Pseudo entropy under joining local quenches

TL;DR

This work analyzes pseudo entropy in two-dimensional CFTs under joining local quenches, comparing holographic CFTs with free Dirac fermion CFTs. Using replica techniques and conformal mappings across opposing-, single-, and double-slit geometries, the authors compute pseudo entropy and its entropy excess for both ground-state and excited states. They uncover a characteristic dip in pseudo entropy during propagation and show that entropy excess can be positive in holographic CFTs but non-positive in free Dirac fermion CFTs, arguing this as a signature of multipartite entanglement in the holographic vacuum. The results illuminate how pseudo entropy captures multipartite entanglement structure beyond conventional entanglement entropy and suggest broader implications for AdS/CFT and quantum information in QFTs.

Abstract

We compute the pseudo entropy in two-dimensional holographic and free Dirac fermion CFTs for excited states under joining local quenches. Our analysis reveals two of its characteristic properties that are missing in the conventional entanglement entropy. One is that, under time evolution, the pseudo entropy exhibits a dip behavior as the excitations propagate from the joined point to the boundaries of the subsystem. The other is that the excess of pseudo entropy over entanglement entropy can be positive in holographic CFTs, whereas it is always non-positive in free Dirac fermion CFTs. We argue that the entropy excess can serve as a measure of multi-partite entanglement. Its positivity implies that the vacuum state in holographic CFTs possesses multi-partite entanglement, in contrast to free Dirac fermion CFTs.

Figures (29)

• Figure 1: A sketch of the quantum state created by a joining local quench and subsystem $A$, where we measure the pseudo entropy.
• Figure 2: A sketch of examples (a) and (b), that are states in an eight-qubit system with only bipartite quantum entanglement. The red/blue dots and green links represent the qubits (in A/B) and quantum entanglement between two qubits. The state $\ket{\psi}$ represents the original state, in which $A_2$ and $A_3$ are disentangled. On the other hand, $\ket{\varphi}$ is the one after the joining quench which connects $A_2$ and $A_3$. We find $\varDelta{S}_A=0$ for (a) and $\varDelta{S}_A<0$ for (b).
• Figure 3: A plot of entropy excess $\varDelta{S}_A$ for the four-qubit states \ref{['fLQSa']} and \ref{['fLQSb']}. The horizontal and vertical coordinates are $\theta$ and $\theta'$, in the range $0\leq \theta, \theta' \leq \pi/2$.
• Figure 4: Plots of entropy excess $\varDelta{S_A}$ for the four-qubit states \ref{['spinchain1']} and \ref{['spinchain2']}. The horizontal and vertical coordinates are $h$ and $g$ in the Hamiltonian \ref{['spinHamiltonian']} with $J = 1$ (left) and $J = -1$ (right).
• Figure 5: The imaginary time-space region with opposing-slit geometry for the density matrix under a local quench at $x=x^*$ (left) is mapped to the upper half-plane (right) by $z = f(w)$. This geometry corresponds to the path integral calculation of the entanglement entropy of $\ket{\mathrm{JQ}(x^*, t)}$.