Universal short-time quantum critical dynamics in imaginary time

Abstract

We propose a scaling theory for the universal imaginary-time quantum critical dynamics for both short times and long times. We discover that there exists a universal critical initial slip related to a small initial order parameter $M_0$. In this stage, the order parameter $M$ increases with the imaginary time $\tau$ as $M\propto M_0{\tau }^{\theta }$ with a universal initial slip exponent $\theta$. For the one-dimensional transverse-field Ising model, we estimate $\theta$ to be $0.373$, which is markedly distinct from its classical counterpart. Apart from the local order parameter, we also show that the entanglement entropy exhibits universal behavior in the short-time region. As the critical exponents in the early stage and in equilibrium are identical, we apply the short-time dynamics method to determine quantum critical properties. The method is generally applicable in both the Landau-Ginzburg-Wilson paradigm and topological phase transitions.

15 pages, 17 figures

References in corpus (22)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Universal adiabatic dynamics across a quantum critical point
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Scaling of entanglement support for Matrix Product States
• Effective thermal dynamics following a quantum quench in a spin chain
• Entanglement growth in quench dynamics with variable range interactions
• Defect production in non-linear quench across a quantum critical point
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Quantum quenches in a spinor condensate
• Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Luttinger liquid universality in the time evolution after an interaction quench
• Universal Rephasing Dynamics after a Quantum Quench via Sudden Coupling of Two Initially Independent Condensates
• Quantum Phase Diagram and Excitations for the One-Dimensional S=1 Heisenberg Antiferromagnet with Single-Ion Anisotropy
• On $c=1$ critical phases in anisotropic spin-1 chains
• Fidelity approach to Gaussian transitions
• Nonequilibrium critical relaxations of the order parameter and energy in the two-dimensional ferromagnetic Potts model
• Finite-time scaling of dynamic quantum criticality

Cited by in corpus (25)

• Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in $d$ spatial dimensions
• Scaling of the entanglement spectrum in driving critical dynamics
• Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region
• Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
• Kibble-Zurek mechanism beyond adiabaticity: Finite-time scaling with critical initial slip
• Universal short time quantum critical dynamics of finite size systems
• Generalized dynamic scaling for quantum critical relaxation in imaginary time
• Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Dual dynamic scaling in deconfined quantum criticality
• Universal imaginary-time critical dynamics on a quantum computer
• Fermion-induced Dynamical Critical Point
• Imaginary-time Mpemba effect in quantum many-body systems
• Short-time Monte Carlo simulation of the majority-vote model on cubic lattices
• Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• Short-imaginary-time quantum critical dynamics in the J-Q${}_3$ spin chain
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Imaginary-time relaxation quantum critical dynamics in two-dimensional dimerized Heisenberg model
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Imaginary-time Quantum Relaxation Critical Dynamics with Semi-ordered Initial States
• Short-time critical dynamics in the classical cubic dimer model
• Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states