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arXiv:cond-mat/9807083 · Physical review. B, Condensed matter

Improved stability regions for ground states of the extended Hubbard model

Zsolt Szabó

Published Apr 15, 1999• 13 citations
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Abstract

The ground-state phase diagram of the extended Hubbard model containing nearest- and next-to-nearest-neighbor interactions is investigated in the thermodynamic limit using an exact method. It is found that taking into account local correlations and adding next-to-nearest-neighbor interactions both have significant effects on the position of the phase boundaries. Improved stability domains for the $\ensuremath{\eta}$-pairing state and for the fully saturated ferromagnetic state at half-filling have been constructed. The results show that these states are the ground states for model Hamiltonians with realistic values of the interaction parameters.

DOI
10.1103/physrevb.59.10007

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Physical review. B, Condensed matter•Jan 1, 1997•40 citations
The ground-state phase diagram of the extended Hubbard model containing nearest- and next-to-nearest-neighbor interactions is investigated in the thermodynamic limit using an exact method. It is found that taking into account local correlations and adding next-to-nearest-neighbor interactions both have significant effects on the position of the phase boundaries. Improved stability domains for the \ensuremathη\ensuremath{\eta}\ensuremathη-pairing state and for the fully saturated ferromagnetic state at half-filling have been constructed. The results show that these states are the ground states for model Hamiltonians with realistic values of the interaction parameters.
Exact results related to extended Hubbard model containing couplings up to next-nearest-neighbour terms were deduced for restricted regions of parameter space in arbitrary D > 1 dimensions at half-filling and T = 0 temperature. Different types of commensurate charge-density waves and spin-density waves, a ferromagnetic domain and a phase separation region were found, the last being for the first time signalled at the level of approximation-free results in dimensions higher than one. In connection with other presented phases we extended their stability domains in comparison with previously published data. The deduced phase diagram is complete in the localized limit. The dependences on the interaction range and dimension were studied. The obtained results emphasize the importance of next-nearest neighbour terms in the development of ordered phases within the studied system.
Exact results related to extended Hubbard model containing couplings up to next-nearest-neighbour terms were deduced for restricted regions of parameter space in arbitrary D > 1 dimensions at half-filling and T = 0 temperature. Different types of commensurate charge-density waves and spin-density waves, a ferromagnetic domain and a phase separation region were found, the last being for the first time signalled at the level of approximation-free results in dimensions higher than one. In connection with other presented phases we extended their stability domains in comparison with previously published data. The deduced phase diagram is complete in the localized limit. The dependences on the interaction range and dimension were studied. The obtained results emphasize the importance of next-nearest neighbour terms in the development of ordered phases within the studied system.
We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH.
We discuss global structures of ground-state phase diagrams in a one-dimensional half-filled electron system with on-site and spin-dependent nearest-neighbor-site Coulomb interactions. We compare our numerical calculation data for phase boundary lines with their analytical expressions in three limiting regions of interaction parameters and find good agreement between them. In the intermediate-coupling region, however, we observe nontrivial structures of phase diagrams: For systems with weak easy-plain anisotropy, both the bond-located spin- and charge-density-wave phases are realized. The latter contacts with the ferromagnetic phase stabilized in the strong-coupling region. On the other hand, when anisotropy becomes large, the intermediate phase disappears and consequently a direct transition between the former and ferromagnetic phase is observed.
A half-filled one-dimensional (1D) extended Hubbard model (U-V_⊥-V_∥) with on-site and nearest-neighbor spin-dependent interactions is studied analytically. The ground state phase diagram is obtained in the weak-coupling regime by performing the bosonization and renormalization group methods. The result shows that the nearest-neighbor spin-dependent attraction influences the low-energy physics of the 1D correlated electron system, and changes the topological structure of the ground state phase diagram of the U-V model.
We consider a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and nearest-neighbor hopping for spin \ensuremath{\sigma}, which depends on the sum of particles ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$ with opposite spin in the two sites involved. The hopping matrix elements are denoted by tAA{\mathrm{t}}_{\mathrm{AA}}tAA​,tAB{\mathrm{t}}_{\mathrm{AB}}tAB​,tBB{\mathrm{t}}_{\mathrm{BB}}tBB​ for ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$=0,1,2, respectively. For 0tAB{\mathrm{t}}_{\mathrm{AB}}tAB​tAA{\mathrm{t}}_{\mathrm{AA}}tAA​=tBB{\mathrm{t}}_{\mathrm{BB}}tBB​, we have determined the regions of parameters for which the ground-state (GS) of the one-dimensional system is a charge-density wave (CDW), a spin-density wave (SDW), or a metal (M), using Hartree-Fock, exact diagonalization of finite chains and quantum Monte Carlo. The results agree qualitatively with the exactly solvable limit of tAB{\mathrm{t}}_{\mathrm{AB}}tAB​=0. For 0tAB{\mathrm{t}}_{\mathrm{AB}}tAB​tAA{\mathrm{t}}_{\mathrm{AA}}tAA​=tBB{\mathrm{t}}_{\mathrm{BB}}tBB​, the GS is a M for sufficiently low values of U and V. In contrast, when tAA{\mathrm{t}}_{\mathrm{AA}}tAA​+tBB{\mathrm{t}}_{\mathrm{BB}}tBB​-2tAB{2\mathrm{t}}_{\mathrm{AB}}2tAB​=0, our results suggest that the GS is either a CDW or a SDW, with the boundary between them lying near the line U=2V.