Ground-state properties of a supersymmetric fermion chain

Details Ground-state properties of a supersymmetric fermion chain Ground-state properties of a supersymmetric fermion chain

2010-11-29

arxiv.org/abs/1011.6386v2

J.Stat.Mech.1102:P02014,2011

Physics

Condensed Matter

Statistical Mechanics

v2: added more information on scaling function, fixed typos

Scientific paper

10.1088/1742-5468/2011/02/P02014

We analyze the ground state of a strongly interacting fermion chain with a supersymmetry. We conjecture a number of exact results, such as a hidden duality between weak and strong couplings. By exploiting a scale free property of the perturbative expansions, we find exact expressions for the order parameters, yielding the critical exponents. We show that the ground state of this fermion chain and another model in the same universality class, the XYZ chain along a line of couplings, are both written in terms of the same polynomials. We demonstrate this explicitly for up to N = 24 sites, and provide consistency checks for large N. These polynomials satisfy a recursion relation related to the Painlev\'e VI differential equation, and using a scale-free property of these polynomials, we derive a simple and exact formula for their limit as N goes to infinity.

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