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Physical Review B

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

G. P. Zhang

Published May 4, 2005• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.71.197102

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

Eric Jeckelmann

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.

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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

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.

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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.

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Ground-state phase diagram of the one-dimensional extended Hubbard model: A density-matrix renormalization-group approach

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Comment on “One-Dimensional Disordered Bosonic Hubbard Model: A Density-Matrix Renormalization Group Study”

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We present the phase diagram of the system obtained by continuous-time worldline Monte Carlo simulations, and demonstrate that the actual phase diagram is in sharp contrast with that found in Phys. Rev. Lett., 76 (1996) 2937.

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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.
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.
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.
We use the density-matrix renormalization group to calculate the phase diagram of the one-dimensional extended Hubbard chain at half filling. We find that for one specific U,U,U, the critical value of Vc{V}_{c}Vc​ for the charge-density-wave versus spin-density-wave phase transition is smaller than that predicted from the Monte Carlo simulation. Our results are consistent with the strong- and weak-coupling limit results, whereas the previous results from the Monte Carlo simulations deviate from the weak-coupling limit result. As UUU increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at Uc=4−−6,{U}_{c}=4--6,Uc​=4−−6, not Uc=3{U}_{c}=3Uc​=3 as previously predicted from the Monte Carlo simulation. Due to the topological difference, we observe that with the periodic boundary condition, the phase transition is more abrupt for finite chains of length N=4MN=4MN=4M than for chains of N=4M+2,N=4M+2,N=4M+2, where MMM is an integer, for the same UUU and V.V.V. The difference will diminish in the thermodynamic limit.