Phase diagram of an extended Agassi model

TL;DR

This paper explores the phase diagram of an extended Agassi model, revealing complex phase coexistence and degeneracies, and compares approximate solutions with exact results to understand quantum phase transitions.

Contribution

The study extends the Agassi model, providing a detailed phase diagram with multiple phase coexistences and degeneracies, and compares Hartree-Fock-Bogoliubov results with exact solutions.

Findings

Multiple phases coexist in broad regions of the parameter space.

Degeneracy lines and points with four and five phases.

Rich variety of quantum phase transitions identified.

Abstract

Background: The Agassi model is an extension of the Lipkin-Meshkov-Glick model that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960's by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases. Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.