Ground-state properties of the one-dimensional attractive Hubbard model with confinement: A comparative study (original) (raw)
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Journal of Physics: Condensed Matter, 2011
We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including among others bicritical, tricritical, critical-end and isolated critical points.
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.
One-dimensional pair-hopping and attractive Hubbard models: A
2008
The low-energy physics of the one-dimensional Pair-Hopping (PH) and attractive Hubbard models are expected to be similar. Based on numerical calculations on small chains, several authors have recently challenged this idea and predicted the existence of a phase transition at half-filling and finite positive coupling for the pair-hopping model. We reexamine the controversy by making systematic comparisons between numerical results obtained for the PH and attractive Hubbard models. To do so, we have calculated the Luttinger parameters (spin and charge velocities, stiffnesses, etc...) of the two models using both the Density Matrix Renormalization Group method for large systems and Lanczós calculations with twisted boundary conditions for smaller systems. Although most of our results confirm that both models are very similar we have found some important differences in the spin properties for the small sizes considered by previous numerical studies (6-12 sites). However, we show that these differences disappear at larger sizes (14-42 sites) when sufficiently accurate eigenstates are considered. Accordingly, our results 1 strongly suggest that the ground-state phase transition previously found for small systems is a finite size artefact. Interpreting our results within the framework of the Luttinger liquid theory, we discuss the origin of the apparent contradiction between the predictions of the perturbative Renormalization group approach and numerical calculations at small sizes.
One-dimensional pair hopping and attractive Hubbard models: A comparative study
Physical Review B, 1996
The low-energy physics of the one-dimensional Pair-Hopping (PH) and attractive Hubbard models are expected to be similar. Based on numerical calculations on small chains, several authors have recently challenged this idea and predicted the existence of a phase transition at half-filling and finite positive coupling for the pair-hopping model. We re-examine the controversy by making systematic comparisons between numerical results obtained for the PH and attractive Hubbard models. To do so, we have calculated the Luttinger parameters (spin and charge velocities, stiffnesses, etc...) of the two models using both the Density Matrix Renormalization Group method for large systems and Lancz\'os calculations with twisted boundary conditions for smaller systems. Although most of our results confirm that both models are very similar we have found some important differences in the spin properties for the small sizes considered by previous numerical studies (6-12 sites). However, we show that these differences disappear at larger sizes (14-42 sites) when sufficiently accurate eigenstates are considered. Accordingly, our results strongly suggest that the ground-state phase transition previously found for small systems is a finite size artefact. Interpreting our results within the framework of the Luttinger liquid theory, we discuss the origin of the apparent contradiction between the predictions of the perturbative Renormalization group approach and numerical calculations at small sizes.
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.
Ground-state properties of the one-dimensional Hubbard model with pairing potential
Physica B: Condensed Matter, 2020
We consider a modification of the one-dimensional Hubbard model by including an external pairing potential. We determine the grand-canonical zero-temperature phase diagram using both finite and infinite density matrix renormalization group algorithm based on the formalism of matrix product states and matrix product operator, respectively. By computing various local quantities as well as the half-system entanglement, we are able to distinguish between Mott, metallic and superconducting phases. We point out the compressible nature of the Mott phase and the fully gaped nature of the many-body spectrum of the superconducting phase, in the presence of explicit U(1)-charge symmetry breaking.
Role of the attractive intersite interaction in the extended Hubbard model
The European Physical Journal B, 2008
We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination number z. By using the equations of motion formalism, the model is exactly solved for both attractive and repulsive intersite potential V. By focusing on the case of negative V , i.e., attractive intersite interaction, we study the phase diagram at finite temperature and find, for various values of the filling and of the on-site coupling U , a phase transition towards a state with phase separation. We determine the critical temperature as a function of the relevant parameters, U/|V |, n and z and we find a reentrant behavior in the plane (U/|V |,T). Finally, several thermodynamic properties are investigated near criticality.
Optimized effective potential for the extended Hubbard model
Physical Review B, 1999
Antiferromagnetic and charge ordered Hartree-Fock solutions of the one-band Hubbard model with on-site and nearest-neighbor Coulomb repulsions are exactly mapped onto an auxiliary local Kohn-Sham (KS) problem within a density-functional theory. The mapping provides a new insight into the interpretation of the KS equations. (i) With an appropriate choice of the basic variable, there is a universal form of the KS potential, which is applicable both for the antiferromagnetic and the charge ordered solutions. (ii) The Kohn-Sham and Hartree-Fock eigenvalues are interconnected by a scaling transformation. (iii) The band-gap problem is attributed to the derivative discontinuity of the basic variable as the function of the electron number, rather than a finite discontinuity of the KS potential. (iv) It is argued that the conductivity gap and the energies of spin-wave excitations can be entirely defined by the parameters of the ground state and the KS eigenvalues.
Partially filled linear Hubbard model near the atomic limit
Physical Review B
The linear Hubbard model is considered when the intrasite Coulomb repulsion is very large compared to the intersite charge-transfer interaction. The solution for a general density of electrons per site is carried out by a perturbative treatment which relates this Hubbard model to a generalized Heisenberg spin Hamiltonian describing effective exchange interactions between {partially) delocalized electrons. Accurate numerical results for the linear Heisenberg model are employed to obtain good estimates of the static thermodynamic properties for Hubbard models near the atomic limit. Some modifications of the simple Hubbard model are also briefly discussed.