Mesoscopic Effects in Quantum Phases of Ultracold Quantum Gases in Optical Lattices

TL;DR

This paper investigates finite-size effects in 1D Bose- and Fermi-Hubbard models relevant to ultracold gases in optical lattices, analyzing quantum measures and ensemble differences using advanced numerical methods.

Contribution

It provides a comprehensive analysis of finite-size effects on quantum phases in 1D Hubbard models, including comparisons of simulation techniques and ensemble types.

Findings

Finite size causes blurring of Mott lobe tips in bosonic systems.

Higher depletion observed near Mott lobe tips due to finite size.

First Mott lobe tip approaches thermodynamic value as system size increases.

Abstract

We present a wide array of quantum measures on numerical solutions of 1D Bose- and Fermi-Hubbard Hamiltonians for finite-size systems with open boundary conditions. Finite size effects are highly relevant to ultracold quantum gases in optical lattices, where an external trap creates smaller effective regions in the form of the celebrated "wedding cake" structure and the local density approximation is often not applicable. Specifically, for the Bose-Hubbard Hamiltonian we calculate number, quantum depletion, local von-Neumann entropy, generalized entanglement or Q-measure, fidelity, and fidelity susceptibility; for the Fermi-Hubbard Hamiltonian we also calculate the pairing correlations, magnetization, charge-density correlations, and antiferromagnetic structure factor. Our numerical method is imaginary time propagation via time-evolving block decimation. As part of our study we provide a careful comparison of canonical vs. grand canonical ensembles and Gutzwiller vs. entangled simulations. The most striking effect of finite size occurs for bosons: we observe a strong blurring of the tips of the Mott lobes accompanied by higher depletion, and show how the location of the first Mott lobe tip approaches the thermodynamic value as a function of system size.