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Area-law-like systems with entangled states can preserve ergodicity
The European Physical Journal Special Topics ( IF 2.8 ) Pub Date : 2020-03-12 , DOI: 10.1140/epjst/e2020-900003-3
Andre M. C. Souza , Peter Rapčan , Constantino Tsallis

We study the ground entangled state of the one-dimensional spin-1/2 Ising ferromagnet at its transverse-field critical point. When this problem is expressed in terms of independent fermions, we show that the usual thermostatistical sums emerging within Fermi-Dirac statistics can, for an L-sized subsystem, be indistinctively taken up to L terms or up to lnL terms, providing a neat understanding of the origin of the logarithmic scaling of the entanglement entropy in the system. This is interpreted as a compact occupancy of the phase-space of the L-subsystem, hence standard Boltzmann-Gibbs thermodynamics quantities with an effective system size V ∝ lnL are appropriate and are explicitly calculated. The calculations are then to be done in a Hilbert space whose effective dimension is 2ln L instead of 2L. In this we can assume ergodicity. Our analysis suggests a scenario where the physical systems are essentially grouped into three classes, in terms of their phase-space occupancy, ergodicity and Lebesgue measure.

中文翻译:

具有纠缠态的类区域律系统可以保留遍历性

我们研究了一维自旋1/2 Ising铁磁体在其横向场临界点的基态纠缠态。当这个问题用独立的费米子表示时,我们证明对于L大小的子系统,费米-狄拉克统计中出现的通常的恒温统计总和可以不区分大小写地包含L个项或ln L个项,从而提供一个整齐的理解系统中纠缠熵的对数标度的起源。这被解释为L子系统的相空间的紧凑占据,因此有效系统尺寸为V ∝ ln L的标准Boltzmann-Gibbs热力学量是适当的,并经过明确计算。然后在有效尺寸为2 ln L而不是2 L的希尔伯特空间中进行计算。在这种情况下,我们可以假设遍历。我们的分析提出了一种场景,其中根据相空间占用率,遍历性和Lebesgue量度将物理系统基本分为三类。
更新日期:2020-03-12
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