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 manybody generalization of the LandauZener 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 KibbleZurek 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 manybody 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.
 Publication:

Physical Review A
 Pub Date:
 April 2006
 DOI:
 10.1103/PhysRevA.73.043614
 arXiv:
 arXiv:condmat/0512689
 Bibcode:
 2006PhRvA..73d3614C
 Keywords:

 03.75.Ss;
 74.20.z;
 32.80.Pj;
 Degenerate Fermi gases;
 Theories and models of superconducting state;
 Optical cooling of atoms;
 trapping;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 16 pgs, 7 fgs