of relaxation times, similar to observ ations in other glassy systems with and without quenched disorder., Comment: 12 pages, 17 figures, corrected erroneous figure, and improved quality of manuscript, updated references

We study theoretically the geometrical and temporal commensurability oscillations induced in the resistivity of 2D electrons in a perpendicular magnetic field by surface acoustic waves (SAWs). We show that there is a positive anisotropic dynamical classical contribution and an isotropic non-equilibrium quantum contribution to the resistivity. We describe how the commensurability oscillations modulate the resonances in the SAW-induced resistivity at multiples of the cyclotron frequency. We study the effects of both short-range and long-range disorder on the resistivity corrections for both the classical and quantum non-equilibrium cases. We predict that the quantum correction will give rise to zero-resistance states with associated geometrical commensurability oscillations at large SAW amplitude for sufficiently large inelastic scattering times. These zero resistance states are qualitatively similar to those observed under microwave illumination, and their nature depends crucially on whether the disorder is short- or long-range. Finally, we discuss the implications of our results for current and future experiments on two dimensional electron gases., Comment: 16 pages, 8 figures

We study the geometrical commensurability oscillations imposed onto the resistivity of 2D electrons in a perpendicular magnetic field by a propagating surface acoustic wave (SAW). We show that, for $\omega <\omega_{c}$, this effect is composed of an anisotropic dynamical classical contribution increasing the resistivity and the non-equilibrium quantum contribution isotropically decreasing resistivity, and we predict the appearance of zero-resistance states associated with geometrical commensurability at large SAW amplitude. We also describe how the commensurability oscillations modulate the resonances in the SAW-induced resistivity at multiples of the cyclotron frequency., Comment: 5 pages with 1 figure

Motivated by the recent suggestion of anisotropic effective exchange interactions between Mn spins in Ga$_{1-x}$Mn$_x$As (arising as a result of spin-orbit coupling), we study their effects in diluted Heisenberg spin systems. We perform Monte Carlo simulations on several phenomenological model spin Hamiltonians, and investigate the extent to which frustration induced by anisotropic exchanges can reduce the low temperature magnetization in these models and the interplay of this effect with disorder in the exchange. In a model with low coordination number and purely ferromagnetic (FM) exchanges, we find that the low temperature magnetization is gradually reduced as exchange anisotropy is turned on. However, as the connectivity of the model is increased, the effect of small-to-moderate anisotropy is suppressed, and the magnetization regains its maximum saturation value at low temperatures unless the distribution of exchanges is very wide. To obtain significant suppression of the low temperature magnetization in a model with high connectivity, as is found for long-range interactions, we find it necessary to have both ferromagnetic and antiferromagnetic (AFM) exchanges (e.g. as in the RKKY interaction). This implies that disorder in the sign of the exchange interaction is much more effective in suppressing magnetization at low temperatures than exchange anisotropy., Comment: 9 pages, 8 figures

We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators. We explain why the former describe the fingerprint of quenched disorder when it exists, while the latter are linked to noise-induced mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations of the coarse-grained quantities. We show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. The invariance of the theory under reparametrizations of time underlies these results. We relate the pdfs of local coarse-grained quantities and the theory of dynamic random manifolds. We define a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems., Comment: 47 pages, 60 Figs

We report the results of a Monte Carlo study of a model of (III,Mn)V diluted magnetic semiconductors which uses an impurity band description of carriers coupled to localized Mn spins and is applicable for carrier densities below and around the metal-insulator transition. In agreement with mean field studies, we find a transition to a ferromagnetic phase at low temperatures. We compare our results for the magnetic properties with the mean field approximation, as well as with experiments, and find favorable qualitative agreement with the latter. The local Mn magnetization below the Curie temperature is found to be spatially inhomogeneous, and strongly correlated with the local carrier charge density at the Mn sites. The model contains fermions and classical spins and hence we introduce a perturbative Monte Carlo scheme to increase the speed of our simulations., Comment: 17 pages, 24 figures, 2 tables

We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations of short-range spin glasses. Local fluctuations and responses are shown to be connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. Scaling relationships are uncovered for the slow evolution of heterogeneities at all time scales., Comment: Substantially reorganized to improve clarity of exposition. Accepted for publication in Physical Review Letters. 5 pages, 4 figures

This paper, based on a presentation at the Spintronics 2001 conference, provides a review of our studies on II-VI and III-V Mn-doped Diluted Magnetic Semiconductors. We use simple models appropriate for the low carrier density (insulating) regime, although we believe that some of the unusual features of the magnetization curves should qualitatively be present at larger dopings (metallic regime) as well. Positional disorder of the magnetic impurities inside the host semiconductor is shown to have observable consequences for the shape of the magnetization curve. Below the critical temperature the magnetization is spatially inhomogeneous, leading to very unusual temperature dependence of the average magnetization as well as specific heat. Disorder is also found to enhance the ferromagnetic transition temperature. Unusual spin and charge transport is implied., Comment: 10 pages + 10 figures; Spintronics 2001

We show that the generating functional describing the slow dynamics of spin glass systems is invariant under reparametrizations of the time. This result is general and applies for both infinite and short range models. It follows simply from the assumption that a separation between short time-scales and long time-scales exists in the system, and the constraints of causality and unitarity. Global time reparametrization invariance suggests that the low action excitations in a spin glass may be smoothly spatially varying time reparametrizations. These Goldstone modes may provide the basis for an analytic dynamical theory of short range spin glasses., Comment: 4 pages, 1 figure

We study the long time dynamics of quantum spin glasses of rotors using the non-equilibrium Schwinger-Keldysh formalism. These models are known to have a quantum phase transition from a paramagnetic to a spin glass phase, which we approach by looking at the divergence of the spin relaxation rate at the transition point. In the aging regime, we determine the dynamical equations governing the time evolution of the spin response and correlation functions, and show that all terms in the equations that arise solely from quantum effects are irrelevant at long times under time reparametrization group (RpG) transformations. At long times, quantum effects enter only through the renormalization of the parameters in the dynamical equations for the classical counterpart of the rotor model. Consequently, quantum effects only modify the out of equilibrium fluctuation dissipation relation (OEFDR), i.e. the ratio X between the temperature and the effective temperature, but not the form of the classical OEFDR., Comment: 14 pages, 4 figures

We examine the feasibility of a simple description of Mn ions in III-V diluted magnetic semiconductors (DMSs) in terms of two species (components), motivated by the expectation that the Mn-hole exchange couplings are widely distributed, expecially for low Mn concentrations. We find, using distributions indicated by recent numerical mean field studies, that the thermodynamic properties (magnetization, susceptibility, and specific heat) cannot be fit by a single coupling as in a homogeneous model, but can be fit well by a two-component model with a temperature dependent number of ``strongly'' and ``weakly'' coupled spins. This suggests that a two-component description may be a minimal model for the interpretation of experimental measurements of thermodynamic quantities in III-V DMS systems., Comment: 10 pages, 9 figures, 1 new figure, substantial revisions

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations, and within this language the long time behaviour of this model is controlled by a reparametrization group (R$_p$G) fixed point of the classical dynamics. The irrelevance of the quantum terms in the dynamical equations in the aging regime explains the classical nature of the violation of the fluctuation-dissipation theorem., Comment: 4 pages

Neutrino emission via the plasma process using the vertex formalism for QED in a strongly magnetized plasma is considered. A new vertex function is introduced to include the axial vector part of the weak interaction. Our results are compared with previous calculations, and the effect of the axial vector coupling on neutrino emission is discussed. The contribution from the axial vector coupling can be of the same order as or greater than the vector vector coupling under certain plasma conditions., Comment: 20 pages, 3 figures