Excited-state quantum phase transitions in a two-fluid Lipkin model

Abstract

Background: Composed systems have became of great interest in the framework of the ground state quantum phase transitions (QPTs) and many of their properties have been studied in detail. However, in these systems the study of the so called excited-state quantum phase transitions (ESQPTs) have not received so much attention. Purpose: A quantum analysis of the ESQPTs in the two-fluid Lipkin model is presented in this work. The study is performed through the Hamiltonian diagonalization for selected values of the control parameters in order to cover the most interesting regions of the system phase diagram. [Method:] A Hamiltonian that resembles the consistent-Q Hamiltonian of the interacting boson model (IBM) is diagonalized for selected values of the parameters and properties such as the density of states, the Peres lattices, the nearest-neighbor spacing distribution, and the participation ratio are analyzed. Results: An overview of the spectrum of the two-fluid Lipkin model for selected positions in the phase diagram has been obtained. The location of the excited-state quantum phase transition can be easily singled out with the Peres lattice, with the nearest-neighbor spacing distribution, with Poincaré sections or with the participation ratio. Conclusions: This study completes the analysis of QPTs for the two-fluid Lipkin model, extending the previous study to excited states. The ESQPT signatures in composed systems behave in the same way as in single ones, although the evidences of their presence can be sometimes blurred. The Peres lattice turns out to be a convenient tool to look into the position of the ESQPT and to define the concept of phase in the excited states realm.

References in corpus (16)

• Chaos and the Quantum Phase Transition in the Dicke Model
• Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
• Entanglement and the Phase Transition in Single Mode Superradiance
• Excited state quantum phase transitions in many-body systems
• Quantum phase transitions in the interacting boson model
• Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
• Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
• Structure of eigenstates and quench dynamics at an excited state quantum phase transition
• Phase structure of a two-fluid bosonic system
• Classical chaos in atom-field systems
• Phase structure of the two-fluid proton-neutron system
• Phase Diagram of the Proton-Neutron Interacting Boson Model
• Critical point symmetries in boson-fermion systems. The case of shape transition in odd nuclei in a multi-orbit model
• Phase transitions in the Interacting Boson Fermion Model: the gamma-unstable case
• Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential
• Phase diagram of the two-fluid Lipkin model: a butterfly catastrophe

Cited by in corpus (13)

• Excited-state quantum phase transitions
• Dynamical and excited-state quantum phase transitions in collective systems
• Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates
• Constant of motion identifying excited-state quantum phases
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects
• Phase transitions of the Dicke model: a unified perspective
• Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules
• Characterizing the excited-state quantum phase transition via the dynamical and statistical properties of the diagonal entropy
• Phase diagram of an extended Agassi model
• Critical phenomena in light-matter systems with collective matter interactions
• Excited-state quantum phase transitions in constrained systems
• Spectral fluctuations in the interacting boson model
• Energy cat states induced by a parity-breaking excited-state quantum phase transition