Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
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DOI：
10.1103/physrevb.99.075123
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发表时间：
2018-12
影响因子：
3.7
通讯作者：
L. Hackl;L. Vidmar;M. Rigol;Eugenio Bianchi
中科院分区：
文献类型：
--
作者：
L. Hackl;L. Vidmar;M. Rigol;Eugenio Bianchi
我们最近展示了[物理学]。量子Ising链的所有能量本征态的平均二部纠缠熵表现出一个与子系统体积线性扩展的通用（对于平动不变的二次费米子模型）主导项。而在热力学极限下，第一次次级修正在临界场并不消失（它只取决于子系统的体积与系统的体积之间的比率f），否则就消失了。在这里，我们用解析法求边界，用数值法求平均值，证明在横向磁场中自旋为1/2的XY链也是如此。然后，我们收紧了通用体积律项系数的边界，这是f的凹函数。我们开发了一种系统的方法来计算上界和下界，并为四阶边界提供了显式的解析表达式。
We recently showed [Phys. Rev. Lett. 121, 220602 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.220602] that the average bipartite entanglement entropy of all energy eigenstates of the quantum Ising chain exhibits a universal (for translationally invariant quadratic fermionic models) leading term that scales linearly with the subsystem's volume, while in the thermodynamic limit the first subleading correction does not vanish at the critical field (it only depends on the ratio f between the volume of the subsystem and volume of the system) and vanishes otherwise. Here we show, analytically for bounds and numerically for averages, that the same remains true for the spin-1/2 XY chain in a transverse magnetic field. We then tighten the bounds for the coefficient of the universal volume-law term, which is a concave function of f. We develop a systematic approach to compute upper and lower bounds, and we provide explicit analytic expressions for up to the fourth-order bounds.