Matrix Product States: Symmetries and Two-Body Hamiltonians

TL;DR

This paper investigates the symmetry properties of translationally invariant matrix product states (MPS) and extends fundamental theorems in many-body physics, providing insights into their invariance and ground state characterization.

Contribution

It establishes conditions for MPS invariance under local transformations and extends the Lieb-Schultz-Mattis theorem within the MPS framework.

Findings

Characterization of MPS symmetry groups

Extension of Lieb-Schultz-Mattis theorem for MPS

Identification of SU(2)-invariant two-body Hamiltonians with MPS ground states

Abstract

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.