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

Richter, Jonas; Jin, Fengping; Raedt, Hans De; Michielsen, Kristel; Gemmer, Jochen; Steinigeweg, Robin

doi:10.1103/physrevb.97.174430

Cited by 32 publications

(38 citation statements)

References 94 publications

(204 reference statements)

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“…For this clean case, we find that D q (t) is approximately constant for times 2 tJ 10. Furthermore, at these times, we find that D q (t) coincides for all three momenta q depicted [10,46]. Visible differences for longer times are a consequence of finite-size effects, as evident when comparing the two q = 0 curves for L = 20 and L = 34 [80].…”

Section: Broadening Of Non-equilibrium Profilesmentioning

confidence: 51%

“…On the contrary, for quantum systems in strict isolation, a non-equilibrium situation can only be induced by the preparation of suitable initial states, e.g., by means of a quench [6][7][8]. These initial states can be mixed or pure, entangled or non-entangled, and their properties might be of essential importance for the subsequent relaxation process [9][10][11]. In this context, the intriguing question arises whether the system will eventually reach thermal equilibrium under its own unitary dynamics governed by the Schrödinger equation.…”

Section: Introductionmentioning

confidence: 99%

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Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport

2018

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We study the real-time dynamics of local occupation numbers in a one-dimensional model of spinless fermions with a random on-site potential for a certain class of initial states. The latter are thermal (mixed or pure) states of the model in the presence of an additional static force, but become non-equilibrium states after a sudden removal of this static force. For this class and high temperatures, we show that the induced dynamics is given by a single correlation function at equilibrium, independent of the initial expectation values being prepared close to equilibrium (by a weak static force) or far away from equilibrium (by a strong static force). Remarkably, this type of universality holds true in both, the ergodic phase and the many-body localized regime. Moreover, it does not depend on the specific choice of a unit cell for the local density. We particularly discuss two important consequences. First, the long-time expectation value of the local density is uniquely determined by the fluctuations of its diagonal matrix elements in the energy eigenbasis. Thus, the validity of the eigenstate thermalization hypothesis is not only a sufficient but also a necessary condition for thermalization. Second, the real-time broadening of density profiles is always given by the current autocorrelation function at equilibrium via a generalized Einstein relation. In the context of transport, we discuss the influence of disorder for large particle-particle interactions, where normal diffusion is known to occur in the disorder-free case. Our results suggest that normal diffusion is stable against weak disorder, while they are consistent with anomalous diffusion for stronger disorder below the localization transition. Particularly, for weak disorder, Gaussian density profiles can be observed for single disorder realizations, which we demonstrate for finite lattices up to 31 sites. * jonasrichter@uos.de †

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Section: Broadening Of Non-equilibrium Profilesmentioning

confidence: 51%

Section: Introductionmentioning

confidence: 99%

Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport

2018

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“…To examine whether Eqs. (14) hold in the perturbed Ising field theory, we compute the expectation value of the local spin operator σ(0) within eigenstates [so-called eigenstate expectation values (EEVs)] in a finite volume, R. Results as a function of energy density E/R with m = 1, g = 0.1 for R = 25, 35, 45 are presented in Figs. 2.…”

Section: B Diagonal Matrix Elementsmentioning

confidence: 99%

“…[11][12][13] Such states are often called nontypical, see Ref. 14 for a recent example. The presence of rare states in the finite volume leads to two interpretations of ETH.…”

Section: Introductionmentioning

confidence: 99%

Signatures of rare states and thermalization in a theory with confinement

2019

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There is a dichotomy in the nonequilibrium dynamics of quantum many body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new 'meson' excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously. arXiv:1808.10782v2 [cond-mat.str-el]

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“…It is known, however, that nonthermal states that violate the ETH can also exist in finite size systems [7,8,[19][20][21], usually being observed at the very edges of the spectrum. The presence of such nonthermal states in the spectrum can have important consequences for nonequilibrium dynamics [13,[20][21][22][23], in particular leading to an absence of thermalization following a quantum quench [19,21]. Thermalization is used here in the sense that EVs in the diagonal ensemble (DE) agree with the microcanonical ensemble (MCE) result [4,5].…”

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confidence: 99%

Nonthermal States Arising from Confinement in One and Two Dimensions

2019

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We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete 'meson' modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy E do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two meson threshold, due to a surprising lack of hybridization with the (n ≥ 4)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous post-quench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. The nonthermal states are confined to the ordered phase -the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability.

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

Cited by 32 publications

References 94 publications

Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport

Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport

Signatures of rare states and thermalization in a theory with confinement

Nonthermal States Arising from Confinement in One and Two Dimensions

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