A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z$_{2}$ spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator

TL;DR

This paper explores a slave-fermion gauge-theory approach to the t-J model, revealing how doping induces complex magnetic structures and a Z$_{2}$ spin-gapped anomalous metal phase in an antiferromagnetic doped Mott insulator.

Contribution

It introduces a Z$_{2}$ gauge structure resulting from doping-induced magnetic complexity, differing from the conventional U(1) gauge theory in the t-J model.

Findings

Doped holes enhance ferromagnetic correlations.

Complex magnetic textures reduce gauge symmetry from U(1) to Z$_{2}$.

The Z$_{2}$ phase lacks gapless gauge fluctuations, affecting low-temperature properties.

Abstract

We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromagnetic state, analogous to the U(1) spin liquid phase in the slave-boson approach of the t-J model. We argue that the emergent U(1) gauge structure in this approach is based on a simplified picture for antiferromagnetic correlations. Considering that dynamics of doped holes frustrates a collinear antiferromagnetic spin configuration, we show that doped holes enhance ferromagnetic spin correlations and result in a complex magnetic structure. The presence of such a complex spin texture reduces the U(1) gauge structure down to Z$_{2}$, thus a different effective field theory results for the spin-gapped non-Fermi liquid metal at low temperatures because there are no gapless U(1) gauge fluctuations.