Symmetries of the Solution of the t-J Model

Abstract

This paper describes a group-theoretical classification of the mean-field solutions of the t-J model and the extended t-J model on a planar square lattice. It is shown that the mean-field solutions can be classified into four categories, spin density wave (SDW), charge density wave (CDW), bond order wave (BOW) and charve current wave (CCW) with distinct behavior under spatial inversion, spin rotation and time reversal. We derived systematically all types of broken-symmetry solutions, each of which is characterized by a single order parameter, for the ordering vector q= Q≡(π, π) and those for q= q1≡(π, 0). It is shown that for the t-J model there are four states (flux, Peierls, kite and SDW) with q= Q and six states (two CDWs, two BOWs and two CCWs) with q= Q and six states (two CDWs, two BOWs and two CCWs) with q= q1. For the t-J-J′ model including next-nearest-neighbour Heisenberg coupling, other four states (one CDW, one BOW and two CCWs) with q= Q and seven states (three SDWs, two BOWs and two CCWs) with q= q1 are possible. These phases are derived naturally from the irreducible spectral decomposition of the Σ JSiSj term and the self-consistent condition of the renormalized mean-field theory. The role of local SU(2) symmetry present at half filling is also discussed.