Ground state many-body quantum entanglement of frustrated transverse field models on square lattice

TL;DR

This paper investigates the ground state quantum entanglement in frustrated transverse field models on a square lattice, revealing how entanglement varies with coupling strength and frustration, and highlighting differences due to degeneracy.

Contribution

It provides a detailed analysis of multipartite entanglement in two models, emphasizing the impact of frustration and degeneracy on ground state entanglement.

Findings

Maximum frustration leads to a peak in concurrence.

Entanglement behavior varies with degeneracy and frustration levels.

Differences in entanglement between models are linked to ground state degeneracy.

Abstract

We study the ground state (GS) many-body quantum entanglement of two different transverse field models on a quasi-2D square lattice relevant to a Hydrogen-bonded crystal, i.e, squaric acid. We measure the genuine multipartite qubit-entanglement ($C_{\text{GME}}(\psi)$) of the ground state of very generic models with all the possible cases of exchange couplings considered under defect free and one lattice site defect conditions. Our results show that creation, decay of multipartite entanglement occur for different combinations of coupling strength. When frustration is maximum the system exhibits a peak in concurrence after a gradual increase from disentangled state at zero field followed by an asymptotic decay at large fields. In contrast, for a marginally frustrated (degenerate) case though the concurrence shows a peak, the entanglement is non-zero and large at zero fields. Our results discuss the sensitivity of the qubit-entanglement with underlying GS of varying degree of degeneracy. We conclude that despite of their similarities in ground state properties, yet we see a difference in the degree of entanglement between the two models. We conjecture this result could be due to the difference in the amount of degeneracy and the quantum ground states of both Hamiltonians that could dictate the results even in the thermodynamic limit.