Chain and ladder models with two-body interactions and analytical ground states

TL;DR

This paper introduces new spin-1/2 chain and ladder models with analytical ground states, exploring how their properties change with the geometry of spin placement on a cylinder, revealing critical and non-critical phases.

Contribution

It presents a family of two-body exchange interaction models with analytical ground states based on the Haldane-Shastry wavefunction, extending to chain and ladder geometries with tunable parameters.

Findings

Large ratio leads to decoupled critical chains with Haldane-Shastry-like properties.

Small ratio results in a product of singlets with exponential decay of correlations.

Intermediate ratios show distance-dependent critical and area law behaviors.

Abstract

We consider a family of spin-1/2 models with few-body, SU(2) invariant Hamiltonians and analytical ground states related to the 1D Haldane-Shastry wavefunction. The spins are placed on the surface of a cylinder, and the standard 1D Haldane-Shastry model is obtained by placing the spins with equal spacing in a circle around the cylinder. Here, we show that another interesting family of models with two-body exchange interactions is obtained if we instead place the spins along one or two lines parallel to the cylinder axis, giving rise to chain and ladder models, respectively. We can change the scale along the cylinder axis without changing the radius of the cylinder. This gives us a parameter that controls the ratio between the circumference of the cylinder and all other length scales in the system. We use Monte Carlo simulations and analytical investigations to study how this ratio affects the properties of the models. If the ratio is large, we find that the two legs of the ladder decouple into two chains that are in a critical phase with Haldane-Shastry-like properties. If the ratio is small, the wavefunction reduces to a product of singlets. In between, we find that the behavior of the correlations and the Renyi entropy depends on the distance considered. For small distances the behavior is critical, and for long distances the correlations decay exponentially and the entropy shows an area law behavior. The distance up to which there is critical behavior gets larger and larger as the ratio increases.