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Quantum spin chains


Quantum chains emerge as fundamental and natural tools on three interconnected topics of physics and mathematical physics, namely: a) exactly integrable quantum chains, b) critical phenomena and the thermodynamic properties of general quantum chains, and c) nonequilibrium stochastic models, where the quantum chains govern the time fluctuations. 1n the topic a) the search of new exactly integrable quantum chains will be done by exploiting the Matrix Product Ansatz, introduced recently by our group. In topic b), by extensive use of finite-size scaling and the machinery coming from Conformal Invariance the phase diagrams and the critical exponents of several quantum chains are going to be calculated. Moreover, within this topic the entanglement properties of the wave functions associated to the quantum chains are going to be studied. A special attention will be given to the connexions between these properties and the fluctuations at the quantum transition points of the quantum chains. 1n topic c) it will be derived possible extensions of the raise-peel model. Such models, as well the last one, should exhibit self-organized criticality and are related to quantum chains. (AU)

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