Entanglement gap in 1D long-range quantum spherical models

• Autores: Wald, Sascha; Arias, Raúl Eduardo; Alba, Vincenzo
• Año de publicación: 2023
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Entanglement; Spherical Model; Long range interactions; Phase transition
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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 α. 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 half-system 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 and L is the system size. 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.
Fil: Wald, Sascha. Coventry University; Reino Unido
Fil: Arias, Raúl Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Alba, Vincenzo. Università degli Studi di Pisa; Italia