Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
复制标题
DOI：
10.1103/physreva.81.052324
复制
发表时间：
2010-05-01
影响因子：
2.9
通讯作者：
Scardicchio, A.
中科院分区：
文献类型：
--
作者：
De Pasquale, A.;Facchi, P.;Scardicchio, A.
研究了纯态量子系统的约简密度矩阵的施密特系数分布。应用统计力学的一般方法，引入一个虚拟温度和配分函数，并将问题转化为随机矩阵特征值的分布。我们研究了两种相变的出现，一种是在正温度下，与非常纠缠的状态相关，另一种是在负温度下，这表明在多体波函数中出现了重要的因数分解。我们还关注了亚稳态的存在（与二维量子引力有关），并研究了鞍点解的有限尺寸修正。
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated with very entangled states, and one at a negative temperature, signaling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to two-dimensional quantum gravity) and study the finite size corrections to the saddle point solution.