The Stochastic Series Expansion Method for Quantum Lattice Models

Andreas Hehn

Anders W. Sandvik

A cluster update (the ``operator loop'') is developed within the framework of a numerically exact quantum Monte Carlo method based on the power series expansion of $\mathrm{exp}(\ensuremath{-}\ensuremath{\beta}H)$ (stochastic series expansion). The method is generally applicable to a wide class of lattice Hamiltonians for which the expansion is positive definite. For some important models the operator-loop algorithm is more efficient than loop updates previously developed for ``worldline'' simulations. The method is here tested on a two-dimensional anisotropic Heisenberg antiferromagnet in a magnetic field.

Hans A. De Raedt, Ad Lagendijk

Lei Wang, Ye-Hua Liu, Matthias Troyer

We present an algorithm for the efficient simulation of the half-filled spinless $t\text{\ensuremath{-}}V$ model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless $t\text{\ensuremath{-}}V$ model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.

Roger G. Melko

Sylvain Capponi, Saeed S. Jahromi, Fabien Alet +1 more

We investigate the low-energy properties as well as quantum and thermal phase transitions of the Baxter-Wu model in a transverse magnetic field. Our study relies on stochastic series expansion quantum Monte Carlo and on series expansions about the low- and high-field limits at zero temperature using the quantum finite-lattice method on the triangular lattice. The phase boundary consists of a second-order critical line in the four-state Potts model universality class starting from the pure Baxter-Wu limit meeting a first-order line connected to the zero-temperature transition point (h≈2.4, T=0). Both lines merge at a tricritical point approximately located at (h≈2.3J, T≈J).