Finite-size scaling of the quantum Ising chain with periodic, free, and antiperiodic boundary conditions

Abstract

The authors give exact results for the energy spectrum of a chain of N Ising spins in a transverse field with periodic, free, and antiperiodic boundary conditions. The dependence of the energy gaps on boundary conditions is compatible with predictions of conformal invariance for correlation lengths in two-dimensional strips. The feasibility of calculating surface critical indices using phenomenological renormalisation with free boundary conditions and the convergence for large N are discussed.