Journal of the Physical Society of Japan

Fractionally Charged Solitons in “1100” Charge Order Backgrounds

Kenichi Hirokawa, Akira Terai, Yoshiyuki Ono

Published Feb 17, 2015• 0 citations

Abstract

We reconsider the problem of “binding” of a pair of fractionally charged solitons in “1100” charge order backgrounds, using the variational Monte Carlo method based on the matrix-product state. In the “1100” charge order ground state of the one-dimensional extended Peierls–Hubbard model, the 2kF bond order wave (BOW) coexists with the 4kF BOW. We have found that the fractionally charged soliton with −e/2, −e being an electronic charge, is accompanied with not only a kink in the 2kF BOW but also a kink in the 4kF BOW, which was not allowed to exist in the dimer model used in the previous study. Calculating the total energy of a pair of fractionally charged solitons with the same charge as a function of the soliton–soliton distance, we have found that the soliton–soliton interaction is repulsive. Therefore the “binding” of the solitons does not occur and the elementary charge excitation from the “1100” charge order ground state is a fractionally charged soliton.

DOI: 10.7566/jpsj.84.034707

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Journal of the Physical Society of Japan

Fractionally Charged Solitons in “1100” Charge Order Backgrounds

Kenichi Hirokawa, Akira Terai, Yoshiyuki Ono

Published Feb 17, 2015• 0 citations

Publisher

Abstract

DOI: 10.7566/jpsj.84.034707

Related papers

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The stationary states of a half-filled Peierls-Hubbard chain are calculated. To describe electron correlations, the wave functions as antisymmetrized products of strongly orthogonal geminals are used; wave functions and bond lengths are determined self-consistently by the variational method in an N=50 ring. The neutral soliton pair ${S}^{0}$ ${S}^{0}$ is obtained as corresponding to a local total-energy minimum above the perfectly dimerized ground state. The charged soliton pair ${S}^{+}$ ${S}^{\mathrm{\ensuremath{-}}}$ refers to the minimum in the subspace of wave functions which are odd with respect to charge conjugation. The creation energies for each of the pairs are estimated as functions of Hubbard parameter U and compared with the exact excitation energies of the uniform Hubbard chain. The electron correlation is shown to make the in-gap ${S}^{0}$ ${S}^{0}$ state stable even for a moderate electron-lattice coupling; the soliton width turns out to be much smaller than that in the U=0 model and comparable with the lattice constant. Applicability of the results to polyacetylene is discussed.The stationary states of a half-filled Peierls-Hubbard chain are calculated. To describe electron correlations, the wave functions as antisymmetrized products of strongly orthogonal geminals are used; wave functions and bond lengths are determined self-consistently by the variational method in an N=50 ring. The neutral soliton pair ${S}^{0}$${S}^{0}$ is obtained as corresponding to a local total-energy minimum above the perfectly dimerized ground state. The charged soliton pair ${S}^{+}$${S}^{\mathrm{\ensuremath{-}}}$ refers to the minimum in the subspace of wave functions which are odd with respect to charge conjugation. The creation energies for each of the pairs are estimated as functions of Hubbard parameter U and compared with the exact excitation energies of the uniform Hubbard chain. The electron correlation is shown to make the in-gap ${S}^{0}$${S}^{0}$ state stable even for a moderate electron-lattice coupling; the soliton width turns out to be much smaller than that in the U=0 model and comparable with the lattice constant. Applicability of the results to polyacetylene is discussed.

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{E}_{m}

for on-site repulsion $U<{U}^{\ensuremath{\ast}}$, the critical point, and nearest-neighbor interaction ${V}_{c}\ensuremath{\approx}U/2$ near the boundary of the charge-density wave (CDW) phase. Potentials with more extended interactions that retain the EHM symmetry are shown to have a less cooperative CDW transition with higher ${U}^{\ensuremath{\ast}}$ and wider BOW phase. Density-matrix renormalization group is used to obtain

{E}_{m}

directly as the singlet-triplet gap, with finite

{E}_{m}

marking the BOW boundary

{V}_{s}(U)

. The BOW/CDW boundary

{V}_{c}(U)

is obtained from exact finite-size calculations that are consistent with previous EHM determinations. The kinetic energy or bond order provides a convenient new estimate of ${U}^{\ensuremath{\ast}}$ based on a metallic point at

{V}_{c}(U)

for $U<{U}^{\ensuremath{\ast}}$. Tuning the BOW phase of half-filled Hubbard models with different intersite potentials indicates a ground state with large charge fluctuations and magnetic frustration. The possibility of physical realizations of a BOW phase is raised for Coulomb interactions.

0.5

for the parameters we have considered. We also discuss advantages of using parallel tempering (or exchange Monte Carlo)---an extended ensemble method that we here combine with quantum Monte Carlo---in studies of quantum phase transitions.

{S}^{0}

{S}^{0}

is obtained as corresponding to a local total-energy minimum above the perfectly dimerized ground state. The charged soliton pair

{S}^{+}

${S}^{\mathrm{\ensuremath{-}}}$ refers to the minimum in the subspace of wave functions which are odd with respect to charge conjugation. The creation energies for each of the pairs are estimated as functions of Hubbard parameter U and compared with the exact excitation energies of the uniform Hubbard chain. The electron correlation is shown to make the in-gap

{S}^{0}

{S}^{0}

state stable even for a moderate electron-lattice coupling; the soliton width turns out to be much smaller than that in the U=0 model and comparable with the lattice constant. Applicability of the results to polyacetylene is discussed.