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Physical review. B, Condensed matter

One-dimensional narrow-band model for heavy fermions and resonating valence bonds

P. Schlottmann

Published Mar 1, 1990• 13 citations
Publisher

Abstract

A one-dimensional-lattice model consisting of a single narrow band and excluded double occupancy of the sites is considered. The electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. In a previous paper we discussed the exact solution of the model for special values of the coupling constants [related to SU(3) invariance]. Here we construct an asymptotically exact solution in the low-electron-density limit for coupling parameters deviating from SU(3) symmetry. The results are compared to those obtained via multiplicative renormalization for the model in the continuum limit and used to discuss the phase diagram.

DOI
10.1103/physrevb.41.4164

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A one-dimensional-lattice model consisting of a single narrow band and excluded double occupancy of the sites is considered. The electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. In a previous paper we discussed the exact solution of the model for special values of the coupling constants [related to SU(3) invariance]. Here we construct an asymptotically exact solution in the low-electron-density limit for coupling parameters deviating from SU(3) symmetry. The results are compared to those obtained via multiplicative renormalization for the model in the continuum limit and used to discuss the phase diagram.
A lattice model consisting of a single narrow band is introduced to describe some aspects of heavy electrons. The model excludes double occupancy of the sites and electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. The model is integrable in one dimension for some special values of the coupling constants. These cases are related to the SU(3) invariance. The Bethe-ansatz equations are obtained and ground-state and thermodynamic properties are discussed and solved in some limiting cases.
A lattice model consisting of a single narrow band is introduced to describe some aspects of heavy electrons. The model excludes double occupancy of the sites and electrons on nearest-neighbor sites interact via a charge interaction and spin exchange. The model is integrable in one dimension for some special values of the coupling constants. These cases are related to the SU(3) invariance. The Bethe-ansatz equations are obtained and ground-state and thermodynamic properties are discussed and solved in some limiting cases.
A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle and particle-hole channels are derived in weak-coupling conditions. It is shown that lattice effects manifest themselves through the curvature of the spectrum and the dependence of the coupling constants on momenta. This method is then applied to the one-dimensional extended Hubbard model; we thoroughly discuss the evolution of the phase diagram, and in particular the fate of the bond-centered charge-density-wave phase, as the system is doped away from half-filling. Our findings are compared to the predictions of the field-theory continuum limit and available numerical results.
In this paper we study a generalization of the 1D Hubbard model in the atomic limit by considering density-density and Ising-type spin-spin nearest neighbor (NN) interactions, parameterized by V and J , respectively. We present the T = 0 phase diagram for both ferro ( J > 0) and anti-ferro ( J < 0) coupling obtained in the narrow-band limit by means of an extension to zero-temperature of the transfer-matrix method. Based on the values of the Hamiltonian parameters, we identify a number of phases that involve orderings of the double occupancy, NN density and spin correlations.
An exact solution of the one-dimensional electron gas on a lattice is given for the special case in which two of the four coupling constants have particular values. It is shown that umklapp scattering has the same effect on the charge-density waves as backward scattering across the Fermi "surface" has on the spin-density waves and that the method of Luther and Emery can be used to solve this more general problem. For repulsive electron-electron interactions the umklapp scattering produces a gap in the charge-density wave spectrum and this appears for low-lying excitations when there is a half-filled band. The use of renormalization-group scaling to solve for general values of the coupling constants is discussed.
A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction T∗{T}^{*}T∗ is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.