2005/12/28 by R. W. Cherng, Leonid Levitov, L. S. Levitov · 9 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physreva.73.043614
published as Phys. Rev. A 73, 043614 (2006) · 16 pgs, 7 fgs
arxiv created 2005/12/28 · openalex publication_date 2006/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 a 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 and 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 determinant 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 the formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.