Prethermalization and Thermalization in Models with Weak Integrability Breaking

Bertini, Bruno; Eßler, Fabian H. L.; Groha, Stefan; Robinson, Neil J.

doi:10.1103/physrevlett.115.180601

Cited by 210 publications

(241 citation statements)

References 66 publications

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“…Such behavior is often phrased in terms of prethermalization [45][46][47][48][49][50] or prerelaxation plateaus [51][52][53], where a system's observables, in relaxing from some nonequilibrium initial state, remain nearly constant over some finite time interval before decaying to their final equilibrium value. Such plateaus have been argued to be controlled by the remnants of the conserved quantities of the nearby integrable system [48,49].…”

Section: Introductionmentioning

confidence: 99%

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

2015

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Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess nontrivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low-dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasiconserved quantities, thus providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasiconserved quantities can be probed experimentally.

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Section: Introductionmentioning

confidence: 99%

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

2015

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“…Accurate and reliable calculations of these phenomena are challenging, at least when going beyond the small system sizes of O(10) where exact diagonalisation (ED) is feasible. Perturbative techniques around the integrable limit suggest themselves for the problem at hand, and various types of such techniques have been employed in the context of prethermalisation, including a flow-equation methods [10], self-consistent mean-field techniques [11], self-consistent time-dependent spin-wave theory [12], and quantum kinetic theory [13][14][15][16]. The notion of quantum kinetic theory subsumes a number of approximate methods based on identifying certain classes of operators (usually those of higher degree in the normal-ordered ladder operators; see section 3 for more precise statements) as negligible, and deriving a reduced set of equations of motion for the remaining operators only [17].…”

Section: Introductionmentioning

confidence: 99%

Quantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions

Duval

Kastner

2019

New J. Phys.

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For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several truncations of the time evolution equations up to eighth order in the Jordan-Wigner fermionic operators. The resulting set of differential equations can be solved for lattices with O(10 2 ) sites and facilitates the computation of spin expectation values and correlation functions to high accuracy, at least for moderate timescales. We use this scheme to study the relaxation dynamics of the model, involving prethermalisation and thermalisation. The techniques developed here can be generalised to other spin models with weak integrability-breaking terms.

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“…For integrable systems this issue has long been in the focus of research with many interesting findings (cf., for instance, Refs. [20][21][22][23][24][25][26][27]). Generically, integrable systems with a large number of degrees of freedom turn chaotic for a weak perturbation.…”

Section: Introductionmentioning

confidence: 99%

Many-body localization phase in a spin-driven chiral multiferroic chain

et al. 2017

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Many-body localization (MBL) is an emergent phase in correlated quantum systems with promising applications, particularly in quantum information. Here, we unveil the existence and analyze this phase in a chiral multiferroic model system. Conventionally, MBL occurrence is traced via level statistics by implementing a standard finite-size scaling procedure. Here, we present an approach based on the full distribution of the ratio of adjacent energy spacings. We find a strong broadening of the histograms of counts of these level spacings directly at the transition point from MBL to the ergodic phase. The broadening signals reliably the transition point without relying on an averaging procedure. The fast convergence of the histograms even for relatively small systems allows monitoring the MBL dynamics with much less computational effort. Numerical results are presented for a chiral spin chain with a dynamical DzyaloshinskiiMoriya interaction, an established model to describe the spin excitations in a single-phase spin-driven multiferroic system. The multiferroic MBL phase is uncovered and it is shown how to steer it via electric fields.

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Prethermalization and Thermalization in Models with Weak Integrability Breaking

Cited by 210 publications

References 66 publications

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

Quantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions

Many-body localization phase in a spin-driven chiral multiferroic chain

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