Dynamical Quantum Phase Transitions: A Geometric Picture

Abstract

The Loschmidt echo (LE) is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model (FC-TFIM) as an example, we show that this indeed is not the case, and that a simple semiclassical approximation to systems well described by mean-field theory (MFT) is in fact in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the post-quench dynamics provided in the supplemental material visualize this new point of view.

Accepted version. 7 pages with 4 Figures in main file. 3 pages including 2 Figures of supplemental material. 3 videos linked in the references of the main file

References in corpus (51)

• Many-Body Physics with Ultracold Gases
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Effective quantum spin systems with ion traps
• Observation of entanglement propagation in a quantum many-body system
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Dynamical quantum phase transitions: a review
• Phase space representation of quantum dynamics
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Interaction Quench in the Hubbard model
• Quantum enhanced measurements without entanglement
• Observation of a dynamical topological phase transition
• Entanglement and Tunable Spin-Spin Couplings Between Trapped Ions Using Multiple Transverse Modes
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Dynamical Topological Order Parameters far from Equilibrium
• Dynamical quantum phase transitions: scaling and universality
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Topological classification of dynamical phase transitions
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Mixed-state fidelity and quantum criticality at finite temperature
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Dynamical phase diagram of spin chains with long-range interactions
• Probing real-space and time resolved correlation functions with many-body Ramsey interferometry
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Quantum quenches, dynamical transitions and off-equilibrium quantum criticality
• Dynamical transitions and quantum quenches in mean-field models
• Mixed state dynamical quantum phase transition and emergent topology
• Dynamical Topological Quantum Phase Transitions for Mixed States
• Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics
• Observation of scaling in the dynamics of a strongly quenched quantum gas
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
• Quantum quenches as classical critical films
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Exact infinite-time statistics of the Loschmidt echo for a quantum quench
• On equilibration and coarsening in the quantum O(N) model at infinite $N$
• Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
• Aging and coarsening in isolated quantum systems after a quench: exact results for the quantum $O(N)$ model with $N\to \infty$
• Exploring dynamical phase transitions and prethermalization with quantum noise of excitations
• Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
• Dynamical crossovers in prethermal critical states
• Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
• Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
• The fate of dynamical phase transitions at finite temperatures and in open systems
• Quasiparticles in quantum spin chains with long-range interactions
• Quantum metrology with non-equilibrium steady states of quantum spin chains
• Prethermalization from a low-density Holstein-Primakoff expansion

Cited by in corpus (81)

• Long-range interacting quantum systems
• Quench dynamics and zero-energy modes: the case of the Creutz model
• 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
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• Out-of-equilibrium phase diagram of long-range superconductors
• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Floquet dynamical quantum phase transitions under synchronized periodic driving
• Quasiparticle origin of dynamical quantum phase transitions
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Local measures of dynamical quantum phase transitions
• Finite-component dynamical quantum phase transitions
• Detecting dynamical quantum phase transition via out-of-time-order correlations in a solid-state quantum simulator
• Dynamical and excited-state quantum phase transitions in collective systems
• Dynamical quantum phase transitions and non-Markovian dynamics
• Finite temperature dynamical quantum phase transition in a non-Hermitian system
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems
• Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates
• Dynamical topological quantum phase transitions in nonintegrable models
• Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing
• Dynamical phase transitions in dissipative quantum dynamics with quantum optical realization
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Many-body dynamical phase transition in quasi-periodic potential
• Topological dynamical quantum phase transition in a quantum skyrmion phase
• Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
• Nonanalyticity of circuit complexity across topological phase transitions
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Non-equilibrium criticality in quench dynamics of infinite-range spin models
• Dynamical quantum phase transitions in spin-$S$ $\mathrm{U}(1)$ quantum link models
• Unconventional critical exponents at dynamical quantum phase transitions in a random Ising chain
• Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing
• Dynamical quantum phase transition in a bosonic system with long-range interactions
• Work statistics and symmetry breaking in an excited state quantum phase transition
• Dynamical Quantum Phase Transitions in Extended Toric-Code Models
• Hybrid infinite time-evolving block decimation algorithm for long-range multi-dimensional quantum many-body systems
• Dynamical quantum phase transitions in Weyl semimetals
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Dynamical quantum phase transitions following a noisy quench
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids
• Quantum spin fluctuations in dynamical quantum phase transitions
• Crossover from fast to slow dynamics in quantum Ising chains with long range interactions
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Wehrl entropy production rate across a dynamical quantum phase transition
• Metamorphic dynamical quantum phase transition in double-quench processes at finite temperatures
• Dynamical quantum phase transitions on cross-stitch flat band networks
• Functional field integral approach to quantum work
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Dynamical phase transition in the 1D-transverse field Ising chain characterized by the transverse magnetization spectral function
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• Fermion-induced Dynamical Critical Point
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter
• Exotic signature of dynamical quantum phase transition in the time evolution of engineered initial state
• Continuous time crystal from a spontaneous many-body Floquet state
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Quantum coherence assisted dynamical phase transition
• Relaxation time as a control parameter for exploring dynamical phase diagrams
• Dynamical Phase Transitions in Open Quantum Walks
• Phase space theory for open quantum systems with local and collective dissipative processes
• Dynamical quantum phase transitions from random matrix theory
• Simultaneous symmetry breaking in spontaneous Floquet states: temporal Floquet-Nambu-Goldstone modes, Floquet thermodynamics, and the time operator
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• Out of equilibrium mean field dynamics in the transverse field Ising model
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Speedup of thermodynamic entropy production via quantum dynamical criticality
• Dynamical dimerization phase in Jaynes-Cummings lattices
• The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• Dynamical Phase Transitions, Caustics, and Quantum Dark Bands
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
• Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses
• Time Crystal from Self-Amplification of Spontaneous Analog Hawking Radiation
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Floquet dynamical quantum phase transitions in periodically flux-quenched systems