Exact ground states of extended t–J_z models on a square lattice

Abstract

We examine special extended spin S = 1/2 fermionic and hard core bosonic t–J_z models with nearest neighbour and next nearest neighbour interactions to find exact ground states. Some of these models display an exponentially large degeneracy with diagonal stripe-like patterns.

Acknowledgements

This work was partially sponsored by the Center for Material Innovation at Washington University, St. Louis, and by the Swedish Research Council.

Notes

†“Quasi-exactly solvable” here means that we can exactly determine all ground states yet do not solve the finite temperature problem.

†All of the results in the article are exact. In this footnote (and here alone), we depart from the rigorous results derived in this work and briefly speculate about possible extensions. As within the ground state of equation (22) there is no kinetic motion of the electrons – we might speculate that the transmutation statistics might well become irrelevant (as no transmutations occur). If this is the case, | ψ ⟩  of equation (22), will be an eigenstate of equation (20) with all phases set to zero.