Formation probabilities in quantum critical chains and Casimir effect

TL;DR

This paper establishes a link between formation probabilities in quantum critical chains and the Casimir effect, providing a universal formula and an efficient numerical method for calculating Casimir energies in 1+1 dimensional critical systems.

Contribution

It introduces a novel connection between quantum critical chain formation probabilities and Casimir energies, enabling universal predictions and improved numerical computations.

Findings

Derived a formula relating formation probabilities to Casimir energy.

Validated the formula with numerical results on the transverse field Ising model and XX chain.

Discussed implications for mutual Rényi information of disjoint intervals.

Abstract

We find a connection between logarithmic formation probabilities of two disjoint intervals of quantum critical spin chains and the Casimir energy of two aligned needles in two dimensional classical critical systems. Using this connection we provide a formula for the logarithmic formation probability of two disjoint intervals in generic $1+1$ dimensional critical systems. The quantity is depenedent on the full structure of the underlying conformal field theory and so useful to find the universality class of the critical system. The connection that we find also provides a very efficient numerical method to calculate the Casimir energy between needles using quantum critical chains. The agreement between numerical results performed on critical transverse field Ising model and XX chain with our exact results is very good. We also comment on the mutual R\'enyi information of two disjoint intervals.