Entropy and Correlation Functions of a Driven Quantum Spin Chain
Abstract
We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The resulting nonequilibrium state of the system, while being a pure quantum state, has local properties of a mixed state characterized by finite entropy density associated with Kibble-Zurek defects. The entropy, as well as the finite spin correlation length, are functions of the rate of sweep through the critical point. We analyze the anisotropic XY spin 1/2 model evolved with a full many-body evolution operator. With the help of Toeplitz determinants calculus, we obtain an exact form of correlation functions. The properties of the evolved system undergo an abrupt change at a certain critical sweep rate, signaling formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.
Cite
@article{arxiv.cond-mat/0512689,
title = {Entropy and Correlation Functions of a Driven Quantum Spin Chain},
author = {R. W. Cherng and L. S. Levitov},
journal= {arXiv preprint arXiv:cond-mat/0512689},
year = {2008}
}
Comments
16 pgs, 7 fgs