J. Phys. I France
Volume 6, Numéro 8, August 1996
Page(s) 993 - 1006
J. Phys. I France 6 (1996) 993-1006
DOI: 10.1051/jp1:1996103

Monopoles in the Gauge Theory of the t-J Model

R. Mélin and B. Douçot

CRTBT-CNRS, BP 166X, 38042 Grenoble Cedex 9, France

Received 4 March 1996, accepted 2 May 1996

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 $\alpha \geq 1$ and a possibility of transition towards a Debye screening phase arises if $\alpha < 1$, so that there exists a critical Fermi wave vector $k_{\rm f}^*$ such as the plasma is Debye screening if $k_{\rm f} < k_{\rm f}^*$ and confined if $k_{\rm f} > k_{\rm f}^*$. The 2+1 dimensional problem is treated numerically. We show that $k_{\rm f}^*$ 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.

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