Dynamical and excited-state quantum phase transitions in collective systems

Abstract

We study dynamical phase transitions (DPTs) in quantum many-body systems with infinite-range interaction, and present a theory connecting the two kinds of known DPTs (sometimes referred to as DPTs-I and DPTs-II) with the concept of excited-state quantum phase transition (ESQPT), traditionally found in collective models. We show that DPTs-I appear as a manifestation of symmetry restoration after a quench from the broken-symmetry phase, the limits between these two phases being demarcated precisely by an ESQPT. We describe the order parameters of DPTs-I with a generalization of the standard microcanonical ensemble incorporating the information of an additional conserved charge identifying the corresponding phase. We also show that DPTs-I are linked to a mechanism of information erasure brought about by the ESQPT, and quantify this information loss with the statistical ensemble that we propose. Finally, we show analytically that DPTs-II are forbidden in these systems for quenches leading a broken-symmetry initial state to the same broken-symmetry phase, on one side of the ESQPT, and we provide a formulation of DPTs-II depending on the side of the ESQPT where the quench ends. We analyze the connections between various indicators of DPTs-II. Our results are numerically illustrated in the infinite-range transverse-field Ising model and are applicable to a large class of collective quantum systems satisfying a set of conditions.

arXiv commentSome comments added, published in Phys. Rev. B; see also arXiv:2205.03443

References in corpus (71)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• The approach to thermal equilibrium in quantized chaotic systems
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Exploring dynamical phase transitions with cold atoms in an optical cavity
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Observation of Lee-Yang zeros
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Dynamical phase diagram of spin chains with long-range interactions
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Thermodynamics of quantum systems with multiple conserved quantities
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Excited-State Quantum Phase Transitions in Dicke Superradiance Models
• Quantum quenches, dynamical transitions and off-equilibrium quantum criticality
• Dynamical transitions and quantum quenches in mean-field models
• Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Observation of a Transition Between Dynamical Phases in a Quantum Degenerate Fermi Gas
• Dynamical Quantum Phase Transitions: A Geometric Picture
• Quantum quench influenced by an excited-state phase transition
• Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
• Quench dynamics and zero-energy modes: the case of the Creutz model
• Entanglement view of dynamical quantum phase transitions
• Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• Structure of eigenstates and quench dynamics at an excited state quantum phase transition
• Floquet dynamical phase transition and entanglement spectrum
• Decoherence as a signature of an excited state quantum phase transition
• Excited-state quantum phase transition in the Rabi model
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking
• Excited-state phase transition leading to symmetry-breaking steady states in the Dicke model
• Floquet dynamical quantum phase transitions under synchronized periodic driving
• Quantum quench dynamics in Dicke superradiance models
• Dissipative Floquet Dynamical Quantum Phase Transition
• Noncommuting conserved quantities in quantum many-body thermalization
• Entropy, chaos and excited-state quantum phase transitions in the Dicke model
• Finite-component dynamical quantum phase transitions
• Excited-state quantum phase transitions in spinor Bose-Einstein condensates
• Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model
• Constant of motion identifying excited-state quantum phases
• Non-thermal quantum phase transitions
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential
• Excited-state quantum phase transitions in a two-fluid Lipkin model
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Simulation of XXZ Spin Models using Sideband Transitions in Trapped Bosonic Gases
• Chaos in a deformed Dicke model

Cited by in corpus (30)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Noncommuting conserved charges in quantum thermodynamics and beyond
• Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates
• Engineering Floquet Dynamical Quantum Phase Transition
• Phase space geometry and optimal state preparation in quantum metrology with collective spins
• Anatomy of Dynamical Quantum Phase Transitions
• Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Quantum spin fluctuations in dynamical quantum phase transitions
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Measurement-induced multipartite-entanglement regimes in collective spin systems
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Constants of motion characterizing continuous symmetry-broken phases
• Quantum coherence assisted dynamical phase transition
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Dynamical quantum phase transitions from random matrix theory
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Speedup of thermodynamic entropy production via quantum dynamical criticality
• Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model
• Multifractality and excited-state quantum phase transition in ferromagnetic spin-$1$ Bose-Einstein condensates
• Dynamical Phase Transitions, Caustics, and Quantum Dark Bands
• Quantum information scrambling in adiabatically-driven critical systems
• Asymmetry and dynamical criticality
• Chaos, thermalization and breakdown of quantum-classical correspondence in a collective many-body system
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses