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Journal of the Physical Society of Japan

Collective Modes of Incommensurate Spin Density Wave in One-Dimensional Hubbard Model

Masanori Ichioka, Eiji Kaneshita, Kazushige Machida

Published Mar 15, 2001• 12 citations
Publisher

Abstract

Dynamical spin and charge susceptibility and collective modes are studied in the framework of the random phase approximation. They are calculated from the wave function of the selfconsistently obtained ground state, including all possible higher harmonics components of the ordering vector Q . We investigate a spin wave excitation in the spin transverse mode, and phason excitation related to the domain-wall motion in the spin longitudinal and charge modes. We consider the dispersion curve of the collective mode, and discuss the dependence on the on-site U interaction and the period of the incommensurate structure.

DOI
10.1143/jpsj.70.818

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Physical review. B, Condensed matter•Nov 1, 1992•41 citations
Dynamical spin and charge susceptibility and collective modes are studied in the framework of the random phase approximation. They are calculated from the wave function of the selfconsistently obtained ground state, including all possible higher harmonics components of the ordering vector Q . We investigate a spin wave excitation in the spin transverse mode, and phason excitation related to the domain-wall motion in the spin longitudinal and charge modes. We consider the dispersion curve of the collective mode, and discuss the dependence on the on-site U interaction and the period of the incommensurate structure.
We investigate collective modes of the incommensurate spin-density wave state for a one-dimensional two-band model within the random phase approximation. For this model, compact expressions of the two-particle Green functions can be obtained. Three types of collective modes are found; an amplitude mode, a phase mode in a real space (a sliding mode) and a phase mode in a spin space (a spin wave mode). The amplitude mode appears in the longitudinal susceptibility and the spin wave mode appears in the transverse susceptibility, but the sliding mode is found to have no contribution to the susceptibilityes. The amplitude mode has the same energy with the energy gap of single particle excitations, but if it is couplied with phonons, its frequency is lowered and it makes a mid-gap mode.
The collective modes representing density fluctuation in a spin density wave (SDW) have been examined for a one-dimensional electron system of a quarter-filled extended Hubbard model with the next-nearest-neighbor interaction ( V 2 ). Within the random phase approximation (RPA), we obtain a new collective mode, which appears with increasing V 2 . The mode describes the relative motion between density wave with up spin and that with down spin. The gap in the excitation spectrum vanishes at a critical value of V 2 corresponding to the onset of the coexistence of 2 k F -SDW, 2 k F -charge density wave and 4 k F -SDW in the ground state ( k F being the Fermi wave vector).
We investigate the structure of the pairing potential in the stripe phase of the two-dimensional Hubbard model. Based on the random-phase approximation we discuss in detail the interactions in the charge and spin channel and compare our calculations with related considerations in commensurate antiferromagnets. Our main finding is that due to the incommensurate charge-density wave formation the exchange of collective modes in the charge channel is significantly enhanced with respect to the spin-bag approach whereas due to the inhomogeneous charge distribution the coupling to transverse spin fluctuations tends to be suppressed.
The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2 D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω ( Q )= c | Q −(π, π)| near Q ∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X ″( Q,ω →0) gives the same mode with a peak at Q ∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X ″( Q,ω →0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector.
A variational estimate for the spin-wave velocity of the one-band Hubbard model on a square lattice in the spin-density-wave regime is studied. The estimate is given by the ratio of the f-sum rule to the static structure factor of the transverse-spin response function. The known results for the Heisenberg model are used to obtain results for those quantities in the large-U limit of the Hubbard model. The f-sum rule and static structure factor are calculated using the random-phase approximation (RPA). The spin-wave velocity calculated in the RPA, in the spin-density wave ground state, violates the variational bound.
By use of a diagrammatic method we determine the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. The energy of the collective modes, given by the poles of these response functions, is found to be a linear function of the wave vector (for small k and short-range intersite interaction) with the velocity interpolating smoothly between the weak- (\ensuremath{\propto}2zt, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\ll}2zt) and strong-coupling (\ensuremath{\propto}zt2{\mathit{zt}}^{2}zt2/\ensuremath{\Vert}U\ensuremath{\Vert}, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}2zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong-coupling limit. The numerical analysis for a two-dimensional (2D) square lattice shows the occurrence of a rotonlike minima near the zone boundary. In the weak-coupling regime we find that apart from a commensurate charge-density-wave (CDW) instability, an increase in the intersite Coulomb repulsion can give rise to a CDW incommensurate with the lattice period, away from half-filling. The resulting phase diagram for the 2D square lattice, including a singlet superconducting ground state, electronic-droplet formation, and CDW's, is determined. Finally, the effects of a long-range Coulomb interaction are analyzed briefly and it is shown that the energy of collective excitations evolves smoothly from the weak- to the strong-coupling limit for a 2D lattice.