Exact formalism for the quench dynamics of integrable models

Iyer, Deepak; Guan, Huijie; Andrei, Natan

doi:10.1103/physreva.87.053628

Cited by 75 publications

(55 citation statements)

References 51 publications

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“…44,45 Considering that the density decreases as the gas expands, it is conceivable that the dynamics for the expansion from ground states of the Bose-Hubbard model can be described by the Lieb-Liniger model at long times. A formal proof of this interpretation is left for future research.…”

Section: Bosonsmentioning

confidence: 99%

“…Note that similar questions have been addressed in the literature, mostly for integrable models. [44][45][46][47][48][49][50][51][52][53][54][55][56][57] The main goal of our study is to investigate three questions. First, we disentangle the effects of the trap opening from the interaction quench by studying the expansion dynamics from the ground state of the trapped gas.…”

Section: Introductionmentioning

confidence: 99%

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Sudden expansion of Mott insulators in one dimension

et al. 2013

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We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion; the asymptotic density dynamics is identical to that of initially localized, noninteracting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this nonequilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model; while being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the noninteracting limit. These results are compared to the setup of a recent experiment [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. In the latter case, the interaction quench breaks the universal dynamics in the asymptotic regime and the expansion depends on the interaction strength. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways; while the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.

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Section: Bosonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sudden expansion of Mott insulators in one dimension

et al. 2013

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“…In the special case V (x) = V 0 δ(x) the model becomes the integrable Lieb-Liniger model, 56 whose Bethe-ansatz solution can be used to study its time evolution after a sudden quench. [57][58][59][60][61][62][63][64] In the presence of a lattice a natural starting point would be the BoseHubbard model…”

Section: Relation To Bosonic Systemsmentioning

confidence: 99%

Time evolution during and after finite-time quantum quenches in Luttinger liquids

Chudziński

Schuricht

2016

Phys. Rev. B

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We consider finite-time quantum quenches in the interacting Tomonaga-Luttinger model, for example time-dependent changes of the nearest-neighbour interactions for spinless fermions. We use the exact solutions for specific protocols including the linear and cosine ramps (or, more generally, periodic pumping). We study the dynamics of the total and kinetic energy as well as the Green functions during as well as after the quench. For the latter we find that the light-cone picture remains applicable, however, the propagating front is delayed as compared to the sudden quench. We extract the universal behaviour of the Green functions and in particular provide analytic, nonperturbative results for the delay applicable to quenches of short to moderate duration but arbitrary time dependency.

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“…Other calculations make explicit use of the integrability of the system. These are based on various Bethe ansatz approaches, and include utilizing Fermi-Bose mapping [70,71] and strong coupling expansions of the coordinate Bethe ansatz wave function [298][299][300], combining the algebraic Bethe ansatz with other numerical methods [209][210][211], and using the Yudson contour-integral representation for infinite-length systems [301,302]. Recently, it was conjectured that the dynamics following an interaction strength quench are captured by a thermodynamic Bethe ansatz saddle point state and excitations around it -the so-called quench action approach [202, 204-206, 303, 304].…”

Section: Introductionmentioning

confidence: 99%

“…References [301,302] introduced a Betheansatz method for calculations of dynamical correlation functions for a few particles and in…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Zill¹

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This thesis is concerned with non-equilibrium phenomena in interacting quantum manybody systems. Specifically, we investigate the time-evolution and relaxation dynamics of Bose gases in a highly restricted geometry, which constrains the dynamics to one spatial dimension. This leads to a description of the system in terms of a simple model Hamiltonian which permits exact many-body quantum mechanical solutions due to its integrability.In the first part of this thesis, a computational method is developed to obtain experimentally relevant correlation functions in the framework of the coordinate Bethe ansatz.We employ this method to compute exact ground-state correlation functions of the LiebLiniger gas for up to seven particles covering the whole regime of repulsive interactions. We also investigate the dynamics of the system after an instantaneous change of the interaction strength. This quantum quench deposits large amounts of energy that cannot be dissipated due to the system being closed, and so the dynamics far from equilibrium are probed. We prepare the system in two different initial states, and quench to the same final interaction strength. The latter is determined in such a way that the added energy due to the quench is the same for both scenarios. Conventional statistical mechanics predicts the same relaxed state, but due to the integrability of the system all considered correlation functions of the relaxed states differ from each other and also from the thermal ones.We then investigate the dynamics and relaxed state for a quench from zero to repulsive interactions in more detail, focussing on the mechanism of relaxation and the involved time-scales. We find that local correlation functions relax on time-scales determined by the interaction strength, in contrast to non-local correlation functions, whose relaxation time-scale is proportional to the system size.Next, we employ the same methodology to study the one-dimensional Bose gas with attractive interactions. In this case many-body bound states are permissible solutions of the Lieb-Liniger model. We compare exact ground-state correlation functions of up to seven particles to their corresponding mean-field solution. The latter displays a quantum phase transition at a critical interaction strength, marking the transition from a uniformdensity state to a localized bright soliton. Our exact results agree remarkably well with the corresponding mean-field solution past the critical point. We also investigate the dynamics following an interaction strength quench, starting again from the non-interacting ground state. Bound states strongly influence correlation functions for all post-quench interaction strengths, and local correlation functions are largely increased compared to their initial value.In the last part of this thesis, we investigate the behavior of the one-dimensional Bose gas under periodic driving of the interaction strength. To this end, we extend the coordinate Bethe-ansatz formalism by employing Floquet theory to obtain solutions for the...

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Exact formalism for the quench dynamics of integrable models

Cited by 75 publications

References 51 publications

Sudden expansion of Mott insulators in one dimension

Sudden expansion of Mott insulators in one dimension

Time evolution during and after finite-time quantum quenches in Luttinger liquids

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

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