Dealing with the Sign Problem in the Hubbard Model

Robert Sedgewick, University of California, Santa Barbara

Photo of Robert Sedgewick

The Hubbard model is a simple quantum model for electrons hopping between sites on a lattice under the influence of a short-range Coulomb repulsion. The Hubbard model can be simulated on a computer using Monte Carlo techniques, but for many values of electron filling, the simulation suffers from a numerical problem known as the “sign problem.” This effectively bars low-temperature simulation of the model at these fillings. While we are interested in the specific case of the Hubbard model, the sign problem occurs in numerical studies in many different areas of physics and engineering.

We have studied a method for extending the temperature range of systems that suffer from the sign problem. This involves breaking up an observable into the contributions from different particle number sectors. After the breakup, the sign can be interpolated, reducing the error in the measurement. On small lattices, our results show the correct zero-temperature limit predicted by exact calculation.

Abstract Author(s): Robert Sedgewick, Luca Capriotti, Bob Sugar, and Doug Scalapino