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.

arXiv commentv2: added more information on scaling function, fixed typos

References in corpus (22)

• Spin chains and combinatorics
• Lattice Models with N=2 Supersymmetry
• Scattering and Thermodynamics of Fractionally-Charged Supersymmetric Solitons
• Lattice fermion models with supersymmetry
• Combinatorial nature of ground state vector of O(1) loop model
• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• Spin chains and combinatorics: twisted boundary conditions
• Temperley-Lieb Stochastic Processes
• Symmetry Classes of Alternating Sign Matrices
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Eight-vertex model and non-stationary Lame equation
• Non-local space-time supersymmetry on the lattice
• The XXZ spin chain at $\Delta =-1/2$: Bethe roots, symmetric functions and determinants
• 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
• Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model
• Exact and simple results for the XYZ and strongly interacting fermion chains
• A possible combinatorial point for XYZ-spin chain
• Exact conjectured expressions for correlations in the dense O$(1)$ loop model on cylinders
• Proof of the Razumov-Stroganov conjecture
• Picard solution of Painlevé VI and related tau-functions

Cited by in corpus (13)

• A supersymmetric multicritical point in a model of lattice fermions
• Exact ground states of a staggered supersymmetric model for lattice fermions
• Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
• Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality
• Special polynomials related to the supersymmetric eight-vertex model: A summary
• Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D
• Special polynomials related to the supersymmetric eight-vertex model. I. Behaviour at cusps
• Order and supersymmetry at high filling zero energy states on the triangular lattice
• Special polynomials related to the supersymmetric eight-vertex model. III. Painlevé VI equation
• On the ground states of the $M_{\ell }$ models
• A staggered fermion chain with supersymmetry on open intervals
• A multiplet analysis of spectra in the presence of broken symmetries
• Local symmetries and extensive ground-state degeneracy of a 1D supersymmetric fermionic chain