Boundary States as Holographic Duals of Trivial Spacetimes

Abstract

We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs). First, we argue that boundary states essentially have no real-space entanglement by computing the entanglement entropy when we bipartite the system into two spatial regions. From the viewpoint of holography, this shows that boundary states are dual to trivial spacetimes of zero spactime volume. Next, we point out that a continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs can be formulated by employing a boundary state as its infrared unentangled state with an appropriate regularization. Exploiting this idea, we propose an approximation scheme of cMERA construction for general CFTs.

Figures (3)

• Figure 1: Sketches of path-integral representation of the regularized unentangled state $|\Omega_M\rangle$ and $n$ point functions $\langle O(x_1)O(x_2)\cdot\cdot\cdot O(x_n)\rangle_{Strip}$.
• Figure 2: The numerically calculated time-evolution of the entanglement entropy, $S_A(t)$ of the SSH model, after a global quench into the critical state for different boundary states (denoted by "BS I" and "BS II", corresponding to the case of $t_1=0, t_2>0$ and $t_1>0, t_2=0$ in (\ref{['BS SSH']}), respectively). We choose the size of the subregion $A$$l=10$ and the total system size $L=200$ (both measured in the lattice constant). (a) $S(t)$ as a function of time $t$. (b) The velocity ($v$) dependence of $S_A(t)$.
• Figure 3: Interpretations of two different cMERA states $|\Psi(u)\rangle$ and $|\Phi(u)\rangle$ in terms of MERA for discretized lattice models. In the former state, we always rescale the distance between two adjacent lattice points to be $\epsilon$, whereas in the latter state we do not rescale.