Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories

TL;DR

This paper uses conformal field theory to compute finite size corrections to formation probabilities and the Casimir effect in quantum critical chains, providing exact formulas and numerical validation.

Contribution

It introduces exact CFT-based formulas for formation probabilities and Casimir energies in finite quantum critical systems, including disjoint intervals.

Findings

Formulas for formation probabilities in finite open and periodic chains

Numerical validation in the transverse field Ising chain

Connection between formation probabilities and Casimir energies

Abstract

We calculate formation probabilities of the ground state of the finite size quantum critical chains using conformal field theory (CFT) techniques. In particular, we calculate the formation probability of one interval in the finite open chain and also formation probability of two disjoint intervals in a finite periodic system. The presented formulas can be also interpreted as the Casimir energy of needles in particular geometries. We numerically check the validity of the exact CFT results in the case of the transverse field Ising chain.