Finite temperature dynamics of the Mott insulating Hubbard chain

TL;DR

This paper investigates the finite-temperature dynamical properties of the 1D Hubbard model, revealing a crossover to a spin-incoherent regime and identifying thermal broadening effects in spectral functions through combined numerical and analytical methods.

Contribution

It introduces a comprehensive analysis of finite-temperature dynamics in the 1D Hubbard model, including a strong-coupling analytical approach and numerical tDMRG results.

Findings

Spectral function crosses over to spin-incoherent Luttinger liquid at T ~ J for large U.

Spectral function shows thermally broadened bands at smaller U and higher T.

Dynamical density response exhibits a finite temperature resonance inside the Mott gap.

Abstract

We study the dynamical response of the half-filled one-dimensional(1d) Hubbard model for a range of interaction strengths $U$ and temperatures $T$ by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group (tDMRG) computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures $T \sim J=4t^2/U$ for sufficiently large $U > 4t$. At smaller values of $U$ and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.