Quantum spin chains

Abstract

Introduction of the Heisenberg model to describe the dynamics of localized spins, quantum chains become useful tools for the appropriate understanding of the fluctuations in several physical systems. The quantum chains emerge in three interconnected topics of physics and mathematical physics, that we split in: a) Exactly integrable quantum chains - where they describe the simple evolution operators we can formulate for several interacting many body system; b) Critical phenomena and the thermodynamic properties of general quantum chains - where they usually describe the quantum fluctuations at the temperature T = 0 or/and thermal ones at T ≠ 0, and c) Stochastic models - where they describe the time fluctuations in asymptotic equlibrium and non equilibrium states. On this FAPESP project, in continuation with the last ones, we are going to study quantum chains along the above three topics. In topic a) we are going to search for new exactly integrable chains by using the Matrix Product ansatz introduced in our last FAPESP project. In topic b) we are going to study some quantum chains whose phase diagram are unknown. We are going to exploit the consequences of the conformal invariance in the finite-size properties of the eigenspectrum of the quantum chain. In topic c) we are going to introduce new models, as well to generalize several known models in order to understand which are the necessary basic ingredients that produce a space-time conformal invariance in a non-equilibrium asymptotic state. Due to the recent common interests in Information Theory and Condensed Matter Physics we intend to study, along topics a), b) and c), the shared information among extensive parts of the systems. (AU)