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Journal of the Physical Society of Japan

The SDW-CDW Phase Transition in the One Dimensional Extended Hubbard Model

Norikazu Tomita, Atsushi Ikawa, Hideo Fukutome

Published Jan 15, 1996• 22 citations
Publisher

Abstract

We study the SDW-CDW phase transition in the one dimensional extended Hubbard model at a half-filling. A scaling analysis using the resonating Hartree-Fock method with the numbers of electrons from 8 to 20 strongly suggests that the ground state is many-fold degenerate( 1 A 1 + , 1 B 1 + , 3 A 2 - , and 3 B 2 - states) in the SDW region while it is doubly degenerate( 1 A 1 + and 1 B 2 - states) in the CDW region. Only the 1 A 1 + state makes a continuous phase transition from the SDW state to the CDW one. The 1 B 1 + , 3 A 2 - , and 3 B 2 - states cross the 1 B 2 - state around the phase boundary. We show that the continuous phase transition in the 1 A 1 + state is brought about by defects connecting the SDW-CDW domains called halfons. The correlation structures of these states are shown to clarify the origin of the degeneracies of the ground states.

DOI
10.1143/jpsj.65.195

Related papers

Elementary Defects, Halfons, Connecting the SDW and CDW in the One Dimensional Extended Hubbard Model

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We show in the Hartree-Fock approximation that electronic defects which are SDW-CDW domain walls exist in the one dimensional extended Hubbard model of half filling. In the vicinity of the SDW-CDW phase boundary, SDW and CDW polarons and charged solitons split into confined pairs of these defects. They become freely mobile along a chain on the phase boundary. They have ±1/4 spins and ±1/2 charges in an equidistant lattice and are called halfons. Halfon pairs can convert smoothly the SDW and CDW and can be major quantum fluctuations in the SDW-CDW phase transition. In a bond alternated lattice their spins and charges, respectively, deviate from 1/4 and 1/2. On the SDW-CDW phase boundary, there exist new density waves called the mixed density waves (MDW). Halfons are classified by their trajectories connecting the SDW and CDW via the MDW. We derive the counting rules to explain their fractional spins and charges.

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An intervening metallic phase at the CDW–SDW transition region in the one-dimensional Holstein-Hubbard model at half filling: a semi-exact solution

Mohammed Zahid Malik, Ashok Chatterjee

Abstract The one-dimensional Holstein–Hubbard model is analyzed at half filling at the CDW-SDW transition region by using a series of unitary transformations. The phonon degrees of freedom are eliminated by averaging the transformed Hamiltonian with respect to a generalized many-phonon state and the resulting effective electronic Hamiltonian is finally solved exactly by employing the Bethe-ansatz technique. The present variational state leads to a lower ground state energy as compared to those obtained from the previous variational calculations and yields a wider intermediate metallic phase at the SDW-CDW transition region confirming the prediction of Takada and Chatterjee.

Journal of Physics Communications•Sep 11, 2020•3 citations
We study the SDW-CDW phase transition in the one dimensional extended Hubbard model at a half-filling. A scaling analysis using the resonating Hartree-Fock method with the numbers of electrons from 8 to 20 strongly suggests that the ground state is many-fold degenerate( 1 A 1 + , 1 B 1 + , 3 A 2 - , and 3 B 2 - states) in the SDW region while it is doubly degenerate( 1 A 1 + and 1 B 2 - states) in the CDW region. Only the 1 A 1 + state makes a continuous phase transition from the SDW state to the CDW one. The 1 B 1 + , 3 A 2 - , and 3 B 2 - states cross the 1 B 2 - state around the phase boundary. We show that the continuous phase transition in the 1 A 1 + state is brought about by defects connecting the SDW-CDW domains called halfons. The correlation structures of these states are shown to clarify the origin of the degeneracies of the ground states.
We show in the Hartree-Fock approximation that electronic defects which are SDW-CDW domain walls exist in the one dimensional extended Hubbard model of half filling. In the vicinity of the SDW-CDW phase boundary, SDW and CDW polarons and charged solitons split into confined pairs of these defects. They become freely mobile along a chain on the phase boundary. They have ±1/4 spins and ±1/2 charges in an equidistant lattice and are called halfons. Halfon pairs can convert smoothly the SDW and CDW and can be major quantum fluctuations in the SDW-CDW phase transition. In a bond alternated lattice their spins and charges, respectively, deviate from 1/4 and 1/2. On the SDW-CDW phase boundary, there exist new density waves called the mixed density waves (MDW). Halfons are classified by their trajectories connecting the SDW and CDW via the MDW. We derive the counting rules to explain their fractional spins and charges.
The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by the Gaussian and the spin-gap transitions under charge-spin separation, or by a direct CDW-SDW transition. We determine these phase boundaries by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and the spin-gap transitions take place separately from weak- to intermediate-coupling region. This means that the third phase exists between the CDW and the SDW states. Our results are also consistent with those of the strong-coupling perturbative expansion and of the direct evaluation of order parameters.
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 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.
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.
Abstract The one-dimensional Holstein–Hubbard model is analyzed at half filling at the CDW-SDW transition region by using a series of unitary transformations. The phonon degrees of freedom are eliminated by averaging the transformed Hamiltonian with respect to a generalized many-phonon state and the resulting effective electronic Hamiltonian is finally solved exactly by employing the Bethe-ansatz technique. The present variational state leads to a lower ground state energy as compared to those obtained from the previous variational calculations and yields a wider intermediate metallic phase at the SDW-CDW transition region confirming the prediction of Takada and Chatterjee.