Exploring entanglement in finite-size quantum systems with degenerate ground state

TL;DR

This paper introduces a method to analyze quantum entanglement in finite-size spin systems with degenerate ground states, revealing new features of quantum correlations and connecting theoretical insights with experimental measurements.

Contribution

The authors develop a novel approach using random linear combinations of degenerate eigenstates to characterize quantum correlations in degenerate ground states.

Findings

Enhanced entanglement entropy in spin spiral phases

Correlation functions explain entanglement behavior

Quantum simulations accurately capture entanglement in noisy conditions

Abstract

We develop an approach for characterizing non-local quantum correlations in spin systems with exactly or nearly degenerate ground states. Starting with linearly independent degenerate eigenfunctions calculated with exact diagonalization we generate a finite set of their random linear combinations with Haar measure, which guarantees that these combinations are uniformly distributed in the space spanned by the initial eigenstates. Estimating the von Neumann entropy of the random wave functions helps to reveal previously unknown features of the quantum correlations in the phases with degeneracy of the ground state. For instance, spin spiral phase of the quantum magnet with Dzyaloshinskii-Moriya interaction is characterized by the enhancement of the entanglement entropy, which can be qualitatively explained by the changes in behaviour of two- and three-spin correlation functions. To establish the connection between our theoretical findings and real experiments we elaborate on the problem of estimating observables on the basis of the single-shot measurements of numerous degenerate eigenstates. By the example of solving a simple Ising model it is shown that digital quantum simulations performed with quantum computers can provide accurate description of the entanglement of the degenerate systems even in the presence of noise. We also discuss the ground state properties of degenerate fermionic and bosonic models, which can be useful for theoretical analysis of the experiments with ultracold atoms.