Theory of defect production in nonlinear quench across a quantum critical point

Abstract

We study defect production in a quantum system subjected to a nonlinear power law quench which takes it either through a quantum critical or multicritical point or along a quantum critical line. We elaborate on our earlier work [D. Sen, K. Sengupta, S. Mondal, \prl 101, 016806 (2008)] and present a detailed analysis of the scaling of the defect density $n$ with the quench rate $\tau$ and exponent $\al$ for each of the above-mentioned cases. We also compute the correlation functions for defects generated in nonlinear quenches through a quantum critical point and discuss the dependence of the amplitudes of such correlation functions on the exponent $\al$. We discuss several experimental systems where these theoretical predictions can be tested.

arXiv comment9+ pages, v1

References in corpus (40)

• Many-Body Physics with Ultracold Gases
• Anyons in an exactly solved model and beyond
• Quantum Criticality in Heavy Fermion Metals
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependence of correlation functions following a quantum quench
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Bose-Einstein Condensation in Magnetic Insulators
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Universal adiabatic dynamics across a quantum critical point
• Quantum magnetism and criticality
• The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective
• Quench dynamics across quantum critical points
• Non-zero temperature transport near quantum critical points
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Defect production in non-linear quench across a quantum critical point
• Exact results for quench dynamics and defect production in a two-dimensional model
• Entropy and Correlation Functions of a Driven Quantum Spin Chain
• Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Optimal non-linear passage through a quantum critical point
• Vortex String Formation in a 3D U(1) Temperature Quench
• Symmetry Breaking with a Slant: Topological Defects after an Inhomogeneous Quench
• Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $\sigma$-model
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Adiabatic dynamics in open quantum critical many-body systems
• Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid
• Dynamics of a quantum phase transition in the random Ising model
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Quenching along a gapless line: A different exponent for defect density
• Winding up by a quench: vortices in the wake of rapid Bose-Einstein condensation
• Characteristic BEC scaling close to Quantum Critical Point in BaCuSi2O6
• Adiabatic quenches through an extended quantum critical region
• Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires

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• Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing