Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems
Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems
复制标题
非临界量子系统的统计力学系综的等价性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Cramer
中科院分区：
文献类型：
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作者：
F. Brandão;M. Cramer
本文考虑d维晶格上N个自旋的短程量子哈密顿量的正则系综和微正则系综是否局部等价的问题。对于任何温度下的系统有一个有限的相关长度，我们证明了正则和微正则状态是近似相等的区域包含多达O（N^（1/（d+1）的自旋。这个证明依赖于量子晶格系统的贝里-埃辛定理的一个变体和量子信息理论的思想。
We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of N spins arranged on a d-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to O(N^(1/(d+1))) spins. The proof rests on a variant of the Berry-Esseen theorem for quantum lattice systems and ideas from quantum information theory.