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Physica C Superconductivity

Spontaneous breaking of charge symmetry in a frustrated one-dimensional Hubbard Model: Dimer states from charge motion

C A Hayward, M W Long

Published Dec 1, 1994• 0 citations
Publisher
DOI
10.1016/0921-4534(94)92300-0

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Recent studies on the frustrated quantum spin chains with easy-plane anisotropy are reviewed. We are particularly interested in novel “chiral ” phases characterized by the spontaneous breaking of the parity symmetry. The ground-state phase diagrams of the chains are discussed. The low-energy properties of one-dimensional quantum spin systems with frustrating interactions have been studied extensively for many years. This is mainly because they exhibit a variety of ground-state phases accompanied with various types of spontaneous symmetry breaking, e.g., the dimer phase with the translational symmetry
The ground-state properties of the two-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hoppings at half filling are studied by the path-integral-renormalization-group method. The nonmagnetic-insulator phase sandwiched by the the paramagnetic-metal phase and the antiferromagnetic-insulator phase shows evidence against translational symmetry breaking of the dimerized state, plaquette singlet state, staggered flux state, and charge ordered state. These results support that the genuine Mott insulator which cannot be adiabatically continued to the band insulator is realized generically by Umklapp scattering through the effects of geometrical frustration and quantum fluctuation in the two-dimensional system.
To the conventional Peierls-Hubbard model, involving both on-site (U) and nearest-neighbor (V) Coulomb repulsions, we add ``off-diagonal'' terms, not expressible purely in terms of site densities, representing bond-bond (W) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weak- and strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U,V), including the values believed to be relevant to trans-polyacetylene, we find that the off-diagonal terms (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and W. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation (``particle-hole'') symmetry by the X term.