Monopoles in the gauge theory of the t-J model

TL;DR

This paper investigates magnetic monopoles in the t-J model using a renormalization group approach, revealing a phase transition between confined and Debye screening states influenced by doping and the number of colors.

Contribution

It derives the interaction parameters for monopole plasma in the t-J model and analyzes the phase transition behavior under different conditions.

Findings

Critical Fermi wave vector decreases with increasing colors.

Transition from dipolar to Debye screening phase depends on doping.

Self-consistency of spin-charge decoupling at large N.

Abstract

We consider a RG approach for the plasma of magnetic monopoles of the Ioffe-Larkin approach to the t-J model. We first derive the interaction parameters of the 2+1 plasma of magnetic monopoles. The total charge along the time axis is constrained to be zero for each lattice plaquette. Under the one-plaquette approximation, the problem is equivalent to a one dimensional neutral plasma interacting via a potential $V(t) \sim t^{\alpha}$, with $\alpha=1/3$. The plasma is in a dipolar phase if $\alpha \ge 1$ and a possibility of transition towards a Debye screening phase arises if $\alpha < 1$, so that there exists a critical Fermi wave vector $k_f^{*}$ such as the plasma is Debye screening if $k_f<k_f^{*}$ and confined if $k_f>k_f^{*}$. The 2+1 dimensional problem is treated numerically. We show that $k_f^{*}$ decreases and goes to zero as the number of colors increases. This suggests that the assumption of spin-charge decoupling within the slave-boson scheme is self-consistent at large enough values of $N$ and small enough doping. Elsewhere, a confining force between spinons and antiholons appears, suggesting a transition to a Fermi liquid state.