Loschmidt Echo in interacting spin systems

D. BENDERSKY; P. R. ZANGARA; H. M. PASTAWSKI

San Carlos de Bariloche, Río Negro

Congreso; 98° Reunión Nacional de Física de la Asociación Física Argentina; 2013

Asociación de Física Argentina

Nuclear Magnetic Resonance experiments with interacting spin arrays [1] have shown intrinsic instabilities in the quantum dynamics. Inspired by these experiments, the Loschmidt echo (LE) [2] arises as the natural quantifier of the fragility in the dynamics of an interacting many-body system. The LE is defined in terms of the refocusing produced by a slightly imperfect time reversal procedure applied to a deterministic evolution. This imperfection stands for the presence of uncontrolled degrees of freedom, which play the role of an environment. In this work, we present a series of numerical simulations, in which we evaluated local and global observables, defined in the form of the LE. The role of the non-reversed degrees of freedom is given by non-secular terms of the dipole-dipole interaction, a situation that is consistent with experimental realizations. We present a quantitative study of time scales for the LE decay. The strategy used for the calculation of the observables involves the use of superposition states [3] and an implementation of the Trotter Suzuki algorithm in massively parallelized general purpose Graphical Processing Units [4].