Unfrustrated Qudit Chains and their Ground States

TL;DR

This paper explores conditions for unfrustrated ground states in non-translationally invariant qudit chains and examines the entanglement complexity of these states using numerical MPS methods.

Contribution

It identifies criteria for unfrustrated ground states in qudit chains and assesses the limitations of MPS in approximating highly entangled ground states.

Findings

Unfrustrated conditions depend on specific local interactions.

Highly entangled ground states are difficult to approximate with MPS.

Numerical methods reveal the entanglement range in qudit chains.

Abstract

We investigate chains of 'd' dimensional quantum spins (qudits) on a line with generic nearest neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, i.e. when the ground states are also the common ground states of all the local terms in the Hamiltonians. The states of a quantum spin chain are naturally represented in the Matrix Product States (MPS) framework. Using imaginary time evolution in the MPS ansatz, we numerically investigate the range of parameters in which we expect the ground states to be highly entangled and find them hard to approximate using our MPS method.