Correlation Effect on Peierls Transition

Abstract

The effect of correlation on Peierls transition, which is accompanied by a dimerization, t d , of a bond alternation for transfer energy, has been examined for a half-filled one-dimensional electron system with on-site repulsive interaction (U ). By applying the renormalization group method to the interaction of the bosonized Hamiltonian, the dimerization has been calculated variationally and self-consistently with a fixed electron-phonon coupling constant (λ) and it is shown that t d takes a maximum as a function of U . The result is examined in terms of charge gap and spin gap and is compared with that of the numerical simulation by Hirsch [Phys. Rev. Lett 51 (1983) 296]. Relevance to the spin Peierls transition in organic conductors is discussed. KEYWORDS: Peierls transition, Hubbard model, dimerization, renormalization, charge gap, spin gapPeierls transition for a one-dimensional half-filled electron system coupled with phonon has been studied extensively since the Su-Schrieffer-Heeger model was proposed for the quasi-one-dimensional conductor polyacetylene with a bond alternation.1) The role of correlation in such a model has been examined by introducing an onsite repulsive interaction, U . The calculation using the Hartree-Fock approximation leads to the Peierls state, which exists only for U smaller than a critical value of the order of the band width.2, 3) This study has been further developed by taking into account a one-dimensional quantum fluctuation. The numerical simulation exhibits an enhancement of dimerization in the presence of repulsive interaction. 4,5,6,7,8,9) A notable finding is that the dimerization takes a maximum at a value of U being nearly the band width 5,8,9) and that the charge gap becomes much larger than the dimerization gap.5) Regarding the case of weak coupling, the analytical method of a renormalization group (RG) has also exhibited the enhancement of t d as a function of U .10) The effect of finite phonon frequency has been explored using the RG method based on the bosonization.11, 12, 13) It has been shown that the half-filled case leads to a competition between the state with both spin and charge gaps and the state with only a charge gap on the plane of the phonon frequency and the electron-phonon coupling constant.13) In contrast, the case of strong coupling with large U has been examined in terms of the opposite approach, i.e., the expansion of 1/U ) and mapping the electron system into a spin 1/2 chain system, which leads to the spin Peierls transition. The successful treatment of the quantum fluctuation leads to the occurrence of the spin Peierls transition for an arbitrary magnitude of the electron-phonon coupling constant.

Quantum phase transition in the one-dimensional extended Peierls-Hubbard model

“…The low-energy regime can be described by linearising the non-interacting Fermi spectrum around the Fermi-points ±π/2a 0 , where a 0 is the lattice spacing. Applying a bosonization scheme [2,12] in terms of two Bose fields Φ c and Φ s corresponding to collective charge and spin degrees of freedom respectively we arrive at the following form of the low-energy Hamiltonian [7,8,13]…”

“…The effects of weak electron-electron interactions in a Peierls insulator were investigated in [6] by perturbative methods. Most importantly for our purposes, the weak-coupling regime U, |V | t was studied in Refs [7,8]. From the structure of the classical ground state of the bosonized low-energy effective Hamiltonian Tsuchiizu and Furusaki showed that increasing the dimerization δ from zero for a sufficiently large V drives the system through a quantum critical point that was argued to be in the universality class of the two-dimensional Ising model [9].…”

Suppression of the Peierls instability in 1D system: Semi-local approach to Little’s conjecture

“…Not only a Mott insulator is produced for U ) jt 0 j but the intriguing behavior in the low-U regime can be understood from our inspection. Even though the correlation effects have been debated in the literature [14,24,25], our approach provides some original insights into the underlying phenomenon we would like to comment on. Indeed, the spin-exchange CE (see Fig.…”

“…Hückel limit) [11]. Monte Carlo techniques [12][13][14] and more recently cluster perturbation theory [15,16] have produced a wealth of information on various problems. Besides, the ground state phase diagram of 1D half-filled Hubbard systems has been thoroughly inspected by means of renormalization-group approaches [17][18][19].…”

Correlation Effect on the Two-Dimensional Peierls Phase

“…In this system the lattice distortion which has a wave number Q π plays a very important role in the all range of e-e interaction parameter [1].…”