Exact results on quantum many-body systems in one dimension

Abstract

In the course of the completion of this thesis we have addressed several problems concerning quantum many-body systems and one-dimensional lattice models. Before getting into details, let me briefly outline some of them together with our main contributions, and sketch out some central concepts we shall develop later. To begin with, we have studied the entanglement properties of the ground state of several one-dimensional systems (see Refs. [P1]–[P4]), and investigated several exact spectral properties of lattice models in one dimension, obtaining an analytic expression for the partition function of certain models with long-range interactions (see [P4] and [P5] for a detailed description of the models involved). We have completely characterized the spectrum of the so-called long range t-J model for the first time and, in particular, rigorously proved a conjecture proposed by Saiga and Kuramoto in the nineties for the spin 1/2 case...Durante el desarrollo de esta tesis, hemos abordado diferentes problemas relacionados con sistemas cuánticos de muchos cuerpos y cadenas de espines o modelos discretos en una dimensión. Intentaremos resumir brevemente las palabras e ideas clave asociadas a cada uno de ellos así como nuestras contribuciones a la resolución de los mismos.En primer lugar, hemos estudiado el entrelazamiento del estado fundamental de varios sistemas unidimensionales (ver [P1]–[P4]) e investigado distintas propiedades exactas relativas al espectro de cadenas de espines, obteniendo una expresión analítica para la función de partición de ciertos modelos con interacciones de largo alcance (ver [P4] y [P5] para una descripción detallada de los modelos tratados)...