We address the computation of the Loschmidt echo in interacting integrable spin chains after a quantum quench. We focus on the massless regime of the XXZ spin-1/2 chain and present exact results for the dynamical free energy (Loschmidt echo per site) for a special class of integrable initial states. For the first time we are able to observe and describe points of non-analyticities using exact methods, by following the Loschmidt echo up to large real times. The dynamical free energy is computed as the leading eigenvalue of an appropriate Quantum Transfer Matrix, and the non-analyticities arise from the level crossings of this matrix. Our exact results are expressed in terms of “excited-state” thermodynamic Bethe ansatz equations, whose solutions involve non-trivial Riemann surfaces. By evaluating our formulas, we provide explicit numerical results for the quench from the Néel state, and we determine the first few non-analytic points. © 2018 The Author(s)

Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results / Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 933:August(2018), pp. 454-481. [10.1016/j.nuclphysb.2018.06.015]

Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results

Piroli, Lorenzo;
2018-01-01

Abstract

We address the computation of the Loschmidt echo in interacting integrable spin chains after a quantum quench. We focus on the massless regime of the XXZ spin-1/2 chain and present exact results for the dynamical free energy (Loschmidt echo per site) for a special class of integrable initial states. For the first time we are able to observe and describe points of non-analyticities using exact methods, by following the Loschmidt echo up to large real times. The dynamical free energy is computed as the leading eigenvalue of an appropriate Quantum Transfer Matrix, and the non-analyticities arise from the level crossings of this matrix. Our exact results are expressed in terms of “excited-state” thermodynamic Bethe ansatz equations, whose solutions involve non-trivial Riemann surfaces. By evaluating our formulas, we provide explicit numerical results for the quench from the Néel state, and we determine the first few non-analytic points. © 2018 The Author(s)
2018
933
August
454
481
10.1016/j.nuclphysb.2018.06.015
https://arxiv.org/abs/1803.04380
Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85918
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