Universal term in the free energy at a critical point and the conformal anomaly

Abstract

We show that the leading finite-size correction to lnZ for a two-dimensional system at a conformally invariant critical point on a strip of length L width β(β≪L) is (π/6)c(L/β), where c is the conformal anomaly. Equivalently, the leading low-temperature correction to the free energy of a one-dimensional quantum system is -(π/6)cL(kT${)}^2$ħv, where v is the effective ‘‘velocity of light.’’ The latter formula is used to check recently derived critical theories of spin-s quantum chains against Bethe-Ansatz solutions.