Entanglement gap in 1D long-range quantum spherical models

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.

35 pages, 4 appendices, 7+3 figures. Minor modifications. Added one figure. Similar to published version

References in corpus (20)

• Entanglement spectrum in one-dimensional systems
• Entanglement entropy for the long range Ising chain
• Entanglement entropy in fermionic Laughlin states
• Fractional Laplacian in Bounded Domains
• Entanglement Entropy in the O(N) model
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Negativity spectrum of one-dimensional conformal field theories
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• An order parameter for impurity systems at quantum criticality
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Symmetry-resolved entanglement in a long-range free-fermion chain
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Operator content of real-space entanglement spectra at conformal critical points
• Negativity Spectrum in the Random Singlet Phase
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Quantum spherical model with competing interactions
• Phase Diagram Detection via Gaussian Fitting of Number Probability Distribution
• Quantum dynamics far from equilibrium: a case study in the spherical model

Cited by in corpus (1)

• Entanglement in the Quantum Spherical Model -- a Review