Finite-size effects in transport data from Quantum Monte Carlo simulations

TL;DR

This paper investigates finite-size effects in quantum Monte Carlo simulations of the Hubbard model, focusing on various transport and spectral properties, and assesses their reliability as indicators of metal-insulator transitions.

Contribution

The study systematically analyzes finite-size and discretization effects on key physical quantities, highlighting the robustness of the Drude weight and clarifying the impact of simulation parameters.

Findings

The Drude weight is less sensitive to finite-size effects than other probes.

The average sign correlates with the compressibility and spectrum gaps.

Discretization in imaginary time significantly affects the average sign and density.

Abstract

We have examined the behavior of the compressibility, the dc-conductivity, the single-particle gap, and the Drude weight as probes of the density-driven metal-insulator transition in the Hubbard model on a square lattice. These quantities have been obtained through determinantal quantum Monte Carlo simulations at finite temperatures on lattices up to 16 X 16 sites. While the compressibility, the dc-conductivity, and the gap are known to suffer from `closed-shell' effects due to the presence of artificial gaps in the spectrum (caused by the finiteness of the lattices), we have established that the former tracks the average sign of the fermionic determinant (<sign>), and that a shortcut often used to calculate the conductivity may neglect important corrections. Our systematic analyses also show that, by contrast, the Drude weight is not too sensitive to finite-size effects, being much more reliable as a probe to the insulating state. We have also investigated the influence of the discrete imaginary-time interval (\Delta\tau) on <sign>, on the average density (\rho), and on the double occupancy (d): we have found that <sign> and \rho are more strongly dependent on \Delta \tau away from closed-shell configurations, but d follows the \Delta\tau^2 dependence in both closed- and open-shell cases.