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Physical review. B, Condensed matter

Phase diagram and correlation functions of the half-filled extended Hubbard model in one dimension

Johannes Voit

Published Feb 15, 1992• 142 citations
Publisher

Abstract

The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.

DOI
10.1103/physrevb.45.4027

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The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.
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.
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 examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.
Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction V)V)V) at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from the renormalization of the Umklapp- and the backward-scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the $\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{SU}(2)$ symmetry of the electron system. Near the U=2VU=2VU=2V line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term, which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-VVV region involving spin-gap and BKT-type metal-insulator transitions.
A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction T∗{T}^{*}T∗ is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.
We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on-site interaction U and a nearest-neighbor interaction V. We focus on the ground state phases of the model in the $V\ensuremath{\gg}U$ region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=VPS.{V=V}_{\mathrm{PS}}.V=VPS​. Using quantum Monte Carlo methods on lattices much larger than in previous Lancz\"os diagonalization studies, we determine the boundary of phase separation, the Luttinger-liquid correlation exponent ${K}_{\ensuremath{\rho}},$ and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state reenters from phase separation as the electron density is increased towards half filling. For V<VPS,V<{V}_{\mathrm{PS}},V<VPS​, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger liquid with ${K}_{\ensuremath{\rho}}<1,$ but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger liquid.