The ground state of the one-dimensional t-J model coupled with phonons in the adiabatic limit is numerically investigated by use of the Lanczos technique at quarter filling. Due to the interplay between the electron-electron Coulomb repulsion and electron-phonon interaction, this model shows a sequence of lattice distortions leading to the formation of charge-density-waves and bondorder-waves. Moderate electron-electron and electron-lattice coupling may lead to coexistence of dimerization and tetramerization in the distortion pattern. Dimerization leads to the formation of an "antiferromagnetic" Mott insulator, while tetramerization gives rise to a spin-Peierls phase. By increasing the super-exchange coupling, antiferromagnetism is inhibited due to the change of the distortion periodicity.
We show the importance of both strong frustration and spin-lattice coupling for the stabilization of magnetization plateaus in translationally invariant two-dimensional systems. We consider a frustrated spin-1/2 Heisenberg model coupled to adiabatic phonons under an external magnetic field. At zero magnetization, simple structures with two or at most four spins per unit cell are stabilized, forming dimers or 2 × 2 plaquettes, respectively. A much richer scenario is found in the case of magnetization m = 1/2, where larger unit cells are formed with non-trivial spin textures and an analogy with the corresponding classical Ising model is detectable. Specific predictions on lattice distortions and local spin values can be directly measured by X-rays and Nuclear Magnetic Resonance experiments.PACS numbers: 75.10. Jm, 71.27.+a, 74.20.Mn A magnetization plateau occurs when the magnetization remains constant over a range ∆h of applied magnetic fields. The width of the plateau can be expressed in term of the excitation spectrum ∆h = E(M + 1) − 2E(M ) + E(M − 1), where E(M ) is the total energy at fixed magnetization M (measured in units of gµ B ). This, in turn, implies that the energy (per site) as a function of the magnetization (per site) displays a cusp-like singularity in the thermodynamic limit. In general, plateaus are absent in classical models with magnetic ground states whenever the magnetization is not collinear with the field.[1] Instead, they identify particularly stable quantum phases characterized by a spin gap.Usually, gaps in the excitation spectrum directly reflect the structure of the primitive cell of the lattice according to the commensurability condition [2] ℓS(1 − m) = integer (1) where S is the magnitude of the spin, m the magnetization per site in units of gµ B S (i.e., the average onsite spin component parallel to the magnetic field), and ℓ the number of spins in the primitive cell. Some evidence for a m = 1/3 plateau has been proposed for the triangular lattice, [9,10] while in the square lattice, the m = 0 properties of the J 1 −J 2 model are still debated. Indeed, although for J 2 /J 1 ∼ 1/2 the ground state is believed to be disordered, the existence of a finite triplet gap is much less clear, [11,12] casting some doubt as to the possibility of having an m = 0 plateau. The interest in the J 1 −J 2 model has grown due to the recent discovery of two materials well described by a two-dimensional (2D) quantum antiferromagnet, i.e., Li 2 VOSiO 4 and VOMoO 4 . [13,14] Although the experimental magnetization curve of these compounds has not yet been considered, the magnetization properties of the J 1 −J 2 model have been recently considered by using exact diagonalization calculations, leading to some evidence in favor of a magnetization plateau at m = 1/2. [15] This outcome has been interpreted as a consequence of the emergence of a 2 × 2 super-cell. According to this scenario, inside each cell the magnetic moments acquire a preferential orientation along the direction of the magnetic field, lea...
We investigate the nature of the ground state of the one-dimensional t-J model coupled to adiabatic phonons by use of the Lanczos technique at quarter filling. Due to the interplay between electron-electron and electron-phonon interactions, the model undergoes instabilities toward the formation of lattice and charge modulations. Moderate on-site and intra-site electron-phonon couplings lead to a competition of different spin-Peierls and dimerized states. In the former case two electrons belong to the unit cell and we expect a paramagnetic band insulator state, while lattice dimerization leads to a Mott insulating state with quasi long range antiferromagnetic order. The zero temperature phase diagram is obtained as a function of intra-site and inter-site electron-phonon couplings, analytically in the $J\to 0$ limit and numerically at finite J/t.Comment: 7 pages, 7 figures, to be published in Phys. Rev.
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