Single-Particle Excitations in Narrow Energy Bands

Abstract

Hubbard's model for studying correlation effects in systems with narrow energy bands is analyzed by means of a technique which allows the calculation of moments of the individual peaks in the spectral weight function for single-particle excitations. The analysis of the zeroth moments of the peaks shows that the total weight in the bands depends on the strength of the kinetic-energy term in the Hamiltonian even though the bands may be narrow and widely separated. This conclusion is illustrated and verified by an exact calculation for the case when there are only two lattice sites. Analysis of first and higher moments yields results for nonmagnetic or paramagnetic phases which are in qualitative agreement with Hubbard's improved solution. However, we find that (a) there occurs a spin-dependent shift in the band energies which has not been obtained by other treatments of the model and which energetically favors ferromagnetism, and (b) single-particle excitations are more heavily damped in antiferromagnetic than in isomorphic paramagnetic phases. Hubbard's model for studying correlation eGects in systems with narrow energy bands is analyzed by means of a technique which allows the calculation of moments of the individual peaks in the spectral weight function for single-particle excitations. The analysis of the zeroth moments of the peaks shows that the total weight in the bands depends on the strength of the kinetic-energy term in the Hamiltonian even though the bands may be narrow and widely separated. This conc1usion is illustrated and verified by an exact calculation for the case when there are only two lattice sites. Analysis of first and higher moments yields results for nonmagnetic or paramagnetic phases which are in qualitative agreement with Hubbard's improved solution. However, we 6nd that (a) there occurs a spin-dependent shift in the band energies which has not been obtained by other treatments of the model and which energetically favors ferromagnetism, and (b) single-particle excitations are more heavily damped in antiferromagnetic than in isomorphic paramagnetic phases. Disciplines Physics | Quantum Physics

Magnetic ordering of itinerant systems in modified CPA approximation

“…Comparing the SDA method with our model, one notices that the so called "higher" correlation function (defined as B −σ in [7]) is the interaction very similar to the assisted hopping interaction ∆t used in our paper. Using moments method, introduced by Harris and Lange [27] and more recently by Herrmann and Nolting [7], the CPA technique was applied to two modified atomic levels with modified probabilities, by the spin depended shifted atomic level B −σ . This approach was called Modified Alloy Analogy (MAA).…”

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

“…Present research interests focus on systems in the strong to intermediate coupling regime, where one might expect that weaker interactions lead to increased electron mobility, which in turn should reduce the stability of magnetic phases. In the effective Hamiltonian, the increased electron mobility is taken into account perturbatively by including increasingly higher order corrections to the effective low-energy theory 1,2,3 . More specifically, the effective low-energy spin Hamiltonian, H s , derived from the Hubbard model, away from the strict Heisenberg limit [t/U → 0], contains conventional Heisenberg pairwise spin exchange as well as so-called ring (or cyclic) exchange terms that involve n−spin (n > 2) interactions 2,4 .…”

The two-particle propagator and magnetic susceptibility in the Hubbard model

“…In this subsection we turn our attention to the last term in (6). So far we have found the solution K 0 ijkl of the reduced equation of motion.…”

“…This is the VCA treatment of this term. Calling K ijkl the solution of the whole equation of motion (6), it can be checked that K xxx ′ x ′ can be expressed in terms of the uncorrected solution by…”

“…In addition, the residual interaction between electrons of opposite spin on the same site has to be included separately and is the dominant cause of the appearance of spin waves within the model. These properties are examined in the pure Hubbard CPA case which, as has been pointed out 5,6 , has only a paramagnetic phase except in special circumstances. The treatment can be carried over into the τ -CPA, again requiring a matching of the propagators, for t < τ treated in the CPA with their vertex corrections, to the VCA solutions appropriate to longer times.…”