Entropy and Correlation Functions of a Driven Quantum Spin Chain

TL;DR

This paper provides an exact analysis of a driven quantum spin chain, revealing how entropy and correlations depend on the sweep rate through critical points, and identifying a phase transition in the nonequilibrium state.

Contribution

It introduces an exact solution for a driven quantum spin chain using a many-body Landau-Zener approach and Toeplitz determinants, uncovering a critical sweep rate for domain formation.

Findings

Entropy density depends on sweep rate

Correlation length exhibits abrupt change at critical sweep rate

Ordered domains form beyond a certain sweep rate

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.