An Effective Model for Strongly Correlated Electrons
strongly correlated electrons; $t$-$J$ model; high-$T_c$ cuprates; quantum effective field theory.
In this work we examine an alternative effective formulation for the $t$-$J$ model which is believed
to capture the essential physics behind the underdoped regime of the high-$T_c$ cuprates. After recasting
the original problem in this new representation, we check the consistency of our procedure and discuss
some physical consequences of such a representation including, the crossover between the regimes of small
and large Fermi surfaces which is observed experimentally. We then explore the possiblity of constructing a
path integral representation for the $t$-$J$ quantum partition function departing from the proposed
formulation. Finally, we use the latter formalism to derive a continuum effective field theory in $(2+1)$
spacetime dimensions which features small hole-like pockets near the nodal regions of the Brillouin zone
along with an unconventional mechanism for superconductivity.