Spectral gaps of AKLT Hamiltonians using Tensor Network methods

TL;DR

This paper employs tensor network methods to accurately compute the spectral gap of AKLT Hamiltonians in one and two dimensions, providing evidence for a finite gap in the thermodynamic limit and demonstrating the method's broader applicability.

Contribution

It introduces tensor network techniques to determine the spectral gap of AKLT models directly in the thermodynamic limit, including perturbed cases and beyond the original model.

Findings

Finite spectral gap in 1D and 2D AKLT models

Tensor Network methods effectively analyze quantum critical points

Results extend to models with rotational symmetry

Abstract

Using exact diagonalization and tensor network techniques we compute the gap for the AKLT Hamiltonian in 1D and 2D spatial dimensions. Tensor Network methods are used to extract physical properties directly in the thermodynamic limit, and we support these results using finite-size scalings from exact diagonalization. Studying the AKLT Hamiltonian perturbed by an external field, we show how to obtain an accurate value of the gap of the original AKLT Hamiltonian from the field value at which the ground state verifies e_0<0, which is a quantum critical point. With the Tensor Network Renormalization Group methods we provide evidence of a finite gap in the thermodynamic limit for the AKLT models in the 1D chain and 2D hexagonal and square lattices. This method can be applied generally to Hamiltonians with rotational symmetry, and we also show results beyond the AKLT model.