Ground-state properties of a supersymmetric fermion chain

Abstract

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 Painlevé 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.

v2: added more information on scaling function, fixed typos

References in corpus (5)

• The eight-vertex model and Painleve VI
• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
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Cited by in corpus (3)

• Special polynomials related to the supersymmetric eight-vertex model. III. Painlevé VI equation
• A staggered fermion chain with supersymmetry on open intervals
• Local symmetries and extensive ground-state degeneracy of a 1D supersymmetric fermionic chain