Prosen T
Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Oct;60(4 Pt A):3949-68. doi: 10.1103/physreve.60.3949.
We study a generic but simple nonintegrable quantum many-body system of locally interacting particles, namely, a kicked-parameter (t,V) model of spinless fermions on a one-dimensional lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2 spins). The statistical properties of the dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in the thermodynamic limit are considered as the kick parameters (which control the degree of nonintegrability) are varied. We find and demonstrate ballistic transport and nonergodic, nonmixing dynamics (implying infinite conductivity at all temperatures) in the integrable regime of zero or very small kick parameters, and more generally and importantly, also in the nonintegrable regime of intermediate values of kicked parameters, whereas only for sufficiently large kick parameters do we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness D) which controls the phase transition from nonmixing and nonergodic dynamics (ordered phase, D>0) to mixing and ergodic dynamics (disordered phase, D=0) in the thermodynamic limit. Furthermore, we find exponential decay of time correlation functions in the regime of mixing dynamics. The results are obtained consistently within three different numerical and analytical approaches: (i) time evolution of a finite system and direct computation of time correlation functions, (ii) full diagonalization of finite systems and statistical analysis of stationary data, and (iii) algebraic construction of quantum invariants of motion of an infinite system, in particular the time-averaged observables.
我们研究了一个由局部相互作用粒子构成的一般但简单的非可积量子多体系统，即一维晶格上无自旋费米子的踢参数（t，V）模型（等同于1/2自旋的踢海森堡XX-Z链）。当踢参数（控制非可积程度）变化时，考虑动力学的统计性质（量子遍历性和量子混合）以及热力学极限下量子输运的性质。我们发现在踢参数为零或非常小的可积区域中存在弹道输运以及非遍历、非混合动力学（意味着在所有温度下电导率无穷大），更普遍且重要的是，在踢参数中间值的非可积区域中也存在这种情况，而只有当踢参数足够大时，我们才恢复量子遍历性和混合，这意味着正常（扩散）输运。我们提出一个序参量（电荷刚度D），它在热力学极限下控制从非混合和非遍历动力学（有序相，D>0）到混合和遍历动力学（无序相，D = 0）的相变。此外，我们发现在混合动力学区域中时间关联函数呈指数衰减。这些结果是通过三种不同的数值和解析方法一致获得的：（i）有限系统的时间演化和时间关联函数的直接计算，（ii）有限系统的完全对角化和平稳数据的统计分析，以及（iii）无限系统量子运动不变量的代数构造，特别是时间平均可观测量。
