Journal of Physics Condensed Matter

The generalized Hubbard model in one dimension: a renormalization group study

Bibhas Bhattacharyya, Shreekantha Sil

Published Feb 12, 1996• 2 citations

Abstract

Figure 2 of the above paper contained a small numerical error. The correct version is shown below. Figure 2. The phase diagram of the extended Hubbard model. The phase boundary obtained in the present scheme (solid line) is compared with that obtained in the FS scheme (dotted line) and the Monte Carlo results. The dashed line U = 2V gives the phase boundary in the atomic limit (t = 0) between a singly occupied paramagnetic phase and a CDW region. No other part of the paper is affected by this error.

DOI: 10.1088/0953-8984/8/7/015

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Journal of Physics Condensed Matter

The generalized Hubbard model in one dimension: a renormalization group study

Bibhas Bhattacharyya, Shreekantha Sil

Published Feb 12, 1996• 2 citations

Publisher

Abstract

DOI: 10.1088/0953-8984/8/7/015

Related papers

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

G. P. Zhang

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arXiv:cond-mat/0308157Physical Review BJan 15, 200478 citations

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

Nikolay V. Prokof'ev, Boris V. Svistunov

arXiv:cond-mat/9706169Physical Review LettersMay 11, 199850 citations

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,

the critical value of

{V}_{c}

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

U

increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at

{U}_{c}=4--6,

not

{U}_{c}=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=4M

than for chains of

N=4M+2,

where

M

is an integer, for the same

U

and

V.

The difference will diminish in the thermodynamic limit.

{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.

(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.