Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model

TL;DR

This study uses determinant quantum Monte Carlo simulations to explore how doping influences the transition from one to two dimensions in the Hubbard model, revealing significant changes in magnetic properties and spin excitations.

Contribution

It provides a detailed analysis of the doping-dependent dimensional crossover in the Hubbard model using DQMC and cluster perturbation theory, highlighting the evolution of magnetic properties.

Findings

Magnetic properties change smoothly during the crossover from 1D to 2D.

Spin excitations in doped 2D Hubbard cannot be explained by 1D spinon theory.

Doping significantly impacts magnetic order and spin dynamics.

Abstract

Using determinant quantum Monte Carlo (DQMC) simulations, we systematically study the doping dependence of the crossover from one to two dimensions and its impact on the magnetic properties of the Hubbard model. A square lattice of chains is used, in which the dimensionality can be tuned by varying the interchain coupling $t_\perp$. The dynamical spin structure factor and static quantities, such as the static spin susceptibility and nearest-neighbor spin correlation function, are characterized in the one- and two-dimensional limits as a benchmark. When the dimensionality is tuned between these limits, the magnetic properties, while evolving smoothly from one to two dimensions, drastically change regardless of the doping level. This suggests that the spin excitations in the two-dimensional Hubbard model, even in the heavily doped case, cannot be explained using the spinon picture known from one dimension. The DQMC calculations are complemented by cluster perturbation theory studies to form a more complete picture of how the crossover occurs as a function of doping and how doped holes impact magnetic order.