arXiv 2403.044862024-03cond-mat.stat-mechquant-ph

二维自由费米子系统中的纠缠不对称性与量子Mpemba效应

Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems

Shion Yamashika, Filiberto Ares, Pasquale Calabrese

备注：: 18 pages, 8 figures. Minor clarifications, typos corrected. Final version published in Phys. Rev. B
发表信息：: Phys. Rev. B 110, 085126 (2024)
DOI：: 10.1103/PhysRevB.110.085126

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AI总结：

本研究将量子Mpemba效应的研究拓展至二维自由费米子系统，以纠缠不对称性度量对称性破缺，通过维度约化方法解析计算并分析横向尺寸对该效应的影响，确立了其发生条件，拓展了一维情形下的相关判据。

摘要：

量子Mpemba效应是一种反直觉的非平衡现象，即当初始态表现出更高程度的对称性破缺时，破缺对称性的动态恢复反而更快。该效应近期已在全局量子淬火框架下被理论发现并实验观测，但截至目前仅在一维系统中得到研究。本文聚焦二维自由费米子晶格，采用纠缠不对称性作为对称性破缺的度量。我们的研究从分析含最近邻跃迁和超导配对的系统基态开始，其中超导配对会显式破缺$U(1)$粒子数对称性。我们利用维度约化方法解析计算了周期条带的纠缠不对称性，该方法允许我们调整横向尺寸的大小，实现一维与二维之间的平滑过渡。进一步应用相同方法，我们研究了系统淬火到仅含最近邻跃迁的哈密顿量后纠缠不对称性的时间演化，该哈密顿量保持粒子数对称性，且该对称性会在稳态中恢复。我们发现，量子Mpemba效应受到系统横向维度尺寸的强烈影响，根据初始态的不同，既可能增强也可能削弱该现象。我们基于初始构型的性质确立了该效应发生的条件，拓展了一维情形下得到的判据。

英文摘要：

The quantum Mpemba effect is the counter-intuitive non-equilibrium phenomenon wherein the dynamic restoration of a broken symmetry occurs more rapidly when the initial state exhibits a higher degree of symmetry breaking. The effect has been recently discovered theoretically and observed experimentally in the framework of global quantum quenches, but so far it has only been investigated in one-dimensional systems. Here we focus on a two-dimensional free-fermion lattice employing the entanglement asymmetry as a measure of symmetry breaking. Our investigation begins with the ground state analysis of a system featuring nearest-neighbor hoppings and superconducting pairings, the latter breaking explicitly the $U(1)$ particle number symmetry. We compute analytically the entanglement asymmetry of a periodic strip using dimensional reduction, an approach that allows us to adjust the extent of the transverse size, achieving a smooth crossover between one and two dimensions. Further applying the same method, we study the time evolution of the entanglement asymmetry after a quench to a Hamiltonian with only nearest-neighbor hoppings, preserving the particle number symmetry which is restored in the stationary state. We find that the quantum Mpemba effect is strongly affected by the size of the system in the transverse dimension, with the potential to either enhance or spoil the phenomenon depending on the initial states. We establish the conditions for its occurrence based on the properties of the initial configurations, extending the criteria found in the one-dimensional case.

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