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Physical review. B, Condensed matter

Degenerate ground states of the two-dimensionalU=∞ Hubbard model

Zhenqing Yang, Yu-Lei Li, Ke-Cai Zeng, Kong Fan–mei

Published Jan 15, 1995• 3 citations
Publisher

Abstract

It is shown that for a definite cluster in the two-dimensional U=\ensuremath{\infty} Hubbard model, there are states in any ${\mathit{S}}^{\mathit{z}}$ sector, which are degenerate with the lowest state in the ${\mathit{S}}_{\mathrm{max}}^{\mathit{z}}$ sector. It is shown further that these states become the lowest ones in their sectors as the cluster becomes large enough, keeping the hole concentration constant. Then degenerate ground states of various ${\mathit{S}}^{\mathit{z}}$ are obtained. The properties of the ground state of any ${\mathit{S}}^{\mathit{z}}$${\mathit{S}}_{\mathrm{max}}^{\mathit{z}}$ can be found through those of the ground state of ${\mathit{S}}_{\mathrm{max}}^{\mathit{z}}$.

DOI
10.1103/physrevb.51.1435

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It is shown that for a definite cluster in the two-dimensional U=\ensuremath{\infty} Hubbard model, there are states in any Sz{\mathit{S}}^{\mathit{z}}Sz sector, which are degenerate with the lowest state in the Smaxz{\mathit{S}}_{\mathrm{max}}^{\mathit{z}}Smaxz​ sector. It is shown further that these states become the lowest ones in their sectors as the cluster becomes large enough, keeping the hole concentration constant. Then degenerate ground states of various Sz{\mathit{S}}^{\mathit{z}}Sz are obtained. The properties of the ground state of any {\mathit{S}}^{\mathit{z}}$${\mathit{S}}_{\mathrm{max}}^{\mathit{z}} can be found through those of the ground state of Smaxz{\mathit{S}}_{\mathrm{max}}^{\mathit{z}}Smaxz​.
The ground state of the two-dimensional Hubbard model on a square lattice is studied in the large-U limit in a half-filled band with a dynamical hole. For a 4\ifmmode\times\else\texttimes\fi{}4 lattice with hopping t=1 and coupling JJc{J}_{c}Jc​\ensuremath{\approxeq}0.075, the ground state has zero momentum (k) and spin 15/2 (ferromagnetic background). For J\ensuremath{\ge}Jc{J}_{c}Jc​ the ground state is degenerate with nonzero k and spin 1/2, in agreement with recent variational calculations. The nonzero k of the ground state comes from a nontrivial phase in the overlap of the spin states before and after a hole move. For small lattices we show that the effective Hamiltonian of the hole is that of a particle moving in a magnetic field. We also find that many of the features of the weak-coupling region carry over continuously to the strong-coupling region.