Speaker
Description
Entanglement entropy at one-dimensional criticality typically follows the Calabrese--Cardy scaling.
In non-unitary critical chains, however, we show that a finite system retains a universal sensitivity to a small spectral gap $\Delta$ away from the exceptional point.
Concretely, we find an additional contribution
\begin{equation}
S_A(\ell)=\frac{c}{3}\log!\Big[\frac{L}{\pi}\sin!\Big(\frac{\pi \ell}{L}\Big)\Big]+\log(\Delta L)+\cdots ,
\end{equation}
which appears as an $\ell$-independent offset when $\Delta L\lesssim 1$.
This behavior has no Hermitian analogue: gaps below the finite-size scale $1/L$ are invisible to entanglement in unitary critical chains, while here the entropy continues to resolve $\Delta$ through the combination $\Delta L$.
We give a holographic understanding in de Sitter space: the RT extremal curve generically extends to past infinity (the IR limit), so it necessarily probes the IR completion and yields the $\log(\Delta L)$ term.
We further confirm this interpretation in a circuit realization by showing that the same contribution is precisely the entanglement of the IR state at the end of a finite-depth RG flow, i.e. a residual entanglement left after finite-depth disentangling.