Signatures of a staggered-flux phase in thet−Jmodel with two holes on a 32-site lattice

We study the relevance of the staggered-flux phase in the $t-J$ model using a system with two holes on a 32-site lattice with periodic boundary conditions. We find a staggered-flux pattern in the current-current correlation in the lowest energy d-wave state where there is mutual attraction between the holes. This staggered correlation decays faster with distance when the hole binding becomes stronger. This is in complete agreement with a recent study by Ivanov, Lee, and Wen [Phys. Rev. Lett. 84, 3958 (2000)] based on the SU(2) theory, and strongly suggests that the staggered-flux phase is a key ingredient in the $t-J$ model. We further show that this staggered-flux pattern does not exist in a state where the holes repel each other. Correlations of the chirality operator ${\mathbf{S}}_1\cdot ({\mathbf{S}}_2\times {\mathbf{S}}_3)$ show that the staggered pattern of the chirality is closely tied to the holes.