Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: i) An initial buildup of correlations where the quasiparticles are formed. ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. iii) The long time limit described by a quantum Boltzmann equation leading to thermalization with a temperature T proportional to U.
We investigate the non-equilibrium dynamics of the one-dimensional extended Hubbard model after interaction quenches. In strong-coupling regime with large on-site interaction, the ground states of this model with small and large nearest-neighbor interactions are in spin-density-wave and charge-density-wave phases, respectively. Combining twisted boundary conditions with the time-dependent Lanczos method, we obtain snapshots of the time-dependent single-particle spectrum after quenches. We find that for quench within the same phase, the single-particle spectrum becomes close to that of the quen…
The one-dimensional Fermi-Hubbard model is used as testbed for strong global parameter quenches. With the aid of iterated equations of motion in combination with a suitable scalar product for operators we describe the dynamics and the long-term behavior in particular of the system after interaction quenches. This becomes possible because the employed approximation allows for oscillatory dynamics avoiding spurious divergences. The infinite-time behavior is captured by an analytical approach based on stationary phases; no numerical averages over long times need to be computed. We study the most …
We study the time evolution of a half-filled Hubbard layer coupled to a magnon bath after a quench of the Hubbard interaction. Qualitatively different regimes, regarding the asymptotic long-time dynamics, are identified and characterized within the mean-field approximation. In the absence of the bath, the dynamics of the closed system is similar to that of a quenched BCS condensate. Though the presence of the bath introduces an additional relaxation mechanism, our numerical results and analytical arguments show that equilibration with the bath is not necessarily attained within the approximati…
We study quenches of the interaction and electron-phonon coupling parameter in the Hubbard-Holstein model, using nonequilibrium dynamical mean field theory. The calculations are based on a generalized Lang-Firsov scheme for time-dependent interactions or externally driven phonons, and an approximate strong-coupling impurity solver. The interaction quench calculations reveal the phonon-assisted decay of excess doublons, while the quenches of the electron-phonon coupling lead to persistent oscillations of the phonons and to a phonon-enhanced doublon production.
We show that the non-equilibrium time-evolution after interaction quenches in the one dimensional, integrable Hubbard model exhibits a dynamical transition in the half-filled case. This transition ceases to exist upon doping. Our study is based on systematically extended equations of motion. Thus it is controlled for small and moderate times; no relaxation effects are neglected. Remarkable similarities to the quench dynamics in the infinite dimensional Hubbard model are found suggesting dynamical transitions to be a general feature of quenches in such models.
We investigate the unitary dynamics following a sudden increase $ΔU>0$ of repulsion in the paramagnetic sector of the half-filled Hubbard model on a Bethe lattice, by means of a variational approach that combines a Gutzwiller wavefunction with a partial Schrieffer-Wolff transformation, both defined through time-dependent variational parameters. Besides recovering at $ΔU_c$ the known dynamical transition linked to the equilibrium Mott transition, we find pronounced dynamical anomaly at larger $ΔU_*>ΔU_c$ manifested in a singular behaviour of the long-time average of double occupancy. Although t…
In weakly perturbed systems that are close to integrability, thermalization can be delayed by the formation of prethermalization plateaus. We study the build-up of density-density correlations after a weak interaction quench in the Hubbard model in $d > 1$ dimensions using unitary perturbation theory. Starting from a pre-quench state at temperature $T$, we show that the prethermalization values of the post-quench correlations are equal to the equilibrium values of the interacting model at the same temperature $T$. This is explained by the local character of density-density correlations.
We use non-equilibrium dynamical mean-field theory in combination with a recently developed Quantum Monte Carlo impurity solver to study the real-time dynamics of a Hubbard model which is driven out of equilibrium by a sudden increase in the on-site repulsion U. We discuss the implementation of the self-consistency procedure and some important technical improvements of the QMC method. The exact numerical solution is compared to iterated perturbation theory, which is found to produce accurate results only for weak interaction or short times. Furthermore we calculate the spectral functions and t…
We study the off-equilibrium dynamics of the infinite dimensional Bose Hubbard Model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state. This transition is very similar to the one found for the fermionic Hubbard model by mean field approximations.
The generic non-equilibrium evolution of a strongly interacting fermionic system is studied. For strong quenches, a collective collapse-and-revival phenomenon is found extending over the whole Brillouin zone. A qualitatively distinct behavior occurs for weak quenches where only weak wiggling occurs. Surprisingly, no evidence for prethermalization is found in the weak coupling regime. In both regimes, indications for relaxation beyond oscillatory or power law behavior are found and used to estimate relaxation rates without resorting to a probabilistic ansatz. The relaxation appears to be fastes…
Using numerically exact methods we examine the Fermi-Hubbard model on arbitrary cluster topology. We focus on the question which systems eventually equilibrate or even thermalize after an interaction quench when initially prepared in a state highly entangled between system and bath. We find that constants of motion in integrable clusters prevent equilibration to the thermal state. We discuss the size of fluctuations during equilibration and thermalization and the influence of integrability. The influence of real space topology and in particular of infinite-range graphs on equilibration and the…
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.
We study the time evolution of the antiferromagnetic order parameter after interaction quenches in the Hubbard model. Using the nonequilibrium dynamical mean field formalism, we show that the system, after a quench from intermediate to strong interaction, is trapped in a nonthermal state which is reminiscent of a photo-doped state and protected by the slow decay of doublons. If the effective doping of this state is low enough, it exhibits robust antiferromagnetic order, even if the system is highly excited and the thermal state thus expected to be paramagnetic. We comment on the implication of…
We study the quench dynamics of the one-dimensional Hubbard model through the Quench Action formalism. We introduce a class of integrable initial states -- expressed as product states over two sites -- for which we can provide an exact characterisation of the late-time regime. This is achieved by finding a closed-form expression for the overlaps between our states and the Bethe ansatz eigenstates, which we check explicitly in the limits of low densities and infinite repulsion. Our solution gives access to the stationary values attained by local observables (we show the explicit example of the …
We investigate finite size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy-scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground-states. Both criteria can be computed using ground-state techniques that work for larger system sizes than full spectrum diagonalization. As examples, two models are s…
We study the crossover between the sudden quench limit and the adiabatic dynamics of superconducting states in the attractive Hubbard model. We focus on the dynamics induced by the change of the attractive interaction during a finite ramp time which is varied in order to track the evolution of the dynamical phase diagram from the sudden quench to the equilibrium limit. Two different dynamical regimes are realized for quenches towards weak and strong coupling interactions. At weak coupling the dynamics depends only on the energy injected into the system, whereas a dynamics retaining memory of t…
We introduce the notion of non-Abelian tensors, and use them to construct a general non-Abelian time evolving block decimation (NA-TEBD) scheme that uses an arbitrary number of Abelian and non-Abelian symmetries. Our approach increases the speed and memory storage efficiency of matrix product state based computations by several orders of magnitudes, and makes large bond dimensions accessible even on simple desktop architectures. We use it to study post-quench dynamics in the repulsive SU(3) Hubbard model, and to determine the time evolution of various local operators and correlation functions …
We study the non equilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map…
In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain thermalization. The latter is proposed to stem from what he calls the eigenstate thermalization hypothesis and which boils down to the fact that simple observables are expected to be smooth functions of the energy. In this Reply, we show that there is no contradiction or confusion between the observations and discussions of Roux and the expecte…
We investigate the quench of half-filled 1D and 2D fermionic Hubbard models to models without Coulomb interaction. Since the time propagation is gaussian we can use a variety of time-dependent quantum Monte Carlo methods to tackle this problem without generating a dynamical sign problem. Using a continuous time quantum Monte Carlo method (CTQMC) we achieve a system size of 128 sites in 1D, and using a Blankenbecler-Scalapino-Sugar (BSS) type algorithm we were able to simulate 20 x 20 square lattices. Applying these methods to study the dynamics after the quench, we observe that the final state…
We investigate by means of the time-dependent Gutzwiller approximation the out-of-equilibrium dynamics of an antiferromagnetic state evolved with the Hubbard model Hamiltonian after a sudden change of the repulsion strength $U$. We find that magnetic order survives more than what expected on the basis of thermalization arguments, in agreement with recent DMFT calculations. In addition, we find evidence of a dynamical transition for quenches to large values of $U$ between a coherent antiferromagnet characterized by a finite quasiparticle residue to an incoherent one with vanishing residue, that…
The Lieb-Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolution of prepared initial states in the thermodynamic limit in one-dimensional quantum systems. The algorithm does not require translational invariance and allows for an easy implementation of local conservation laws. We use the algorithm to investigate the relaxation dynamics of double occupancies in …
We investigate how fast and how effective photocarrier excitation can modify the exchange interaction $J_\mathrm{ex}$ in the prototype Mott-Hubbard insulator. We demonstrate an ultrafast quenching of $J_\mathrm{ex}$ both by evaluating exchange integrals from a time-dependent response formalism and by explicitly simulating laser-induced spin precession in an antiferromagnet that is canted by an external magnetic field. In both cases, the electron dynamics is obtained from nonequilibrium dynamical mean-field theory. We find that the modified $J_\mathrm{ex}$ emerges already within a few electron …
We present a Gutzwiller von Neumann dynamics (GvND) method for simulating equilibrium and nonequilibrium phenomena in strongly correlated electron systems. Our approach is a real-space formulation of the time-dependent Gutzwiller approximation method. Applying the GvND method to simulate interaction quenches in the Peierls-Hubbard model, we demonstrate the amplification of initial inhomogeneities, which in turn results in the collapse of quench-induced synchronized oscillation. Moreover, we find a dynamical phase transition separating two quasi-stationary regimes with rather distinct spatial d…
The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of supe…
We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system. We apply our method to the Bose-Hubbard model, to a generalized Jaynes-Cummings model, and to the Ising model in a transverse field. We find that the quantum evolution can be mapped onto a classical effective dynamics, which involves only a few intensive observables. For some special parameters of the quench, peculiar dynamical transitions occur. They resul…
We investigate the competition between superconductivity (SC) and charge density wave (CDW) under a time-dependent periodic field in the attractive Hubbard model. By employing the time-dependent exact diagonalization method, we show that the driving frequency and amplitude of the external field can control the enhancement of either the superconducting pair or the CDW correlations, which are degenerate in the ground state of the half-filled attractive Hubbard model in the absence of the field. In the strong-coupling limit of the attractive Hubbard interaction, the controllability is characteriz…
We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation ($U$) and disorder ($V$) strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling $T^α$ for this metal reveals non Fermi liquid characteristics. Moreover, a continuous dependence of $α$ on $U$ and $V$ from linear to nearly quadrat…
We reformulate the time-dependent Gutzwiller approximation by M. Schiró and M. Fabrizio [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a sp…
Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry -- for instance, the half-filled Hubbard model or graphene near the Dirac point -- the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analogue, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantu…
We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled $t_1{-}t_2$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating…
We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytica…
We study nonequilibrium dynamics in the one-dimensional Bose-Hubbard model starting from an initial product state with one boson per site and a single hole defect. We find that for parameters close to the quantum critical point, the hole splits into a core showing a very slow diffusive dynamics, and a fast mode which propagates ballistically. Using an effective fermionic model at large Hubbard interactions U, we show that the ballistic mode is a consequence of an interference between slow holon and fast doublon dynamics, which occurs once the hole defect starts propagating into the bosonic bac…
We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant Quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical m…
We study the real-time dynamics of the Kondo effect after a quantum quench in which a magnetic impurity is coupled to two metallic Hubbard chains. Using an effective field theory approach, we find that for noninteracting electrons the charge current across the impurity is given by a scaling function that involves the Kondo time. In the interacting case, we show that the Kondo time decreases with the strength of the repulsive interaction and the time dependence of the current reveals signatures of the Kondo effect in a Luttinger liquid. In addition, we verify that the relaxation of the impurity…
Moiré materials formed in two-dimensional semiconductor heterobilayers are quantum simulators of Hubbard-like physics with unprecedented electron-density and interaction-strength tunability. Compared to atomic scale Hubbard-like systems, electrons or holes in moiré materials are less strongly attracted to their effective lattice sites because these are defined by finite-depth potential extrema. As a consequence, non-local interaction terms like interaction-assisted hopping and intersite-exchange are more relevant. We theoretically demonstrate the possibility of tuning the strength of these cou…
We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite size exact diagonalization technique. By comparing with the corresponding 1D Hubbard model results and by using heuristic arguments we conclude that it is \QTR{it}{unlikely} that there is a 2D metal-insulator quantum phase transition although the effect of interaction in some range of parameters is to substantially enhance the non-interacting charge stiffness.
We investigate the dynamics of superconducting fluctuations in the attractive three-dimensional Hubbard model after a quench from the disordered phase to the ordered regime. While the long time evolution is well understood in terms of dissipative time-dependent Ginzburg-Landau models with unstable potentials, early times are more demanding due to the inseparable dynamics of the pairing fluctuations and the electronic quasiparticles. Our simulation using the time-dependent fluctuation exchange approximation treat both degrees of freedom on the same footing and reveal a non-thermal electronic re…
Prethermal cooling with many-body quantum quenches
Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息物质研究所）；Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；Institute for Theoretical Physics, Georg-August-Universität Göttingen（哥廷根大学理论物理研究所）
We study dynamical phase transitions from antiferromagnetic to paramagnetic states driven by an interaction quench in the fermionic Hubbard model using the nonequilibrium dynamical mean-field theory. We identify two dynamical transition points where the relaxation behavior qualitatively changes: one corresponds to the thermal phase transition at which the order parameter decays critically slowly in a power law $\propto t^{-1/2}$, and the other is connected to the existence of nonthermal antiferromagnetic order in systems with effective temperature above the thermal critical temperature. The fr…
A simple and very flexible variational approach to the out-of-equilibrium quantum dynamics in strongly correlated electron systems is introduced through a time-dependent Gutzwiller wavefunction. As an application, we study the simple case of a sudden change of the interaction in the fermionic Hubbard model and find at the mean field level an extremely rich behaviour. In particular, a dynamical transition between small and large quantum quench regimes is found to occur at half-filling, in accordance with the analysis of Eckstein {\sl et al.}, Phys. Rev. Lett. {\bf 103}, 056403 (2009), obtained …
