On quantum phase crossovers in finite systems
arXiv:quant-ph/0602098 · doi:10.1088/1742-5468/2006/11/P11005
Abstract
In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body Schrödinger operator. Bifurcations of the minima for the potential of the Schrödinger operator determine the crossover couplings. By considering the behaviour of particular ground-state correlation functions, these may be identified as quantum phase crossovers in the many-body integrable system with finite particle number. In this approach the existence of the quantum phase crossover is not dependent on the existence of a thermodynamic limit, rendering applications to finite systems feasible. We study two examples of bosonic Hamiltonians which admit second-order crossovers.
11 pages, 2 figures. Final version accepted for publication
References in corpus (18)
- Ground state overlap and quantum phase transitions
- Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
- Quantum Superposition States of Bose-Einstein Condensates
- Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
- Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
- Entanglement of two-mode Bose-Einstein condensates
- Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions
- Quantum effects on the dynamics of a two-mode atom-molecule Bose-Einstein condensate
- Evidence for the super Tonks-Girardeau gas
- Theory of coherent photoassociation of a Bose-Einstein condensate
- Instability and entanglement of the ground state of the Dicke model
- Quantum entanglement and fixed-point bifurcations
- Oscillatory decay of a two-component Bose-Einstein condensate
- Thermodynamic properties of a small superconducting grain
- Classical and quantum dynamics of a model for atomic-molecular Bose--Einstein condensates
- Quantifying ground state entanglement of the BCS model
- Quantum Critical Behavior of Two Coupled Bose-Einstein Condensates
- Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate
Cited by in corpus (6)
- Ground-state properties of the attractive one-dimensional Bose-Hubbard model
- Quantum phase transitions in an interacting atom-molecule boson model
- Emergent quantum phases in a heteronuclear molecular Bose--Einstein condensate model
- Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition
- Phase transitions with finite atom number in the Dicke Model
- Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics