Entanglement gap in 1D long-range quantum spherical models

TL;DR

This paper studies how the entanglement gap scales with system size in a one-dimensional long-range quantum spherical model, revealing phase-dependent behavior and the influence of long-range interactions.

Contribution

It provides a detailed analysis of the finite-size scaling of the entanglement gap in the 1D long-range QSM, highlighting the effects of long-range interactions on quantum critical behavior.

Findings

Entanglement gap is finite in the paramagnetic phase and vanishes in the ferromagnetic phase.

The entanglement gap scales as $L^{-(1/2-eta/4)}$ with a coefficient depending on the long-range exponent.

No multiplicative logarithmic corrections are observed in the scaling, unlike in higher dimensions.

Abstract

We investigate the finite-size scaling of the entanglement gap in the one dimensional long-range quantum spherical model (QSM). We focus on the weak long-range QSM, for which the thermodynamic limit is well-defined. This model exhibits a continuous phase transition, separating a paramagnetic from a ferromagnet phase. The universality class of the transition depends on the long-range exponent $\alpha$. We show that in the thermodynamic limit the entanglement gap is finite in the paramagnetic phase, and it vanishes in the ferromagnetic phase. In the ferromagnetic phase the entanglement gap is understood in terms of standard magnetic correlation functions. The entanglement gap decays as $\delta\xi\simeq C_\alpha L^{-(1/2-\alpha/4)}$, where the constant $C_\alpha$ depends on the low-energy properties of the model. This reflects that the lower part of the dispersion is affected by the long range physics. Finally, multiplicative logarithmic corrections are absent in the scaling of the entanglement gap, in contrast with the higher-dimensional case.