Doped carrier formulation of the t-J model: the projection constraint and the effective Kondo-Heisenberg lattice representation

TL;DR

This paper refines the doped carrier formulation of the t-J model by incorporating a crucial projection constraint, revealing gauge relations among spin-fermion representations and mapping it onto a Kondo-Heisenberg lattice to better understand high-Tc superconductors.

Contribution

It introduces a controlled way to include the projection constraint in the doped carrier formulation, unifies different spin-fermion representations, and maps the t-J model onto a Kondo-Heisenberg lattice.

Findings

The projection constraint relates different spin-fermion representations.

The t-J model can be mapped onto a Kondo-Heisenberg lattice.

Implications for the Fermi surface crossover and spin gap closure.

Abstract

We show that the recently proposed doped carrier Hamiltonian formulation of the t-J model should be complemented with the constraint that projects out the unphysical states. With this new important ingredient, the previously used and seemingly different spin-fermion representations of the t-J model are shown to be gauge related to each other. This new constraint can be treated in a controlled way close to half-filling suggesting that the doped carrier representation provides an appropriate theoretical framework to address the t-J model in this region. This constraint also suggests that the t-J model can be mapped onto a Kondo-Heisenberg lattice model. Such a mapping highlights important physical similarities between the quasi two-dimensional heavy fermions and the high-T$_c$ superconductors. Finally we discuss the physical implications of our model representation relating in particular the small versus large Fermi surface crossover to the closure of the lattice spin gap.