Monopoles in the gauge theory of the t-J model
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 $V(t) \sim t^α$, with $α=1/3$. The plasma is in a dipolar phase if $α\ge 1$ and a possibility of transition towards a Debye screening phase arises if $α< 1$, so that there exists a critical Fermi wave vector $k_f^{*}$ such as the plasma is Debye screening 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.