Exact Results for Quench Dynamics and Defect Production in a Two-Dimensional Model

2007/10/31 by K. Sengupta, Diptiman Sen, Shreyoshi Mondal · 14 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.100.077204

published as Phys. Rev. Lett. 100, 077204 (2008) · 4 pages including 4 figures; generalized the discussion of the defect density scaling to the case of arbitrary critical exponents, and added some references; this version will appear in Physical Review Letters

arxiv created 2008/01/15 · openalex publication_date 2008/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a d-dimensional model in which a quench with a rate tau(-1) takes the system across a (d-m)-dimensional critical surface, the defect density scales as n approximately 1/tau(mnu/(znu+1)), where nu and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d = 2 and m = nu = z = 1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model that can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.

Citations

• Quench dynamics across quantum critical points
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Topology of cosmic domains and strings

Cited by

• Optimal Nonlinear Passage Through a Quantum Critical Point
• Defect Production in Nonlinear Quench across a Quantum Critical Point
• Quench dynamics near a quantum critical point
• Colloquium: Quantum annealing and analog quantum computation
• Optimal suppression of defect generation during a passage across a quantum critical point
• Thermodynamic properties of the one-dimensional extended quantum compass model in the presence of a transverse field
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Dynamics of a quantum phase transition and relaxation to a steady state
• Entanglement and Majorana edge states in the Kitaev model
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling
• Defect production due to quenching through a multicritical point

Related

• Defect Production in Nonlinear Quench across a Quantum Critical Point
• Contact process with a defect: universal oasis, nonuniversal scaling
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process
• Density of kinks just after a quench in an overdamped system
• On the Efficiency of Topological Defect Formation in the Systems of Various Size and (Quasi-) Dimensionality