Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to nonuniform conformal field theory

Abstract

In this work, motivated by the sine-square deformation (SSD) for (1+1)-dimensional quantum critical systems, we study the nonequilibrium quantum dynamics of a conformal field theory (CFT) with SSD, which was recently proposed to have a continuous energy spectrum and continuous Virasoro algebra. In particular, we study the time evolution of entanglement entropy after a quantum quench from a uniform CFT, which is defined on a finite space of length L, to a sine-square deformed CFT. We find that there is a crossover time t^{*} that divides the entanglement evolution into two interesting regions. For t≪t^{*}, the entanglement entropy does not evolve in time; for t≫t^{*}, the entanglement entropy grows as S_{A}(t)≃c/3logt, which is independent of the lengths of the subsystem and the total system. This logt growth with no revival indicates that a sine-square deformed CFT effectively has an infinite length, in agreement with previous studies based on energy spectrum analysis. Furthermore, we study the quench dynamics for a CFT with Möbius deformation, which interpolates between a uniform CFT and a sine-square deformed CFT. The entanglement entropy oscillates in time with period L_{eff}=Lcosh(2θ), with θ=0 corresponding to the uniform case and θ→∞ corresponding to the SSD limit. Our field theory calculation is confirmed by a numerical study on a (1+1)-dimensional critical fermion chain.