Two dimensional quantum quenches and holography

TL;DR

The paper develops a holographic framework for two-dimensional quantum quenches by inserting a spacetime boundary in AdS3, which represents the gravity dual of a boundary state in the CFT. This BCFT-inspired approach yields a dual description of global, local, and inhomogeneous quenches via extremal surfaces, including a novel disconnected surface that ends on the bulk boundary and governs early-time entanglement dynamics. The authors apply the construction to several quenches: global quenches reproduce BTZ-like entanglement growth and phase transitions; infinitesimal and finite inhomogeneous quenches are mapped to bulk geometries with varying black-string temperatures and fusion into an emergent string; local quenches are captured by shock-wave-like bulk excitations with consistent entanglement behavior. Overall, the framework resolves mismatches between holographic and CFT results, clarifies how bulk geometry encodes quench data, and provides a concrete toolkit for analyzing time-dependent entanglement in 2d CFTs.

Abstract

We propose a holographic realization of quantum quenches in two dimensional conformal field theories. In particular, we discuss time evolutions of holographic entanglement entropy in these backgrounds and compare them with CFT results. The key ingredient of the construction is an introduction of a spacetime boundary into bulk geometries, which is the gravity counterpart of a boundary state in the dual CFT. We consider several examples, including local quenches and an inhomogeneous quench which is dual to fusion of two black string into the third one.

Figures (9)

• Figure 1: Left:Plot of the time evolution of entanglement entropy under local quenches for various values of $\epsilon$.As we decrease $\epsilon$, maximum value of entanglement entropy become larger. We take $l_{1}=2,l_{2}=5, c=6$. Right: Plot of the time evolution of energy density $\langle T_{tt}(x,t) \rangle$ during the quench. We take $\epsilon=\frac{1}{2}, c=2$.
• Figure 2: Sketch of the spacetime boundary in the Poincare $AdS_{3}$ (thick red line) at $X=0$ and extremal surfaces in the system.
• Figure 3: The time volution of energy density $\langle T_{tt}(t,x) \rangle$ in the finite inhomogeneous quench.
• Figure 4: Sketch of the fusion of two black strings (string1 and string3) into string 2. Left: When $t<\min \{|l_{1}|,l_{2}\}$, the string 2 is contained in the bulk extension of the subsystem $[l_{1},l_{2}]$. Middle:When $\min \{|l_{1}|,l_{2} \} \leq t<\max \{|l_{1}|,l_{2}\}$, one end point of the string 2 is located outside of the subsystem and the other is in the bulk extension of the subsystem. Right: When $t \geq \max \{|l_{1}|,l_{2}\}$ both end points are located out side the bulk extension of the subsystem.
• Figure 5: Left: Plot of the length of the connected surface as a function of time in the finite inhomogeneous quench (red). We also plot (\ref{['eq:iqcem']}) (blue). Right:Plot of the length of the connected surface as a function of time in the finite inhomogeneous quench(green). We also plot (\ref{['eq:iqdcm']}) We take $l_{1}=-4,l_{2}=6 ,\lambda=\frac{1}{4},\beta=\frac{1}{4}$.