Mean-Field Description of Phase String Effect in the $t-J$ Model

TL;DR

This paper develops a mean-field theory for the phase string effect in the $t-J$ model, unifying antiferromagnetic and metallic phases through bosonic spinon and holon condensations, with implications for understanding high-temperature superconductivity.

Contribution

It introduces a novel mean-field approach that captures both AF and metallic phases within a single framework, emphasizing the bosonic nature of spinons and holons due to the phase string effect.

Findings

Unified description of AF and metallic phases.

Bosonic nature of spinons and holons due to phase string effect.

Existence of an underdoped metallic regime with short-range spin order.

Abstract

A mean-field treatment of the phase string effect in the $t-J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long range ordering (AFLRO) at half-filling and superconducting condensation in metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond (RVB) pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.