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

Abstract

In this work, motivated by the sine-square deformation (SSD) for (1+1)-dimensional quantum critical systems, we study the non-equilibrium quantum dynamics of a conformal field theory (CFT) with SSD, which was recently proposed to have 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 there is a crossover time $t^{\ast }$ that divides the entanglement evolution into two interesting regions. For $t\ll t^{\ast }$, the entanglement entropy does not evolve in time; for $t\gg t^{\ast }$, the entanglement entropy grows as $S_A(t)\simeq \frac{c}{3}\log t$, which is independent of the lengths of the subsystem and the total system. This $\log t$ growth with no revival indicates that a sine-square deformed CFT effectively has an infinite length, in agreement with previous studies based on the energy spectrum analysis. Furthermore, we study the quench dynamics for a CFT with M$\ddot{\text{o}}$bius deformation, which interpolates between a uniform CFT and a sine-square deformed CFT. The entanglement entropy oscillates in time with period $L_{\text{eff}}=L\cosh (2\theta )$, with $\theta =0$ corresponding to the uniform case and $\theta \to \infty$ corresponding to the SSD limit. Our field theory calculation is confirmed by a numerical study on a (1+1)-d critical fermion chain.

are welcome; 10 pages, 4 figures; v2: refs added; v3: refs added; A physical interpretation of t* is added; v4: published version (selected as Editors' Suggestion)

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