Valdez Marc Andrew, Jaschke Daniel, Vargas David L, Carr Lincoln D
Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA.
Phys Rev Lett. 2017 Dec 1;119(22):225301. doi: 10.1103/PhysRevLett.119.225301. Epub 2017 Nov 29.
We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the complexity of electroencephalogram or functional magnetic resonance imaging measurements of the brain. Using matrix product state methods, we show that network density, clustering, disparity, and Pearson's correlation obtain the critical point for both quantum Ising and Bose-Hubbard models to a high degree of accuracy in finite-size scaling for three classes of quantum phase transitions, Z_{2}, mean field superfluid to Mott insulator, and a Berzinskii-Kosterlitz-Thouless crossover.
我们通过基于量子互信息作为邻接矩阵的复杂网络度量，对规则一维晶格上量子临界点附近量子态的涌现复杂性进行量化，这与量化脑电图或大脑功能磁共振成像测量的复杂性直接类似。使用矩阵乘积态方法，我们表明，对于三类量子相变，即Z₂、平均场超流体到莫特绝缘体以及贝津斯基 - 科斯特利茨 - Thouless 转变，网络密度、聚类、差异和皮尔逊相关性在有限尺寸标度下以高度准确性获得了量子伊辛模型和玻色 - 哈伯德模型的临界点。
