Quantum TAP equations

Details Quantum TAP equations Quantum TAP equations

2000-11-02

arxiv.org/abs/cond-mat/0011028v1

Phys. Rev. B64, 014206 (2001)

Physics

Condensed Matter

Disordered Systems and Neural Networks

29 pages, 4 fig

Scientific paper

10.1103/PhysRevB.64.014206

We derive Thouless-Anderson-Palmer (TAP) equations for quantum disordered systems. We apply them to the study of the paramagnetic and glassy phases in the quantum version of the spherical p spin-glass model. We generalize several useful quantities (complexity, threshold level, etc.) and various ideas (configurational entropy crisis, etc), that have been developed within the classical TAP approach, to quantum systems. The analysis of the quantum TAP equations allows us to show that the phase diagram (temperature-quantum parameter) of the p spin-glass model should be generic. In particular, we argue that a crossover from a second order thermodynamic transition close to the classical critical point to a first order thermodynamic transition close to the quantum critical point is to be expected in a large class of systems.

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