Half Landau-Zener ramp to a quantum phase transition in a dissipative single spin sodel

Abstract

We study the dynamics of a single spin coupled to a bosonic bath at zero temperature driven by a ramp of the bias field. A single spin coupled to a bosonic sub-Ohmic bath exhibits a quantum phase transition at a certain strength of spin-boson coupling. When the bias field is ramped from a large value to zero at this critical coupling strength, the system initialized at the ground state ends up with a finite magnetization due to the critical slowing down near the transition. On the basis of the pulse-impulse approximation, we derive a scaling law between the residual magnetization and the ramp speed. The obtained scaling relation is examined using a numerical simulation based on the tensor network. The data are in favor of the scaling law to hold. We discuss the demonstration of our theoretical results by means of quantum simulation using the quantum annealer.

arXiv comment15 pages, 5 figures

References in corpus (31)

• Nonequilibrium dynamics of closed interacting quantum systems
• Dynamics of a Quantum Phase Transition
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Universal adiabatic dynamics across a quantum critical point
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Observation of the Kibble-Zurek scaling law for defect formation in ion crystals
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Quantum critical dynamics in a 5000-qubit programmable spin glass
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Defect production in non-linear quench across a quantum critical point
• Exact results for quench dynamics and defect production in a two-dimensional model
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• The quantum phase transition in the sub-ohmic spin-boson model: Quantum Monte-Carlo study with a continuous imaginary time cluster algorithm
• Optimal non-linear passage through a quantum critical point
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
• Gauging a quantum heat bath with dissipative Landau-Zener transitions
• Quenching along a gapless line: A different exponent for defect density
• Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space
• Observation of macroscopic Landau-Zener transitions in a superconducting device
• Thermodynamics of the dissipative two-state system: a Bethe Ansatz study
• Quantitative verification of the Kibble-Zurek mechanism in quantum non-equilibrium dynamics
• Anomalous non-ergodic scaling in adiabatic multicritical quantum quenches
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
• Numerical Renormalization Group for the sub-ohmic spin-boson model: A conspiracy of errors
• Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Quantum annealing of pure and random Ising chains coupled to a bosonic environment
• Classical simulation and theory of quantum annealing in a thermal environment
• Universal scaling in quenches across a discontinuity critical point