Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model

TL;DR

This paper introduces a quantum spin/Majorana chain model exhibiting a tricritical Ising point, where supersymmetry emerges on the lattice and coexists with order-disorder phases, with exact solutions and phase transition analysis.

Contribution

It presents a lattice model with explicit supersymmetry, exact ground state solutions, and analysis of phase coexistence and transitions in a tricritical Ising context.

Findings

Supersymmetry manifests explicitly on the lattice.

Ground states show coexistence of ordered and disordered phases.

Chiral symmetry breaking leads to a phase transition with exact supersymmetry.

Abstract

We introduce and analyze a quantum spin/Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit, but manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.