Spin density wave selection in the one-dimensional Hubbard model (original) (raw)
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Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model
2004
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 weakcoupling renormalization-group approach (g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for U ≈ 2V in between charge-densitywave (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 ∆ or bond alternation δ. Although the alternating site potential ∆ 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, 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 δ 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 δ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of ∆ or δ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.
Phase separation in the one-dimensional Hubbard model
1996
The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the µ − U plane, restricted to phases with no charge density modulation. This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell ↑↑↓↓. The spiral phase is unstable against phase separation near quarter-, half-and three-quarter-filling. For large U this occurs at hole (or electron) doping of (3t/π 2 U ) 1/3 from half filling.
Nature of ground states in one-dimensional electron-phonon Hubbard models at half filling
Physical Review B, 2015
The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half-filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the (U, g ph) plane for the phonon-mediated interaction g ph and the Coulomb interaction U. The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency ω0. We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical U * ≈ g * ph , followed at larger U ∼ g ph by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on U. For the Peierls-Hubbard model, the region of the (U, g ph) plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency ωD decreases. A power law dependence g ph ∼ U 2η is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term V is added to the Hubbard interaction.
Influence of spin-wave excitations on the ferromagnetic phase diagram in the Hubbard model
Physical Review B, 2002
The subject of the present paper is the theoretical description of collective electronic excitations, i.e. spin waves, in the Hubbard-model. Starting with the widely used Random-Phase-Approximation, which combines Hartree-Fock theory with the summation of the two-particle ladder, we extend the theory to a more sophisticated single particle approximation, namely the Spectral-Density-Ansatz. Doing so we have to introduce a 'screened' Coulomb-interaction rather than the bare Hubbard-interaction in order to obtain physically reasonable spinwave dispersions. The discussion following the technical procedure shows that comparison of standard RPA with our new approximation reduces the occurrence of a ferromagnetic phase further with respect to the phasediagrams delivered by the single particle theories.
Physical Review B, 2003
The Hubbard-Holstein model is studied at half filling in one dimension using a variational method based on the variable-displacement Lang-Firsov canonical transformation and the exact solution to the Hubbard model due to Lieb and Wu. It is usually believed that the system undergoes a direct insulator-to-insulator transition from charge-density wave ͑CDW͒ to spin-density wave ͑SDW͒ with the increase of the on-site Coulomb repulsion U for a given strength of the electron-phonon coupling. Here, we show indications that, at least in the antiadiabatic region, an intervening metallic state may exist in the crossover region of the CDW-SDW transition.
Phase diagram of the one-dimensional Hubbard-Holstein model at quarter filling
Physical Review B, 2010
We derive an effective Hamiltonian for the one-dimensional Hubbard-Holstein model, valid in a regime of both strong electron-electron (e-e) and electron-phonon (e-ph) interactions and in the nonadiabatic limit (t/ω0≤1), by using a nonperturbative approach. We obtain the phase diagram at quarter filling by employing a modified Lanczos method and studying various density-density correlations. The spin-spin AF (antiferromagnetic) interactions and nearest-neighbor repulsion, resulting from the e-e and the e-ph interactions, respectively, are the dominant terms (compared to hopping) and compete to determine the various correlated phases. As e-e interaction (U/t) is increased, the system transits from an AF cluster to a correlated singlet phase through a discontinuous transition at all strong e-ph couplings 2≤g≤3 considered. At higher values of U/t and moderately strong e-ph interactions (2≤g≤2.6), the singlets break up to form an AF order and then to a paramagnetic order all in a single sublattice; whereas at larger values of g (>2.6), the system jumps directly to the spin disordered charge-density-wave (CDW) phase.
Incommensurate spin-density wave in two-dimensional Hubbard model
2011
We consider the magnetic phase diagram of the two-dimensional Hubbard model on a square lattice. We take into account both spiral and collinear incommensurate magnetic states. The possibility of phase separation of spiral magnetic phases is taken into consideration as well. Our study shows that all the listed phases appear to be the ground state at certain parameters of the
Spiral magnetism in the single-band Hubbard model: the Hartree–Fock and slave-boson approaches
Journal of Physics: Condensed Matter, 2015
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for different two-and three-dimensional lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.