An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo

TL;DR

The paper introduces adiabatic quantum Monte Carlo (AQMC), a new method that mitigates the sign problem in quantum simulations, enabling accurate ground-state property calculations for complex strongly correlated systems.

Contribution

AQMC is a novel approach that gradually increases interaction strength to reduce the sign problem, providing a controlled, variational approximation for ground-state energies.

Findings

AQMC exponentially improves the average sign, allowing access to low temperatures.

Benchmarking shows AQMC's high accuracy compared to established methods.

Application to a doped Hubbard model reveals emergent topological order.

Abstract

We introduce the adiabatic quantum Monte Carlo (AQMC) method, where we gradually crank up the interaction strength, as an amelioration of the sign problem. It is motivated by the adiabatic theorem and will approach the true ground-state if the evolution time is long enough. We demonstrate that the AQMC enhances the average sign exponentially such that low enough temperatures can be accessed and ground-state properties probed. It is a controlled approximation that satisfies the variational theorem and provides an upper bound for the ground-state energy. We first benchmark the AQMC vis-\`a-vis the undoped Hubbard model on the square lattice which is known to be sign-problem-free within the conventional quantum Monte Carlo formalism. Next, we test the AQMC against the density-matrix-renormalization-group approach for the doped four-leg ladder Hubbard model and demonstrate its remarkable accuracy. As a nontrivial example, we apply our method to the Hubbard model at $p=1/8$ doping for a $16\times 8$ system and discuss its ground-state properties. We finally utilize our method and demonstrate the emergence of $U(1)_2\sim SU(2)_1$ topological order in a strongly correlated Chern insulator.