arXiv subjects

Marcos Rigol

Publications and source records attributed to Marcos Rigol.

At least 109 records · Page 6Linked to original sources

arXiv2013

Dynamics and thermalization in correlated one-dimensional lattice systems

We review exact approaches and recent results related to the relaxation dynamics and description after relaxation of various one-dimensional lattice systems of hard-core bosons after a sudden quench. We first analyze the integrable case, where the combination of analytical insights and computational techniques enable one to study large system sizes. Thermalization does not occur in this regime. However, after relaxation, observables can be described by a generalization of the Gibbs ensemble. We then utilize full exact diagonalization to study what happens as integrability is broken. We show that thermalization does occur in finite nonintegrable systems provided they are sufficiently far away from the integrable point. We argue that the onset of thermalization can be understood in terms of the eigenstate thermalization hypothesis.

cond-mat.stat-mech↗

arXiv2013

Finite-temperature properties of strongly correlated fermions in the honeycomb lattice

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

cond-mat.str-el↗

arXiv2013

Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench

We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find that fluctuation-dissipation relations hold if the system is nonintegrable after the quench. They also hold if the system is integrable after the quench if the initial state is an equilibrium state of a nonintegrable Hamiltonian. However, they fail if the system is integrable both before and after quenching.

cond-mat.stat-mech↗

arXiv2013

Single-particle and many-body analyses of a quasiperiodic integrable system after a quench

In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-Andre model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.

cond-mat.quant-gas↗

arXiv2013

Electronic spectral properties of the two-dimensional infinite-U Hubbard model

A strong-coupling series expansion for the Green's function and the extremely-correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-U Hubbard model. Results from these two complementary methods agree very well at both, low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where the series converge. We find that a modified first moment, which underestimates the contributions from the occupied states and is accessible in the series through the time-dependent Green's function, best describes the quasiparticle peak location in the strongly-correlated regime. This is examined by the ECFL results at low temperatures, where it is shown that the spectral function is largely skewed towards the occupied states.

cond-mat.str-el↗

arXiv2013

Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model

We investigate the interaction-induced superfluid-to-Mott insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.

cond-mat.str-el↗

arXiv2013

Initial state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states

We study sudden quantum quenches in which the initial states are selected to be either eigenstates of an integrable Hamiltonian that is nonmappable to a noninteracting one or a nonintegrable Hamiltonian, while the Hamiltonian after the quench is always integrable and mappable to a noninteracting one. By studying weighted energy densities and entropies, we show that quenches starting from nonintegrable (chaotic) eigenstates lead to an "ergodic" sampling of the eigenstates of the final Hamiltonian, while those starting from the integrable eigenstates do not (or at least it is not apparent for the system sizes accessible to us). This goes in parallel with the fact that the distribution of conserved quantities in the initial states is thermal in the nonintegrable cases and nonthermal in the integrable ones, and means that, in general, thermalization occurs in integrable systems when the quench starts form an eigenstate of a nonintegrable Hamiltonian (away from the edges of the spectrum), while it fails (or requires larger system sizes than those studied here to become apparent) for quenches starting at integrable points. We test those conclusions by studying the momentum distribution function of hard-core bosons after a quench.

cond-mat.stat-mech↗

arXiv2013

Quantum quenches and thermalization in one-dimensional fermionic systems

We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function [n(k)] and the density-density structure factor [N(k)], respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of N(k) for fermions is very similar to the one of hardcore bosons, the behavior of n(k) is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of n(k) in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.

cond-mat.stat-mech↗

arXiv2013

Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems

We study how the proximity to an integrable point or to localization as one approaches the atomic limit, as well as the mixing of symmetries in the chaotic domain, may affect the onset of thermalization in finite one-dimensional systems. We consider systems of hard-core bosons at half-filling with nearest neighbor hopping and interaction, and next-nearest neighbor interaction. The latter breaks integrability and induces a ground-state superfluid to insulator transition. By full exact diagonalization, we study chaos indicators and few-body observables. We show that when different symmetry sectors are mixed, chaos indicators associated with the eigenvectors, contrary to those related to the eigenvalues, capture the onset of chaos. The results for the complexity of the eigenvectors and for the expectation values of few-body observables confirm the validity of the eigenstate thermalization hypothesis in the chaotic regime, and therefore the occurrence of thermalization. We also study the properties of the off-diagonal matrix elements of few-body observables in relation to the transition from integrability to chaos and from chaos to localization.

cond-mat.stat-mech↗

arXiv2012

Quantum phases of hard-core bosons in a frustrated honeycomb lattice

Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose-Hubbard-Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.

cond-mat.str-el↗

arXiv2012

Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation

We study the dynamics and the resulting state after relaxation in a quasi-disordered integrable lattice system after a sudden quench. Specifically, we consider hard-core bosons in an isolated one-dimensional geometry in the presence of a quasi-periodic potential whose strength is abruptly changed to take the system out of equilibrium. In the delocalized regime, we find that the relaxation dynamics of one-body observables, such as the density, the momentum distribution function, and the occupation of the natural orbitals, follow, to a good approximation, power laws. In that regime, we also show that the observables after relaxation can be described by the generalized Gibbs ensemble, while such a description fails for the momentum distribution and the natural orbital occupations in the presence of localization. At the critical point, the relaxation dynamics is found to be slower than in the delocalized phase.

cond-mat.stat-mech↗

arXiv2012

Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice

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

cond-mat.str-el↗

arXiv2012

Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions

Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons (XY model) in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the condensate fraction and/or the superfluid stiffness. We then discuss how these phase diagrams can be measured in experiments with trapped ultracold gases, where the systems are inhomogeneous. For that, we introduce a method based on the measurement of the zero-momentum occupation, which is adequate for experiments dealing with both homogeneous and trapped systems, and compare it with previously proposed approaches.

cond-mat.quant-gas↗

arXiv2012

Effect of particle statistics in strongly correlated two-dimensional Hubbard models

We study the onset of particle statistics effects as the temperature is lowered in strongly correlated two-dimensional Hubbard models. We utilize numerical linked-cluster expansions and focus on the properties of interacting lattice fermions and two-component hard-core bosons. In the weak-coupling regime, where the ground state of the bosonic system is a superfluid, the thermodynamic properties of the two systems at half filling exhibit very large differences even at high temperatures. In the strong-coupling regime, where the low-temperature behavior is governed by a Mott insulator for either particle statistics, the agreement between the thermodynamic properties of both systems extends to regions where the antiferromagnetic (iso)spin correlations are exponentially large. We analyze how particle statistics affects adiabatic cooling in those systems.

cond-mat.str-el↗

arXiv2012

A Short Introduction to Numerical Linked-Cluster Expansions

We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques that can be used to accelerate the convergence of the series.

cond-mat.stat-mech↗

arXiv2012

Weak and strong typicality in quantum systems

We study the properties of mixed states obtained from eigenstates of many-body lattice Hamiltonians after tracing out part of the lattice. Two scenarios emerge for generic systems: (i) the diagonal entropy becomes equivalent to the thermodynamic entropy when a few sites are traced out (weak typicality); and (ii) the von Neumann (entanglement) entropy becomes equivalent to the thermodynamic entropy when a large fraction of the lattice is traced out (strong typicality). Remarkably, the results for few-body observables obtained with the reduced, diagonal, and canonical density matrices are very similar to each other, no matter which fraction of the lattice is traced out. Hence, for all physical quantities studied here, the results in the diagonal ensemble match the thermal predictions.

cond-mat.stat-mech↗

arXiv2012

Noise Correlation Scalings: Revisiting the Quantum Phase Transition in Incommensurate Lattices with Hard-Core Bosons

Finite size scalings of the momentum distribution and noise correlations are performed to study Mott insulator, Bose glass, and superfluid quantum phases in hard-core bosons (HCBs) subjected to quasi-periodic disorder. The exponents of the correlation functions at the Superfluid to Bose glass (SF-BG) transition are found to be approximately one half of the ones that characterizes the superfluid phase. The derivatives of the peak intensities of the correlation functions with respect to quasiperiodic disorder are shown to diverge at the SF-BG critical point. This behavior does not occur in the corresponding free fermion system, which also exhibits an Anderson-like transition at the same critical point, and thus provides a unique experimental tool to locate the phase transition in interacting bosonic systems. We also report on the absence of primary sublattice peaks in the momentum distribution of the superfluid phase for special fillings.

cond-mat.quant-gas↗

arXiv2012

Initial state dependence of the quench dynamics in integrable quantum systems. II. Thermal states

We study properties of isolated integrable quantum systems after a sudden quench starting from thermal states. We show that, even if the system is initially in thermal equilibrium at finite temperature, the diagonal entropy after a quench remains a fraction of the entropy in the generalized ensembles introduced to describe integrable systems after relaxation. The latter is also, in general, different from the entropy in thermal equilibrium. Furthermore, we examine the difference between the distribution of conserved quantities in the thermal and generalized ensembles after a quench and show that they are also, in general, different from each other. This explains why these systems fail to thermalize. A finite size scaling analysis is presented for each quantity, which allows us making predictions for thermodynamically large lattice sizes.

cond-mat.quant-gas↗