Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model

The study of entanglement spectra is a powerful tool to detect or elucidate universal behaviour in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ, i.e., the lowest laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We...

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Autores principales: Wald, Sascha, Arias, Raúl Eduardo, Alba, Vincenzo
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2020
Materias:
Física
Ciencias Exactas
entanglement spectra
quantum spherical model
Schmidt gap
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/125540
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-125540
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Ciencias Exactas
entanglement spectra
quantum spherical model
Schmidt gap
spellingShingle Física
Ciencias Exactas
entanglement spectra
quantum spherical model
Schmidt gap
Wald, Sascha
Arias, Raúl Eduardo
Alba, Vincenzo
Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model
topic_facet Física
Ciencias Exactas
entanglement spectra
quantum spherical model
Schmidt gap
description The study of entanglement spectra is a powerful tool to detect or elucidate universal behaviour in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ, i.e., the lowest laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition, and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as π 2 / ln(L), with L the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap δξ ln(L) exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zeromode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a non-trivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.
format Articulo
Preprint
author Wald, Sascha
Arias, Raúl Eduardo
Alba, Vincenzo
author_facet Wald, Sascha
Arias, Raúl Eduardo
Alba, Vincenzo
author_sort Wald, Sascha
title Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model
title_short Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model
title_full Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model
title_fullStr Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model
title_full_unstemmed Closure of the entanglement gap at quantum criticality : The case of the Quantum Spherical Model
title_sort closure of the entanglement gap at quantum criticality : the case of the quantum spherical model
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/125540
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AT ariasrauleduardo closureoftheentanglementgapatquantumcriticalitythecaseofthequantumsphericalmodel
AT albavincenzo closureoftheentanglementgapatquantumcriticalitythecaseofthequantumsphericalmodel
bdutipo_str Repositorios
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