Volume Changing Symmetries by Matrix Product Operators

TL;DR

This paper introduces a class of volume-changing symmetries in spin chain models, constructed via generalized Matrix Product Operators, which persist beyond integrability and include known supersymmetries.

Contribution

It demonstrates the existence of volume-changing symmetries in various spin chains using a new tensor network approach, extending beyond the supersymmetric XXZ model.

Findings

Volume-changing symmetries exist in multiple spin chain models.

These symmetries can be represented by generalized Matrix Product Operators.

Symmetries persist under non-integrable perturbations.

Abstract

We consider spin chain models with exotic symmetries that change the length of the spin chain. It is known that the XXZ Heisenberg spin chain at the supersymmetric point $\Delta=-1/2$ possesses such a symmetry: it is given by the supersymmetry generators, which change the length of the chain by one unit. We show that volume changing symmetries exist also in other spin chain models, and that they can be constructed using a special tensor network, which is a simple generalization of a Matrix Product Operator. As examples we consider the folded XXZ model and its perturbations, and also a new hopping model that is defined on constrained Hilbert spaces. We show that the volume changing symmetries are not related to integrability: the symmetries can survive even non-integrable perturbations. We also show that the known supersymmetry generator of the XXZ chain with $\Delta=-1/2$ can also be expressed as a generalized Matrix Product Operator.