Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results
Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results
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DOI：
10.1016/j.nuclphysb.2018.06.015
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发表时间：
2018-03
影响因子：
2.8
通讯作者：
L. Piroli;B. Pozsgay;Eric Vernier
中科院分区：
文献类型：
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作者：
L. Piroli;B. Pozsgay;Eric Vernier
我们解决了量子淬灭后相互作用的可积自旋链中洛施密特回波的计算。我们关注 XXZ 自旋 1/2 链的无质量状态，并为一类特殊的可积初始态提供动态自由能（每个位点的洛施密特回波）的精确结果。我们第一次能够通过跟踪洛施密特回波直至大实时时间，使用精确的方法观察和描述非分析点。动态自由能被计算为适当的量子传递矩阵的主导特征值，并且非解析性由该矩阵的能级交叉引起。我们的精确结果用“激发态”热力学 Bethe ansatz 方程表示，其解涉及非平凡的黎曼曲面。通过评估我们的公式，我们为 Néel 态的淬灭提供了明确的数值结果，并确定了前几个非解析点。
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.