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arXiv:cond-mat/9703213 · Physical review. B, Condensed matter

Phase diagram of the half-filled extended Hubbard model in two dimensions

Biplab Chattopadhyay, D. M. Gaitonde

Published Jun 15, 1997• 24 citations
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Abstract

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 (${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$) 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 ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$, 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 ${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$.

DOI
10.1103/physrevb.55.15364

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The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.
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