SC$^*$ Superconductivity and Spin Stiffnesses in the SU(2) Gauge Theory of the Two-Dimensional Hubbard Model

TL;DR

This paper explores how superconductivity in a fractionalized SU(2) gauge theory of the 2D Hubbard model suppresses spin stiffnesses, thereby amplifying quantum spin fluctuations and potentially stabilizing quantum disordered phases.

Contribution

It provides the first calculation of how superconductivity feedback affects spin stiffnesses in a fractionalized gauge theory of the Hubbard model.

Findings

Superconductivity significantly suppresses spatial and temporal spin stiffnesses.

Enhanced spin fluctuations due to superconductivity may stabilize quantum disordered states.

Coexistence of magnetic and superconducting order in the chargon sector is confirmed.

Abstract

We consider the SU(2) gauge theory for spin fluctuations in the two-dimensional Hubbard model, where the electron field is fractionalized in terms of spinons and chargons. In this theory, spinons are described by a non-linear sigma model, while chargons are treated as fermions at a mean-field level. We investigate the instability to a superconducting state SC*, arising from a fractionalized Fermi liquid (FL*) where pairing between chargons occurs. Consistent with previous studies, our analysis reveals a coexisting phase characterized by both magnetic and superconducting order for the chargons. The central contribution of this work is the calculation of the feedback of superconductivity on spatial and temporal spin stiffnesses, thereby quantifying its impact on spin fluctuations. Our key finding is that superconductivity significantly suppresses these spin stiffnesses, enhancing quantum spin fluctuations. This enhancement suggests that superconductivity can play a crucial role in stabilizing quantum disorder against long-range magnetic ordering.