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

TL;DR

This paper investigates the non-equilibrium dynamics of a single spin coupled to a bosonic bath during a Landau-Zener type ramp, revealing a scaling law for residual magnetization near a quantum phase transition, supported by tensor network simulations.

Contribution

It introduces a new scaling law relating residual magnetization to ramp speed in a dissipative quantum spin system at a phase transition.

Findings

Residual magnetization scales with ramp speed near the critical point.

Tensor network simulations support the proposed scaling law.

Potential implementation in quantum annealers for experimental validation.

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.