Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems

Biroli, Giulio; Kollath, Corinna; Läuchli, Andreas M.

doi:10.1103/physrevlett.105.250401

Cited by 345 publications

(470 citation statements)

References 25 publications

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“…After this intermediate quasi-particle formation, the dynamics eventually crosses over to the thermalization regime, where weak quasi-particle scattering leads to a slow redistribution of energy and establishes detailed balance between the different modes. This causes asymptotic thermalization on long time scales compatible with the Eigenstate-Thermalization-Hypothesis [5,[39][40][41][42].…”

Section: Introductionmentioning

confidence: 97%

Prethermalization and thermalization of a quenched interacting Luttinger liquid

2016

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We study the relaxation dynamics of interacting, one-dimensional fermions with band curvature after a weak quench in the interaction parameter at zero temperature. Our model lies within the class of interacting Luttinger Liquids, where the harmonic Luttinger theory is extended by a weak integrability breaking phonon scattering term. In order to solve for the non-equilibrium time evolution, we use quantum kinetic equations exploiting the resonant but subleading character of the phonon interaction term. The interplay between phonon scattering and the quadratic Luttinger theory leads to the emergence of three distinct spatio-temporal regimes for the fermionic real-space correlation function. It features the crossover from a prequench to a prethermal state, finally evolving towards a thermal state on increasing length and time scales. The characteristic algebraically decaying real-space correlations in the prethermalized regime become modulated by an amplitude, which is decaying in time according to a stretched-exponential as an effect of the interactions. The asymptotic thermalization dynamics is governed by energy transport over large distances from the thermalized to the non-thermalized regions via macroscopic, dynamical slow modes. This is revealed in an algebraic decay of the system's effective temperature. The numerical value of the associated exponent agrees with the dynamical critical exponent of the Kardar-Parisi-Zhang universality class. We also discuss a criterion for the applicability of this theory away from the integrable limit of non-interacting fermions.

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Section: Introductionmentioning

confidence: 97%

Prethermalization and thermalization of a quenched interacting Luttinger liquid

2016

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“…The mechanism of thermalization has been conjectured and numerically tested for certain systems 19,20 to be analogous to the one proposed by Deutsch 37 and Srednicki 38 for systems with a classically chaotic counterpart. Nonetheless, it is worth pointing out that in some specific cases, like for gapped systems, the validity of this scenario has been questioned (the points raised include finite-size effects 23 and the importance of rare events 39 , which may drive the behavior of the long-time dynamics), and the problem is still under debate.…”

Section: Introductionmentioning

confidence: 99%

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

et al. 2010

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We study the dynamics of the quantum Ising chain following a zero-temperature quench of the transverse field strength. Focusing on the behavior of two-point spin correlation functions, we show that the correlators of the order parameter display an effective asymptotic thermal behavior, i.e., they decay exponentially to zero, with a phase coherence rate and a correlation length dictated by the equilibrium law with an effective temperature set by the energy of the initial state. On the contrary, the two-point correlation functions of the transverse magnetization or the density-of-kinks operator decay as a power-law and do not exhibit thermal behavior. We argue that the different behavior is linked to the locality of the corresponding operator with respect to the quasi-particles of the model: non-local operators, such as the order parameter, behave thermally, while local ones do not. We study which features of the two-point correlators are a consequence of the integrability of the model by analizing their robustness with respect to a sufficiently strong integrability-breaking term.

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“…For quenches to finite interaction strengths, the relaxation dynamics have been investigated using a range of techniques, including exact diagonalization within a truncated momentum-mode basis [61], quasiexact numerical simulations of lattice discretizations of the model [62,63], and nonperturbative approximations arXiv:1407.4998v3 [cond-mat.quant-gas] 14 Feb 2015 derived using functional-integral techniques [35][36][37][38]64]. A finite-size scaling analysis [65] of expectation values in energy eigenstates of the LL model indicated that the eigenstate thermalization hypothesis [66][67][68] holds for this model in the weak sense [69] only, implying the absence of thermalization following a quench. A recently proposed generalization of the thermodynamic Bethe ansatz (TBA) [70,71] was used in Ref.…”

Section: Introductionmentioning

confidence: 99%

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

et al. 2015

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We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.

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Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems

Cited by 345 publications

References 25 publications

Prethermalization and thermalization of a quenched interacting Luttinger liquid

Prethermalization and thermalization of a quenched interacting Luttinger liquid

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

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