Fermi Arcs From Dynamical Variational Monte Carlo

TL;DR

This paper extends variational Monte Carlo methods to study Fermi arcs in the Hubbard model, enabling analysis of larger clusters and providing insights into the pseudogap and metallic phases in high-temperature superconductors.

Contribution

It generalizes variational Monte Carlo to open boundary systems, allowing the study of Fermi arcs and phase transitions in larger clusters beyond previous computational limits.

Findings

Captured the transition from Mott insulator to pseudogap with Fermi arcs.

Observed the evolution to a metallic state at high doping.

Minimized finite size effects by studying large clusters.

Abstract

Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada (2020). Here we generalize the approach to systems with open boundary conditions in the absence of translational invariance. Removing these constraints permits the application of embedding techniques like Cluster perturbation theory (CPT). This allows us to solve an enduring problem in the physics of the pseudogap in cuprate high-temperature superconductors, namely the existence or absence of Fermi arcs in the one-band Hubbard model. We study the behavior of the Fermi surface and of the density of states as a function of hole doping for clusters of up to 64 sites, well beyond the reach of modern exact diagonalization solvers. We observe that the technique reliably captures the transition from a Mott insulator at half filling to a pseudogap, evidenced by the formation of Fermi arcs, and finally to a metallic state at large doping. The ability to treat large clusters with quantum cluster methods helps to minimize potential finite size effects and enables the study of systems with long range orders, which will help extend the reach of these already powerful methods and provide important insights on the nature of various strongly correlated many-electron systems, including the high-T$_c$ cuprate superconductors.