Method to identify parent Hamiltonians for trial states

TL;DR

This paper presents a versatile method for finding exact or approximate local parent Hamiltonians for complex quantum states, aiding the understanding and modeling of quantum many-body systems.

Contribution

It introduces a novel general approach to identify both exact and approximate parent Hamiltonians for trial quantum states, including symmetry considerations.

Findings

Successfully identifies exact parent Hamiltonians for quantum Hall and spin liquid states

Provides a systematic way to construct approximate parent Hamiltonians when exact solutions are unavailable

Applicable to a broad class of quantum many-body states

Abstract

We describe a general method to identify exact, local parent Hamiltonians for trial states like quantum Hall or spin liquid states, which we have used extensively during the past decade. It can be used to identify exact parent Hamiltonians, either directly or via the construction of simpler annihilation operators from which a parent Hamiltonian respecting all the required symmetries can be constructed. Most remarkably, however, the method provides approximate parent Hamiltonians whenever an exact solution is not available within the space of presumed interaction terms.