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Weak-coupling Ground State Phase Diagram of the One-dimensional Extended Hubbard Model

Haiming Duan

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

By using the bosonization approach and renormalization group analysis,we study the ground state phase diagram of one-dimensional extended Hubbard model at half-filling in the regime where U and V are both positive but less than t, finding that the system shows three distinct ground states characterized by the spin-density-wave,the charge-density-wave and the bond-charge-density-wave,respectively.These results demonstrate that the ground state phases of the extended Hubbard model are not identical with those of the conventional Hubbard model.

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Physical review. B, Condensed matter•Oct 2, 2003•28 citations
By using the bosonization approach and renormalization group analysis,we study the ground state phase diagram of one-dimensional extended Hubbard model at half-filling in the regime where U and V are both positive but less than t, finding that the system shows three distinct ground states characterized by the spin-density-wave,the charge-density-wave and the bond-charge-density-wave,respectively.These results demonstrate that the ground state phases of the extended Hubbard model are not identical with those of the conventional Hubbard model.
In the weak-coupling regime, we analytically investigate phase diagram of a one-dimensional half-filled extended Hubbard model with nearest neighboring four-electron interaction (Q), in addition to the usual two-electron couplings (U,V>0). The additional four-electron coupling splits independent Gaussian and spin-gap transitions and also leads to the charge-gap transition. For the positive Q, the ground state exhibits three insulating phases, charge-density-wave (CDW), spin-density-wave (SDW) and bond-spin-density-wave (BSDW). For the negative Q, the phase diagram consists of five phases, which, besides the SDW and CDW phases, contain bond-charge-density-wave (BCDW), Luttinger liquid (LL) and Luther–Emery (LE) phases.
We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.
A half-filled one-dimensional (1D) extended Hubbard model (U-V_⊥-V_∥) with on-site and nearest-neighbor spin-dependent interactions is studied analytically. The ground state phase diagram is obtained in the weak-coupling regime by performing the bosonization and renormalization group methods. The result shows that the nearest-neighbor spin-dependent attraction influences the low-energy physics of the 1D correlated electron system, and changes the topological structure of the ground state phase diagram of the U-V model.
Using functional renormalization group method, we studied the phase diagram of the one-dimensional extended Hubbard model at different dopings. At half filling, variety of states strongly compete with each other. These states include spin-density wave, charge-density wave, s-wave and p -wave superconductivity, phase separation, and an exotic bond-order wave. By doping, system favours superconductivity more than density waves. At 1/8 doping, a new area of extended s-wave superconductivity emerges between charge density wave and bond-order wave regions. If the system is doped to 1/4-doping, a new area of p -wave superconductivity emerges between charge-density wave and spin-density wave regions.
The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.
It has been well established that in both the weak- and strong-coupling limits, the phase transition from a spin-density wave (SDW) to a charge-density wave (CDW) in the half-filled extended-Hubbard model occurs precisely at the ratio U/Vc=2,{U/V}_{c}=2,U/Vc​=2, where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.