Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains

TL;DR

This paper investigates the unusual scaling behaviors of quantum entropies in long-range Heisenberg chains using quantum Monte Carlo simulations, revealing non-trivial features beyond traditional models and applicable to various quantum critical systems.

Contribution

It provides a systematic finite-size scaling analysis of entanglement and participation entropies in long-range Heisenberg chains, uncovering novel logarithmic scaling behaviors dependent on the decay exponent.

Findings

Distinctive entropy scaling behaviors identified across different regimes

Quantum entropies reveal information comparable to traditional order parameters

Results applicable to quantum criticality in 1D and 2D systems

Abstract

In this work, building on state-of-the-art quantum Monte Carlo simulations, we perform systematic finite-size scaling of both entanglement and participation entropies for long-range Heisenberg chain with unfrustrated power-law decaying interactions. We find distinctive scaling behaviors for both quantum entropies in the various regimes explored by tuning the decay exponent $\alpha$, thus capturing non-trivial features through logarithmic terms, beyond the case of linear Nambu-Goldstone modes. Our systematic analysis reveals that the quantum entanglement information, hidden in the scaling of the two studied entropies, can be obtained to the same level of order parameters and other usual finite-size observables of quantum many-body lattice models. The analysis and results obtained here can readily apply to more quantum criticalities in 1D and 2D systems.