Local Hamiltonians for one-dimensional critical models

TL;DR

This paper explores local one-dimensional lattice models of fermions and bosons related to Laughlin states, showing they approximate the exact models with long-range interactions, and discusses potential experimental realizations.

Contribution

It introduces local Hamiltonians that closely replicate the ground and excited states of long-range models related to conformal field theory and Laughlin states.

Findings

Ground states are similar between local and exact models.

High overlap of low-energy excited states.

Local models approximate long-range interactions effectively.

Abstract

Conformal field theory has turned out to be a powerful tool to derive interesting lattice models with analytical ground states. Here, we investigate a class of critical, one-dimensional lattice models of fermions and hardcore bosons related to the Laughlin states. The Hamiltonians of the exact models involve interactions over long distances that are difficult to realize experimentally. This motivates us to study the properties of models with the same type of interactions, but now only between nearest and possibly next-nearest neighbor sites. Based on computations of wavefunction overlaps, entanglement entropies, and two-site correlation functions for systems of up to 32 sites, we find that the ground state is close to the ground state of the exact model. There is also a high overlap per site between the lowest excited states for the local and the exact models, although the energies of the low-lying excited states are modified to some extent for the system sizes considered. We also briefly discuss possibilities for realizing the local models in ultracold atoms in optical lattices.