Exact and simple results for the XYZ and strongly interacting fermion chains

Abstract

We conjecture exact and simple formulas for physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects.

References in corpus (2)

• The eight-vertex model and Painleve VI
• Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQ

Cited by in corpus (18)

• A supersymmetric multicritical point in a model of lattice fermions
• Spin chains with dynamical lattice supersymmetry
• Exact ground states of a staggered supersymmetric model for lattice fermions
• The eight-vertex model and lattice supersymmetry
• Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality
• Ground-state properties of a supersymmetric fermion chain
• Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D
• Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-1/2$
• Lattice Supersymmetry in the Open XXZ Model: An Algebraic Bethe Ansatz Analysis
• M${}_k$ models: the field theory connection
• On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
• A staggered fermion chain with supersymmetry on open intervals
• On the ground states of the $M_{\ell }$ models
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Bethe ansatz solvability and supersymmetry of the $M_2$ model of single fermions and pairs
• On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
• A multiplet analysis of spectra in the presence of broken symmetries
• Implicit Divided Differences, Little Schröder Numbers, and Catalan Numbers