Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom

Abstract

Classical stationary points of an analytic Hamiltonian induce singularities of the density of quantum energy levels and their flow with a control parameter in the system's infinite-size limit. We show that for a system with $f$ degrees of freedom, a non-degenerate stationary point with index $r$ causes a discontinuity (for $r$ even) or divergence ($r$ odd) of the $(f-1)$ th derivative of both density and flow of the spectrum. An increase of flatness for a degenerate stationary point shifts the singularity to lower derivatives. The findings are verified in an $f=3$ toy model.

References in corpus (7)

• Excited state quantum phase transitions in many-body systems
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Phase transitions and configuration space topology
• Impact of Quantum Phase Transitions on Excited Level Dynamics
• Phase transitions induced by saddle points of vanishing curvature
• First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries
• Nonanalyticities of the entropy induced by saddle points of the potential energy landscape

Cited by in corpus (38)

• Dynamical quantum phase transitions: a review
• Excited-state quantum phase transitions
• Collective performance of a finite-time quantum Otto cycle
• Quantum quench dynamics in Dicke superradiance models
• From thermal to excited-state quantum phase transitions ---the Dicke model
• Excited-state quantum phase transitions in systems with two degrees of freedom: III. Interacting boson systems
• Excited-state quantum phase transitions in spinor Bose-Einstein condensates
• Spectral kissing and its dynamical consequences in the squeeze-driven Kerr oscillator
• Constant of motion identifying excited-state quantum phases
• Quantum phases and entanglement properties of an extended Dicke model
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Adiabatic invariants for the regular region of the Dicke model
• Excited State Quantum Phase Transitions Studied from a Non-Hermitian Perspective
• Phase transitions of the anisotropic Dicke model
• Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
• Exceptional points near first- and second-order quantum phase transitions
• Regularity and chaos in cavity QED
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects
• Theory of robust quantum many-body scars in long-range interacting systems
• Monodromy in Dicke superradiance
• Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model
• Quasiclassical approach to quantum quench dynamics in the presence of an excited-state quantum phase transition
• Phase transitions of the Dicke model: a unified perspective
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Heat capacity for systems with excited-state quantum phase transitions
• Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
• Complex density of continuum states in resonant quantum tunneling
• Critical phenomena in light-matter systems with collective matter interactions
• Continuum analogues of excited-state quantum phase transitions
• Single-shot determination of quantum phases via continuous measurements
• Phase transitions, symmetries, and tunneling in Kerr parametric oscillators
• Excited-state quantum phase transitions in constrained systems
• Van Hove Singularities and Excited-State Quantum Phase Transitions in Graphene-like Microwave Billiards
• Exceptional Spectral Phase in a Dissipative Collective Spin Model
• Excited-State Quantum Phase Transitions in Bosonic Lattice Systems
• Chaos, thermalization and breakdown of quantum-classical correspondence in a collective many-body system
• Energy cat states induced by a parity-breaking excited-state quantum phase transition
• Stabilization of product states and excited-state quantum phase transitions in a coupled qubit-field system