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arXiv:1911.02456 · Physical Review Letters

Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems

Yuuya Chiba, Kenichi Asano, Akira Shimizu

Published Mar 20, 2020• 5 citations
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Abstract

We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k→0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.

DOI
10.1103/physrevlett.124.110609

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We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k→0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.
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We provide numerical evidence that after a local quench in an isolated infinite quantum spin chain, the quantum state locally relaxes to the ground state of the post-quenched Hamiltonian, i.e. dissipates. This is a consequence of the unitary quantum dynamics. A mechanism similar to the eigenstate thermalization hypothesis is shown to be responsible for the dissipation observed. We also demonstrate that integrability obstructs dissipation. The numerical simulations are done directly in the thermodynamic limit with a time-evolution algorithm based on matrix product states. The area law of entanglement entropy is observed to hold after the local quench. As a result, the simulations can be performed for long times with small bond dimensions. Various local quenches on the Ising chain and the three-state Potts chain are studied.
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Eigenstate thermalization is widely accepted as the mechanism behind thermalization in generic isolated quantum systems. Using the example of a single magnetic defect embedded in the integrable spin-1/2 XXZ chain, we show that locally perturbing an integrable system can give rise to eigenstate thermalization. Unique to such setups is the fact that thermodynamic and transport properties of the unperturbed integrable chain emerge in properties of the eigenstates of the perturbed (nonintegrable) one. Specifically, we show that the diagonal matrix elements of observables in the perturbed eigenstates follow the microcanonical predictions for the integrable model, and that the ballistic character of spin transport in the integrable model is manifest in the behavior of the off-diagonal matrix elements of the current operator in the perturbed eigenstates.
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The static limit of the Kubo susceptibility describes the adiabatic response of an isolated quantum system, in which energy-level occupations remain unchanged, and generally differs from the isothermal susceptibility, where these occupations readjust to thermal equilibrium. In this work, we introduce a single dynamical framework in which the adiabatic and isothermal responses arise naturally as two distinct limiting regimes. This can be done by considering explicitly an open system version of the Kubo approach in which the dissipation is governed by a typical thermalization rate of the system. By exchanging the order of the static limit and of the vanishing thermalization rate limit, the protocol yields either the adiabatic or isothermal response. This protocol has a solid physical motivation in terms of the thermalization dynamics and is valid for generic systems. We apply it to the case of the magnetic response of the electron gas and reproduce the expected results.