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arXiv:cond-mat/0401490 · Physical Review B

Comment on “Accurate ground-state phase diagram of the one-dimensional extended Hubbard model at half filling”

Eric Jeckelmann

Published May 4, 2005• 8 citations
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Abstract

It is shown that Guoping Zhang's results [G. P. Zhang, Phys. Rev. B 68, 153101 (2003)] for the charge-density wave-phase boundary in the half-filled one-dimensional extended Hubbard model are incorrect and that his criticism of my work [E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)] is groundless.
DOI
10.1103/physrevb.71.197101

Related papers

Reply to “Comment on ‘Accurate ground-state phase diagram of the one-dimensional extended Hubbard model at half filling’ ”

G. P. Zhang

We respond to Jeckelman's Comment on our paper [G. P. Zhang, Phys. Rev. B 68, 153101 (2003)], which discusses his previous work [E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)]. We feel that it is important to point out that his previous results show a trend contradicting the weak-coupling limit, a conclusion that is independent of our calculation. Therefore, our comments on his previous results remain valid and our conclusion is unchanged.

Physical Review B•May 4, 2005•2 citations

Comment on “Ground-State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model”

Anders W. Sandvik, Pinaki Sengupta, David K Campbell

In Phys. Rev. Lett. 89, 236401 (2002), Jeckelmann argued that the recently discovered bond-order-wave (BOW) phase of the 1D extended Hubbard model does not have a finite extent in the (U,V) plane, but exists only on a segment of a first-order SDW-CDW phase boundary. We here present quantum Monte Carlo result of higher precision and for larger system sizes than previously and reconfirm that the BOW phase does exist a finite distance away from the phase boundary, which hence is a BOW-CDW transition curve.

arXiv:cond-mat/0301237•Physical Review Letters•Aug 20, 2003•27 citations

Accurate ground-state phase diagram of the one-dimensional extended Hubbard model at half filling

G. P. Zhang

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 ${U/V}_{c}=2,$ 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.

Physical review. B, Condensed matter•Oct 2, 2003•28 citations

Jeckelmann Replies:

Eric Jeckelmann

In their Comment (see cond-mat/0301237), Sandvik, Sengupta, and Campbell present some numerical evidences to support the existence of an extended bond-order-wave (BOW) phase at couplings (U,V) weaker than a tricritical point (U_t,V_t) in the ground state phase diagram of the one-dimensional half-filled U-V Hubbard model. They claim that their results do not agree with the phase diagram proposed in my Letter (cond-mat/0204244), which shows a BOW phase for couplings stronger than the critical point only. However, I argue here that their results are not conclusive and do not refute the phase diagram described in the Letter.

arXiv:cond-mat/0308446•Physical Review Letters•Aug 20, 2003•15 citations

Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model

Masahisa Tsuchiizu, Akira Furusaki

We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach $(g$-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads 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 second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. $83,$ 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.

arXiv:cond-mat/0308157•Physical Review B•Jan 15, 2004•78 citations

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

Haiming Duan

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.

Shinjang dashösi ilmiy jurnili•Jan 1, 2007•0 citations
In Phys. Rev. Lett. 89, 236401 (2002), Jeckelmann argued that the recently discovered bond-order-wave (BOW) phase of the 1D extended Hubbard model does not have a finite extent in the (U,V) plane, but exists only on a segment of a first-order SDW-CDW phase boundary. We here present quantum Monte Carlo result of higher precision and for larger system sizes than previously and reconfirm that the BOW phase does exist a finite distance away from the phase boundary, which hence is a BOW-CDW transition curve.
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.
In their Comment (see cond-mat/0301237), Sandvik, Sengupta, and Campbell present some numerical evidences to support the existence of an extended bond-order-wave (BOW) phase at couplings (U,V) weaker than a tricritical point (U_t,V_t) in the ground state phase diagram of the one-dimensional half-filled U-V Hubbard model. They claim that their results do not agree with the phase diagram proposed in my Letter (cond-mat/0204244), which shows a BOW phase for couplings stronger than the critical point only. However, I argue here that their results are not conclusive and do not refute the phase diagram described in the Letter.
We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g(g(g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads 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 second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83,83,83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.
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.