Abstract

We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time \bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})}t-∼τ2νz/(1+2νz) for when the system falls out of equilibrium and the associated freeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})}ξ‾∼τν/(1+2νz) show power-law scaling with respect to the quench rate 1/\tau1/τ, where the exponents depend on the correlation length exponent \nuν and the dynamical exponent zz associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.

Highlights

  • Nonequilibrium properties associated with quenches across a continuous phase transition are exhibited in a range of physical systems, from quantum magnets at the nanoscale to the cosmos itself

  • Universal properties of the phase transition have powerful implications for the nonequilibrium dynamics associated with the quench

  • One can even drive quantum phase transitions by varying the measurement strength of different Hamiltonian terms. This provides us an opportunity to consider the critical quench dynamics driven by quantum nondemolition measurement of the system energy, and to investigate its effect on universal scaling behaviors

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Summary

Introduction

Nonequilibrium properties associated with quenches across a continuous phase transition are exhibited in a range of physical systems, from quantum magnets at the nanoscale to the cosmos itself. Close to the critical point separating the two phases, the intrinsic relaxation time, equivalently, the correlation time diverges In this regime, no matter how slow the tuning rate for the quench, the system is driven faster than it can respond, and plunges out of equilibrium. One can even drive quantum phase transitions by varying the measurement strength of different Hamiltonian terms This provides us an opportunity to consider the critical quench dynamics driven by quantum nondemolition measurement of the system energy, and to investigate its effect on universal scaling behaviors. In the strong decoherence regime, we derive the critical quench scaling exponents for both length and time scales, and demonstrate how they differ from the standard Kibble-Zurek predictions.

Universal Scaling of Decoherent Critical Quench
Decoherent Quantum Dynamics
Decoherence Time and Excitation Energy
Kibble-Zurek Scaling under Decoherent Quench
Decoherent Quench through Topological Transitions
Model Hamiltonian and Band Topology
Quench Protocol and Density Matrix
Dynamics of Pseudo-Spin Vectors
Universal Scaling for Topological Transition
Numerical Demonstration of Temporal Scaling
Numerical Demonstration of Spatial Scaling

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