Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians

TL;DR

This paper establishes a theorem linking infinite bond-dimension matrix product states with frustration-free Hamiltonians, specifically applied to non-Abelian Moore-Read fractional quantum Hall states, broadening the understanding of their ground state representations.

Contribution

The paper introduces a new theorem connecting infinite bond-dimension MPS with frustration-free parent Hamiltonians, applicable beyond conformal field theory contexts.

Findings

Demonstrated the theorem with Moore-Read FQH states

Showed applicability beyond conformal-field-theory-derived MPSs

Provided insights into infinite-range frustration-free Hamiltonians

Abstract

The study of frustration-free Hamiltonians and their relation to finite bond-dimension matrix product states (MPS) has a long tradition. However, fractional quantum Hall (FQH) states do not quite fit into this theme since the known MPS representations of their ground states have infinite bond dimensions, which considerably obscures the relations between such MPS representations and the existence of frustration-free parent Hamiltonians. This is related to the fact that the latter necessarily are of infinite range in the orbital basis. Here, we present a theorem tailored to establishing the existence of frustration-free parent Hamiltonians in such a context. We explicitly demonstrate the utility of this theorem in the context of non-Abelian Moore-Read FQH states but argue the applicability of this theorem to transcend considerably beyond the realm of conformal-field-theory-derived MPSs or quasi-one-dimensional Hilbert spaces.