Universal nonequilibrium quantum dynamics in imaginary time
arXiv:1106.4078 · doi:10.1103/PhysRevB.84.224303
Abstract
We propose a method to study dynamical response of a quantum system by evolving it with an imaginary-time dependent Hamiltonian. The leading non-adiabatic response of the system driven to a quantum-critical point is universal and characterized by the same exponents in real and imaginary time. For a linear quench protocol, the fidelity susceptibility and the geometric tensor naturally emerge in the response functions. Beyond linear response, we extend the finite-size scaling theory of quantum phase transitions to non-equilibrium setups. This allows, e.g., for studies of quantum phase transitions in systems of fixed finite size by monitoring expectation values as a function of the quench velocity. Non-equilibrium imaginary-time dynamics is also amenable to quantum Monte Carlo (QMC) simulations, with a scheme that we introduce here and apply to quenches of the transverse-field Ising model to quantum-critical points in one and two dimensions. The QMC method is generic and can be applied to a wide range of models and non-equilibrium setups.
8 pages, 3 figures. Expanded, final published version
References in corpus (6)
- Thermalization and its mechanism for generic isolated quantum systems
- Universal adiabatic dynamics across a quantum critical point
- Quantum critical scaling of the geometric tensors
- Stochastic series expansion method for quantum Ising models with arbitrary interactions
- Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
- Slow Mass Transport and Statistical Evolution of An Atomic Gas Across the Superfluid-Mott Insulator Transition
Cited by in corpus (83)
- Geometry and non-adiabatic response in quantum and classical systems
- Quantum critical dynamics in a 5000-qubit programmable spin glass
- The Kibble-Zurek Problem: Universality and the Scaling Limit
- Classifying and measuring the geometry of the quantum ground state manifold
- Non-equilibrium dynamic critical scaling of the quantum Ising chain
- Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
- How to Measure the Quantum Geometry of Bloch Bands
- Dynamical Quantum Hall Effect in the Parameter Space
- On equilibration and coarsening in the quantum O(N) model at infinite
- Universal Rephasing Dynamics after a Quantum Quench via Sudden Coupling of Two Initially Independent Condensates
- Scaling and diabatic effects in quantum annealing with a D-Wave device
- Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
- Dynamic scaling at classical phase transitions approached through non-equilibrium quenching
- Nonequilibrium quantum criticality in open systems: The dissipation rate as an additional indispensable scaling variable
- Correlation functions in the prethermalized regime after a quantum quench of a spin-chain
- Kibble-Zurek Mechanism and Finite-Time Scaling
- Universal post-quench prethermalization at a quantum critical point
- Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
- Non-equilibrium dynamics of Bosonic Mott insulators in an electric field
- Kibble-Zurek scaling in the Yang-Lee edge singularity
- Half-integer quantized topological response in quasiperiodically driven quantum systems
- Crossover from the classical to the quantum Kibble-Zurek scaling
- Theory of Driven Nonequilibrium Critical Phenomena
- Quantum Quenches in Free Field Theory: Universal Scaling at Any Rate
- Velocity of excitations in ordered, disordered and critical antiferromagnets
- Universal post-quench coarsening and quantum aging at a quantum critical point
- Quasi-adiabatic quantum Monte Carlo algorithm for quantum evolution in imaginary time
- Full characterization of the quantum linear-zigzag transition in atomic chains
- Universal driven critical dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates
- Microscopic theory of non-adiabatic response in real and imaginary time
- Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet
- Universal short-time quantum critical dynamics in imaginary time
- Quantum annealing speedup over simulated annealing on random Ising chains
- Kibble-Zurek mechanism in the Ising Field Theory
- General Quantum Fidelity Susceptibilities for the J1-J2 Chain
- Degenerate Adiabatic Perturbation Theory: Foundations and Applications
- Dynamic scaling of topological ordering in classical systems
- Simulated quantum annealing of double-well and multi-well potentials
- Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region
- Ramp and periodic dynamics across non-Ising critical points
- Extracting non-Abelian quantum metric tensor and its related Chern numbers
- Kibble-Zurek mechanism in a one-dimensional incarnation of deconfined quantum critical point
- Kibble-Zurek mechanism beyond adiabaticity: Finite-time scaling with critical initial slip
- Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
- Universal short time quantum critical dynamics of finite size systems
- Generalized dynamic scaling for quantum critical relaxation in imaginary time
- Spin-models, dynamics and criticality with atoms in tilted optical superlattices
- Emergent topological excitations in a two-dimensional quantum spin system
- Scaling in driven dynamics starting in the vicinity of a quantum critical point
- Observation of Near-Critical Kibble-Zurek Scaling in Rydberg Atom Arrays
- Dynamic scaling in the 2D Ising spin glass with Gaussian couplings
- Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism
- Nonequilibrium critical dynamics in the quantum chiral clock model
- Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
- Measuring Berry curvature with quantum Monte Carlo
- Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems
- Quantum optimization within lattice gauge theory model on a quantum simulator
- Quantum adiabatic evolution with energy-degeneracy levels
- Tricritical Kibble-Zurek scaling in Rydberg atom ladders
- Dual dynamic scaling in deconfined quantum criticality
- From fidelity to entanglement of entropy of the one-dimensional transverse-field quantum compass model
- Criticalities of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum Ising model
- Dynamic trapping near a quantum critical point
- Imaginary-time Mpemba effect in quantum many-body systems
- Non-Hermitian quantum gases: a platform for imaginary time crystals
- Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field model
- Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals
- Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
- Adiabatic approximation for the imaginary-time Schroedinger equation and its application to simulated annealing
- Imaginary-field-driven phase transition for the D Ising antiferromagnet: A fidelity-susceptibility approach
- Short-imaginary-time quantum critical dynamics in the J-Q spin chain
- Critical behavior of the fidelity susceptibility for the d=2 transverse-field Ising model
- Nonequilibrium Critical Dynamics with Emergent Supersymmetry
- Hierarchical Theory of Quantum Adiabatic Evolution
- Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
- Kibble-Zurek mechanism in quantum link model
- Separation of the Kibble-Zurek Mechanism from Quantum Criticality
- Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
- Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
- Scaling corrections in driven critical dynamics: Application to a two-dimensional dimerized quantum Heisenberg model
- Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
- Large-scale portfolio optimization with variational neural annealing
- Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model