Quantum Critical Points and the Sign Problem

TL;DR

This paper reveals a quantitative link between the sign problem in quantum Monte Carlo simulations and quantum critical behavior in condensed matter models, suggesting the sign problem can be used to study critical phenomena.

Contribution

It demonstrates that the sign problem in determinant quantum Monte Carlo is connected to quantum critical points, offering a new perspective on using the sign problem as a tool rather than an obstacle.

Findings

Sign problem correlates with quantum critical behavior in models.

Simulations of Hubbard and ionic Hubbard models show this link.

Low average sign indicates pseudogap and exotic superconductivity onset.

Abstract

The "sign problem" (SP) is the fundamental limitation to simulations of strongly correlated materials in condensed matter physics, solving quantum chromodynamics at finite baryon density, and computational studies of nuclear matter. As a result, it is part of the reason fields such as ultra-cold atomic physics are so exciting: they can provide quantum emulators of models that could not otherwise be solved, due to the SP. For the same reason, it is also one of the primary motivations behind quantum computation. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians, since the details of how it onsets, and its eventual occurrence, can be altered by the choice of algorithm or many-particle basis. Despite that, we show that the SP in determinant quantum Monte Carlo (DQMC) is quantitatively linked to quantum critical behavior. We demonstrate this via simulations of a number of fundamental models of condensed matter physics, including the spinful and spinless Hubbard Hamiltonians on a honeycomb lattice and the ionic Hubbard Hamiltonian, all of whose critical properties are relatively well understood. We then propose a reinterpretation of the low average sign for the Hubbard model on the square lattice when away from half-filling, an important open problem in condensed matter physics, in terms of the onset of pseudogap behavior and exotic superconductivity. Our study charts a path for exploiting the average sign in QMC simulations to understand quantum critical behavior, rather than solely as an obstacle that prevents quantum simulations of many-body Hamiltonians at low temperature.