Quantum Spin Chains

Abstract

Quantum chains appearing in three interelated topics of physics and mathematical physics are going to be studied, namely: a) exactly integrable quantum chains, b) physics of critical phenomena and the thermodynamical properties of general quantum chains, and c) quantum chains associated to thc description of the time fluctuations of classical reaction-diffusion processes. In the topic a) the search of new exactly integrable quantum chains will be done by a direct application of the coordinate Bethe ansatz method. Beyond this research, within this topic, it will be also calculated the wave function and correlation functions of already known exactly integrable quantum chains. In topic b) by exploring finite-size scaling and the machinery coming from Conformal lnvariance the phase diagrams and the critical exponents of several quantum chains are going to be calculated. In topic c) through numerical simulations the anomalous behavior of several stochastic dynamical processes are going to be studied. In some cases, whenever the associated quantum chains are exactly integrable, the dynamical critical exponent will bc evaluated by solving directly the associated Bethe ansatz equations. (AU)