Single-hole effective masses in thet-Jmodel

The ground state of a single hole in the one- and two-dimensional t-J model is studied for finite systems as a function of the phase in the kinetic energy term. The coherent effective hopping ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$ and the incoherent hopping ${\mathit{t}}_{\mathit{i}}^{\mathrm{*}}$, evaluated in this way, are connected via the conductivity sum rule. It is shown that for even and odd chains ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$∼${\mathit{t}}_{\mathit{i}}^{\mathrm{*}}$, while their reduction from the free value t remains small even for large J/t. The Bethe ansatz solution, obtained for J=2t, is consistent with the latter result, yielding ${\mathit{t}}_{\mathit{c}}^{\mathrm{*}}$/t∼0.938. In the 4×4 system, the phase variation yields a nontrivial energy manifold. The minimum appears to be near the (π/2,π/2)-(π,0) line in the Brillouin zone for J/t<1, while moving towards the (π/2,π/2)-(π,π) line for J/t≫1.