The Bosonization Study Of Ground State Phase Diagram Of 1-D Hubbard Model

In this paper, by using the bosonization approach and the renormlizationgroup analysis, we study the ground state phase diagram of 1-D extended Hub-bard model at half-filling in the weak-coupling regime. This model is definedby adding an nearest-neighbor repulsive interaction term(V) which is compa-rable to the on-site repulsive interaction term(U) but less than the hoppingterm(t) to the conventional Hubbard model. The added term is nontrivial andwill complete with t and U, rendering the change of the low-energy excitation.By explicitly incorporating the contributions from all terms in the Hamilto-nion, we find that the spin-charge coupling term(g_cs) can be neglected as anirrelevant operator in the very small U and V and that the phase diagramconsists of spin-density-wave(SDW) and charge-density-wave(CDW). However,with the gradual increase of U and V, the spin-charge coupling term will playan important role. Near the U = 2V line, another phase bond-charge-density-wave(BCDW) forms. This new phase is situated in the very narrow regimebetween the CDW and SDW states and terminates at a tricritical point. Theseresults show that the phase diagram consists of three distinct states in theweak regime: (i) U > 2V , the ground state is dominated by the SDW corre-lation, (ii) U < 2V , the ground state is dominated by the CDW correlation,(iii) U≈2V , the ground state is dominated by the BCDW correlation. Toclarify the mechanism of the phase transition, we also investigate the propertyof the phase transition, and find that the transition is of the second order inthe weak-coupling theory while it is of first order in the strong-coupling theory.