Microscopic theory of non-adiabatic response in real and imaginary time

Abstract

We present a general approach to describe slowly driven quantum systems both in real and imaginary time. We highlight many similarities, qualitative and quantitative, between real and imaginary time evolution. We discuss how the metric tensor and the Berry curvature can be extracted from both real and imaginary time simulations as a response of physical observables. For quenches ending at or near the quantum critical point, we show the utility of the scaling theory for detecting the location of the quantum critical point by comparing sweeps at different velocities. We briefly discuss the universal relaxation to equilibrium of systems after a quench. We finally review recent developments of quantum Monte Carlo methods for studying imaginary-time evolution. We illustrate our findings with explicit calculations using the transverse field Ising model in one dimension.

22 pages, 10 figures, revised version, contribution to the special issue of J. Phys. Condensed Matter: "Condensed matter analogues of cosmology", edited by T. Kibble and Ajit Srivastava

References in corpus (18)

• Quantum Quench in the Transverse Field Ising Chain
• Quantum critical scaling of the geometric tensors
• Universal adiabatic dynamics across a quantum critical point
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Non-equilibrium dynamic critical scaling of the quantum Ising chain
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Dynamics in the Ising field theory after a quantum quench
• Quantum relaxation after a quench in systems with boundaries
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Universal nonequilibrium quantum dynamics in imaginary time
• Dynamical Quantum Hall Effect in the Parameter Space
• Universal Rephasing Dynamics after a Quantum Quench via Sudden Coupling of Two Initially Independent Condensates
• Quantum response of dephasing open systems
• Non-equilibrium dynamics of Bosonic Mott insulators in an electric field
• Oscillating fidelity susceptibility near a quantum multicritical point

Cited by in corpus (26)

• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Geometric Speed Limit of Accessible Many-Body State Preparation
• Scaling and diabatic effects in quantum annealing with a D-Wave device
• Dynamic scaling at classical phase transitions approached through non-equilibrium quenching
• Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
• Dynamics of a quantum phase transition in the Aubry-André-Harper model with $p$-wave superconductivity
• Universal short-time quantum critical dynamics in imaginary time
• Direct measurement of quantum Fisher information
• Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Universal short time quantum critical dynamics of finite size systems
• Generalized dynamic scaling for quantum critical relaxation in imaginary time
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Real-time dynamics of open quantum spin systems driven by dissipative processes
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements
• Real-time simulation of non-equilibrium transport of magnetization in large open quantum spin systems driven by dissipation
• Dual dynamic scaling in deconfined quantum criticality
• Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
• Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
• Short-imaginary-time quantum critical dynamics in the J-Q${}_3$ spin chain
• Nonequilibrium Critical Dynamics with Emergent Supersymmetry
• Real-Time Evolution of Strongly Coupled Fermions driven by Dissipation
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Scaling corrections in driven critical dynamics: Application to a two-dimensional dimerized quantum Heisenberg model