Stochastic Series Expansion Quantum Monte Carlo

Abstract

This chapter outlines the fundamental construction of the Stochastic Series Expansion, a highly efficient and easily implementable quantum Monte Carlo method for quantum lattice models. Originally devised as a finite-temperature simulation based on a Taylor expansion of the partition function, the method has recently been recast in the formalism of a zero-temperature projector method, where a large power of the Hamiltonian is applied to a trial wavefunction to project out the groundstate. Although these two methods appear formally quite different, their implementation via non-local loop or cluster algorithms reveals their underlying fundamental similarity. Here, we briefly review the finite- and zero-temperature formalisms, and discuss concrete manifestations of the algorithm for the spin 1/2 Heisenberg and transverse field Ising models.