Kibble-Zurek scaling due to environment temperature quench in the transverse field Ising model

Abstract

The Kibble-Zurek mechanism describes defect production due to non-adiabatic passage through a critical point. Here we study its variant from ramping the environment temperature to a critical point. We find that the defect density scales as ${\tau }^{-d\nu }$ or ${\tau }^{-d/z}$ for thermal or quantum critical points, respectively, in terms of the usual critical exponents and $1/\tau$ the speed of the drive. Both scalings describe reduced defect density compared to conventional Kibble-Zurek mechanism, which stems from the enhanced relaxation due to bath-system interaction. Ramping to the quantum critical point is investigated by studying the Lindblad equation for the transverse field Ising chain in the presence of thermalizing bath, with couplings to environment obeying detailed balance, confirming the predicted scaling. The von-Neumann or the system-bath entanglement entropy follows the same scaling. Our results are generalized to a large class of dissipative systems with power-law energy dependent bath spectral densities as well.

13 pages, 6 figures

References in corpus (17)

• Quantum trajectories and open many-body quantum systems
• Universal adiabatic dynamics across a quantum critical point
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Defect production in non-linear quench across a quantum critical point
• Optimal non-linear passage through a quantum critical point
• Adiabatic dynamics in open quantum critical many-body systems
• Coherent and dissipative dynamics at quantum phase transitions
• Exploring the Kibble-Zurek mechanism with homogeneous Bose gases
• Kibble-Zurek scaling of the irreversible entropy production
• Interference of Quantum Trajectories
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems
• How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate
• Classical simulation and theory of quantum annealing in a thermal environment
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Microscopic modelling of general time-dependent quantum Markov processes
• Universal cooling dynamics toward a quantum critical point

Cited by in corpus (8)

• Kibble-Zurek scaling immune to anti-Kibble-Zurek behavior in driven open systems at the limit of loss difference
• Apparent delay of the Kibble-Zurek mechanism in quenched open systems
• Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields
• Universal Quench Dynamics of an Open Quantum System
• Kibble-Zurek dynamics in the anisotropic Ising model of the Si(001) surface
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Long-range Kitaev chain in a thermal bath: Analytic techniques for time-dependent systems and environments
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath