Calculation of specific heat and susceptibilities with the use of the Trotter approximation

Abstract

The Trotter approximation has been used extensively in quantum Monte Carlo simulations. We consider here different ways of calculating the general zero-field susceptibility \ensuremath{\chi} and the specific heat C when a Trotter approximation is used, deriving analytically the error dependence on the imaginary-time increment \ensuremath{\Delta}\ensuremath{\tau} as well as the low-temperature behavior. We find that certain definitions of \ensuremath{\chi} and C exhibit spurious divergences at low temperatures, and suggest the most appropriate ways to extract these quantities. We test our general predictions on two models, and discuss the implications of our results for numerical simulations.