Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions

TL;DR

This paper reconstructs approximate parent Hamiltonians for Jastrow-Gutzwiller wave functions, revealing their phases and guiding experimental realization of quantum spin liquids using entanglement-based methods.

Contribution

It introduces a systematic entanglement-guided approach to reconstruct parent Hamiltonians for Jastrow-Gutzwiller states, linking them to relativistic field theories.

Findings

Successfully reconstructed parent Hamiltonians for various phases.

Identified phase boundaries through correlation and entanglement analysis.

Provided insights for experimental Hamiltonian engineering.

Abstract

Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental simulation of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave-functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement content. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories - as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states.