Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates

Abstract

We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite-range interactions, both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a nonzero value of the dynamical order parameter characterizing DPTs-I, and precludes the main mechanism giving rise to nonanalyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the incompatibility of the main mechanism for DPTs-II with the presence of this additional conserved charge. Our results are numerically illustrated in the fully-connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions. Finally, we discuss the applicability of our theory to systems with finite-range interactions, where the phenomenology of excited-state quantum phase transitions is absent. We illustrate our findings by means of numerical calculations with experimentally relevant initial states.

arXiv comment4+ pages, 4 figures. To appear in Physical Review Letters

References in corpus (73)

• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• 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
• Dynamical quantum phase transitions: a review
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• 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
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Exploring dynamical phase transitions with cold atoms in an optical cavity
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Dynamical phase diagram of spin chains with long-range interactions
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Thermodynamics of quantum systems with multiple conserved quantities
• Excited-State Quantum Phase Transitions in Dicke Superradiance Models
• Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model
• On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
• Excited-state quantum phase transitions
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• 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
• 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
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Entanglement view of dynamical quantum phase transitions
• Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
• Quasi-localized excitations induced by long-range interactions in translationally-invariant quantum 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
• Dynamical quantum phase transitions: a brief survey
• Decoherence as a signature of an excited state quantum phase transition
• Excited-state quantum phase transition in the Rabi model
• 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
• Quasiparticle origin of dynamical quantum phase transitions
• 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
• Eigenstate Thermalization in Systems with Spontaneously Broken Symmetry
• Finite-component dynamical quantum phase transitions
• Dynamical and excited-state quantum phase transitions in collective systems
• Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model
• Excited-state quantum phase transitions in spinor Bose-Einstein condensates
• Finite-temperature critical behavior of long-range quantum Ising models
• Constant of motion identifying excited-state quantum phases
• Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Signature of nonequilibrium quantum phase transition in the long time average of Loschmidt echo
• 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
• Quasiclassical approach to quantum quench dynamics in the presence of an excited-state quantum phase transition
• Dynamics of the order-parameter statistics in the long-range Ising model
• Chaos in a deformed Dicke model

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• Noncommuting conserved charges in quantum thermodynamics and beyond
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• 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
• Quantum information scrambling in adiabatically-driven critical systems
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Superradiant Quantum Phase Transition in Open Systems: System-Bath Interaction at the Critical Point
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses
• Chaos, thermalization and breakdown of quantum-classical correspondence in a collective many-body system