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arXiv:cond-mat/0209062 · Physical review. B, Condensed matter

Generalized hole-particle transformations and spin reflection positivity in multiorbital systems

Mario Cuoco, Canio Noce

Published May 6, 2002• 9 citations
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Abstract

We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In particular, we rigorously determine at half-filling and for different regions of the parameter space the spin, orbital, and $\ensuremath{\eta}$ pairing pseudospin of the ground state of generalized two-orbital Hubbard models that include the Hund's rule coupling.

DOI
10.1103/physrevb.65.205108

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We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In particular, we rigorously determine at half-filling and for different regions of the parameter space the spin, orbital, and \ensuremathη\ensuremath{\eta}\ensuremathη pairing pseudospin of the ground state of generalized two-orbital Hubbard models that include the Hund's rule coupling.
In the present chapter we review some rigorous results derived with Lieb’s spin-reflectionpositivity method in a pedagogical manner. To begin with, we emphasize the important role played by the sign rule satisfied by the ground-state wave function of a quantum many-body system. For example, we study some localized spin systems, such as the antiferromagnetic Heisenberg model, in detail. Then we argue why such a rule is difficult to establish for the ground-state wave functions of itinerant electron models. By using the spin-reflection-positivity method, we show that this problem can be partially remedied. A weaker form of the sign rule is uncovered. It enables us to prove several inequalities satisfied by either an electron pairing correlation function or a magnetic correlation function of the Hubbard model on a bipartite lattice. These inequalities imply that, if a bipartite lattice has macroscopically unequal numbers of sublattice sites, then the Hubbard model at half-filling is either a supersolid or a ferrimagnet. Similar inequalities can also be proven for the periodic Anderson model and the Kondo lattice model. Finally, by applying a generalized version of the spin-reflection-positivity method, we further establish an inequality satisfied by the charged and spin gaps of these models. Based on them, we make some audacious conjectures, and then we summarize this chapter.
In order to numerically study electron correlation effects in multiorbital systems, we propose a new type of discrete transformation for the exchange (Hund's coupling) and pair-hopping interactions to be used in the dynamical mean field theory+quantum\text{theory}+\text{quantum}theory+quantum Monte Carlo method. The transformation, which is real and exact, turns out to suppress the sign problem in a wide parameter region including non-half-filled bands. This enables us to obtain the dominant pairing symmetry in the double-orbital Hubbard model, which shows that the spin-triplet, orbital-antisymmetric pairing that exploits Hund's coupling is stable in a wide region of the band filling.
Excitonic phases described by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-orbital Hubbard model with the Hund's rule coupling J . Using the variational cluster approximation, we calculate the ground-state energy and order parameters, and show that the Hund's rule coupling always stabilizes the excitonic spin-density- wave state and destabilizes the excitonic charge-density-wave state. The pair coherence lengths calculated in the spin-singlet and spin-triplet states indicate that only the spin-triplet excitons are paired more tightly with increasing J . The single-particle spectrum and density of states are also calculated to clarify the characters of these excitonic density-wave states.
We investigate superconductivity in a two-orbital Hubbard model on a square lattice by applying fluctuation exchange approximation. In the present model, the symmetry of the two orbitals are assumed to be that of an sss orbital. Then, we find that an sss-wave spin-triplet orbital-antisymmetric state and a ppp-wave spin-singlet orbital-antisymmetric state appear when Hund's rule coupling is large. These states are prohibited in a single-orbital model within states with even frequency dependence, but allowed for multiorbital systems. We also discuss pairing symmetry in other models which are equivalent to the two-orbital Hubbard model except for symmetry of orbitals. Finally, we show that pairing states with a finite total momentum, even without a magnetic field, are possible in a system with two Fermi surfaces.