Controlled expansion for correlated electrons with concentrated kinematics

TL;DR

The paper introduces a controlled expansion method for strongly correlated electron systems with concentrated kinematics, enabling analytical calculations of response functions and transport properties.

Contribution

It develops a systematic expansion based on a small parameter to analyze systems with localized kinematic regions, with applications to Hubbard, correlated-hopping, and Chern band models.

Findings

Spectral broadening scales as s^2 in the Hubbard model.

Identification of a high-temperature bad metal with T-linear resistivity.

Computed spectral functions for electron and trion states in Chern bands.

Abstract

We introduce a systematic expansion tailored to systems with strong local interactions and capable of computing response functions, including finite DC transport, analytically. The expansion is controlled by a small parameter $s^2$ that measures the area of the momentum space region where kinematics of the theory is concentrated. In real space, this corresponds to single-particle or correlated hopping terms with amplitudes that decay over a length scale $1/s$ and scale in magnitude as $s^2$ in two dimensions. In the limit $s^2\ll 1$, long, self-avoiding tunneling paths dominate over paths revisiting the same site. This enables systematic controlled calculations of various physical quantities. We illustrate the method with three applications. (i) A Hubbard model with concentrated dispersion: we analytically obtain spectral broadening which scales as $s^2$ and identify a high-temperature bad metal with $T$-linear resistivity coexisting with parametrically long-lived quasiparticles, as well as an intermediate-temperature "thermal FL*" with a small hole pocket that coexists with thermally disordered fluctuating local moments, all within a single controlled framework. (ii) A correlated-hopping model with interesting electron-trion dynamics. (iii) A model of Chern bands with concentrated Berry curvature, motivated by twisted bilayer graphene, which realizes a Mott semimetal where we compute the broadening for the electron and trion spectral functions. At the end, we discuss how our approach paves the way to addressing various challenging questions in strongly correlated systems and outline its various generalizations.