Rung-Rung Current Correlations on a 2-Leg t-J Ladder

We report the results of numerical calculations of rung-rung current correlations on a 2-leg t-J ladder with J/t = 0.35 for dopings x = 0.125 and x = 0.19. We find that the amplitude of these correlations decays exponentially. We argue that this can be understood within a bosonization framework in terms of the pinned phase variables associated with a C1SO phase with dx2−y2-like power law pairing correlations. PACS Numbers: 74.20.Mn, 71.10.Fd, 71.10.Pm Typeset using REVTEX ∗[email protected] †[email protected] ‡[email protected] 1 Variational flux-phase states are known to provide interesting low energy estimates for the ground state of the 2D Heisenberg antiferromagnet. In addition, recent calculations have found signatures of a staggered-flux phase in current vorticity correlations in lightlydoped t-J clusters. In particular, Ivanov et. al. [1] found evidence for a power law decay of the staggered current vorticity for a projected d-wave variational wave function on a 10 × 10 lattice and Leung [2] has reported staggered vorticity correlations from the exact diagonalization of a 32-site t-J cluster with two holes. Prompted by these results, we have carried out density matrix renormalization group (DMRG) calculations of the rung-rung current correlations on doped 2-leg t-J ladders. As is known, near half-filling an isotropic t-J ladder, with J/t in the physical range appropriate to the cuprates, retains a spin gap and exhibits power law dx2−y2-like pair field and 4kF -CDW correlations [3]. Thus, it is of interest to explore whether there may also be staggered current correlations on the 2-leg ladder. Indeed, as discussed below, the DMRG calculations show that there are oscillating rungrung current correlations. However, we find that they are incommensurate at a finite doping, relatively weak, and decay exponentially on a scale of several lattice spacings. Complementing the numerical results, we discuss a bosonization treatment of the 2-leg ladder. Here, one finds that the rung current depends exponentially on various boson phase fields. We argue that in a C1SO phase which has a spin-gapped ground state with power law dx2−y2-like pairing correlations, a phase variable appearing in the rung-current is dual to a pinned variable and that this leads to an exponential decay of the rung-rung current correlations, as seen numerically. Here we will consider an isotropic 2-leg t-J ladder described by the Hamiltonian H = t ∑ i,λ,α ( ci+1λαciλα + h.c. )