Spin liquid phase in the Hubbard model: Luttinger-Ward analysis of the slave-rotor formalism

TL;DR

This paper introduces a novel method combining the Baym-Kadanoff formalism with slave rotor construction to analyze the U(1) quantum spin liquid phase in the Hubbard model, capturing gauge fluctuations and long-range correlations.

Contribution

It extends mean-field theory by incorporating gauge field fluctuations via a Luttinger-Ward functional approach, providing deeper insights into quantum spin liquids.

Findings

Accurately computes the low-temperature linear specific heat in the U(1) spin liquid.

Reproduces resonant peaks in the Mott gap observed experimentally.

Captures long-range correlations and gauge fluctuations beyond mean-field approximation.

Abstract

We propose an approach for studying the spin liquid phase of the Hubbard model on the triangular lattice by combining the Baym-Kadanoff formalism with the slave rotor parton construction. This method enables the computation of a series of two-body Feynman diagrams for the Luttinger-Ward (LW) functional using a one-loop truncation. This approach enables us to study the U(1) quantum spin liquid phase characterized by a spinon Fermi surface and to derive the Green's functions for spinons, chargons, and electrons. Our findings extend beyond the standard mean-field approximation by accounting for the effects of gauge field fluctuations. The spatial components of the U(1) gauge field are equivalently represented by interactions that incorporate corrections from the spinon-chargon two-particle random phase approximation. This framework effectively captures the long-range correlations inherent to the U(1) quantum spin liquid and combines non-perturbative quantum field theory with the projective construction, providing new insights into the study of quantum spin liquids and other strongly correlated electron systems. We demonstrate that our approach correctly computes the low-temperature linear temperature dependence of the specific heat in the U(1) spin liquid, in agreement with the behavior expected for a Fermi surface. Moreover, this approach reproduces the resonant peaks in the Mott gap, as observed in cobalt atoms on single-layer 1T-TaSe2.