Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

Vasseur, Romain; Moore, Joel E.

doi:10.1088/1742-5468/2016/06/064010

Cited by 214 publications

(228 citation statements)

References 137 publications

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“…On the one hand, integrable systems are characterized by a macroscopic number of (quasi)local conservation laws [29][30][31][32][33] and the overlap with these conserved quantities leads to unconventional equilibration and thermalization [34][35][36] and nondecaying currents [37][38][39]. On the other hand, the overlap with one of the conserved quantities is not guaranteed for all parameters * jonasrichter@uos.de † rsteinig@uos.de of the model, observables, and initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Real-time dynamics of typical and untypical states in nonintegrable systems

Richter¹,

Jin²,

Raedt³

et al. 2018

Phys. Rev. B

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Understanding (i) the emergence of diffusion from truly microscopic principles continues to be a major challenge in experimental and theoretical physics. At the same time, isolated quantum many-body systems have experienced an upsurge of interest in recent years. Since in such systems the realization of a proper initial state is the only possibility to induce a nonequilibrium process, understanding (ii) the largely unexplored role of the specific realization is vitally important. Our work reports a substantial step forward and tackles the two issues (i) and (ii) in the context of typicality, entanglement as well as integrability and nonintegrability. Specifically, we consider the spin-1/2 XXZ chain, where integrability can be broken due to an additional next-nearest neighbor interaction, and study the real-time and real-space dynamics of nonequilibrium magnetization profiles for a class of pure states. Summarizing our main results, we show that signatures of diffusion for strong interactions are equally pronounced for the integrable and nonintegrable case. In both cases, we further find a clear difference between the dynamics of states with and without internal randomness. We provide an explanation of this difference by a detailed analysis of the local density of states.

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Section: Introductionmentioning

confidence: 99%

Real-time dynamics of typical and untypical states in nonintegrable systems

Richter¹,

Jin²,

Raedt³

et al. 2018

Phys. Rev. B

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“…In the latter case, a remarkable analytical solution has been found very recently [37], using the method of generalized hydrodynamics (GHD). Another commonly studied example of inhomogeneous initial states is the tensor product of two Gibbs states at different temperatures, which produces nontrivial energy density and current profiles under time evolution, see the recent reviews [38,39] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Front dynamics and entanglement in the XXZ chain with a gradient

Eisler

Bauernfeind

2017

Phys. Rev. B

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We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.

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“…[1][2][3] for recent reviews. Particularly interesting is the case of integrable models in one dimension, where the dynamics is constrained by a large set of conserved charges [4], leading to peculiar features in the transport properties [5] or the relaxation towards a stationary state [6]. A key paradigm of closedsystem dynamics is the quantum quench, where one typically prepares the pure ground state of a Hamiltonian which is then abruptly changed into a new one and the subsequent unitary time evolution is monitored [7].…”

Section: Introductionmentioning

confidence: 99%

Universal front propagation in the quantum Ising chain with domain-wall initial states

2016

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We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.

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Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

Cited by 214 publications

References 137 publications

Real-time dynamics of typical and untypical states in nonintegrable systems

Real-time dynamics of typical and untypical states in nonintegrable systems

Front dynamics and entanglement in the XXZ chain with a gradient

Universal front propagation in the quantum Ising chain with domain-wall initial states

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