Brown Winton G, Santos Lea F, Starling David J, Viola Lorenza
Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 1):021106. doi: 10.1103/PhysRevE.77.021106. Epub 2008 Feb 7.
We investigate disordered one- and two-dimensional Heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many-body and quantum-information perspectives. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implication of the basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin- and fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.
我们从统计多体和量子信息两个角度研究了无序的一维和二维海森堡自旋晶格从可积性到量子混沌的转变。特别强调在存在非平凡对称性的情况下，定量探索本征向量统计、离域化和纠缠之间的相互作用。讨论了态离域化指标（如主成分数量）对基的依赖性的影响，并提出了一种相对离域化的度量，以便在存在无序的情况下稳健地表征混沌的开始。通过使用一族自旋和费米子纯度度量，在广泛的参数范围内研究了标准多体纠缠和广义纠缠，并研究了它们对离域化和能谱统计的依赖性。发现了纠缠、离域化和可积性之间的独特关联，这可能是两体随机系综描述的系统所共有的，并且可能指向一种新的量子混沌诊断工具。还建立了限制在全希尔伯特空间适当子空间内的随机纯态典型纠缠的解析估计，并与随机矩阵理论预测进行了比较。
