Interacting spinless fermions with disorder: the Mott transition for infinite coordination number

Abstract

An analytic expression f o r k dynamical conductivity b(m) of spinless fermions with local disorder and nearest-neighbour repulsion is derived on lattices with infinite coordination number 2. The model in exocIly solvable in the whole paramew range assuming two possible phases: a homogeneous phase and a check&Qard chargedensity wave (COW). Away hom half filling the system displays anomalous behaviour: weak particledensity Ruclualions favour spontane~~s symmetry breaking. F m we invesligate UR effects of this anomaly on the wnductivity in Ihe AC and DC regimes. Second. we focus on the Moll transition occurring al rem temperature aI half filling. The critical exponents for the conductivity are computed for the dependence on the interaction U. the disorder y . the filling n. the temperabn'e 7 and the frequency m.

Drude weight and dc conductivity of correlated electrons

“…; T) which essentially represents the sum of that quantity over an entire shell of nearest-neighbor sites. For the in nite dimensional Hubbard model the conductivity is given diagrammatically by the dressed bubble-diagram 29,30,10,18]. Vertex corrections do not enter since they are of order 1=Z 2 .…”

“…Genuine two-particle interference e ects are described by vertex corrections. They enter as soon as 1=Z-corrections are taken into account and lead, for example, to the renormalization factor = 1 + O( 1 Z ) > 1, (18), in the case of spinless fermions. By including 1=Z corrections, i.e.…”

Transport Properties of Correlated Electrons in High Dimensions

“…In all three cases, the proportionality (4) of the f -sum to the kinetic energy as characteristic for the hc lattice is clearly violated. This is true even for the stacked case (which is otherwise similar to the hc case): while the f -sum is here proportional to the contribution to the kinetic energy associated with hopping in current direction [8], ∞ 0 dω σ xx (ω) = −σ 0 T x /4, this contribution (which is negligible in the limit Z → ∞) is not proportional to the total kinetic energy in this anisotropic case. A more relevant sum rule is derived from (12):…”

“…Therefore, our method has not only the merit of yielding isotropic transport, but also of avoiding unphysical behavior. In order to determine the microscopic model, we have to apply (8) to the numerically evaluated transformation function F. Again, the scaled hopping matrix elements fall off exponentially fast: only a fraction 10 of the total energy variance arises from hopping amplitudes beyond third nearest neighbors and only a fraction 10 −6 results from hopping beyond 9 thnearest neighbors. This result suggests that properties of the model should be robust with respect to truncation.…”

“…Therefore, the periodically stacked Bethe lattice (Fig. 1b) is still a Bethe lattice in the DMFT sense; potentially coherent transport is then well-defined (only) in stacking direction [8]. A semi-elliptic DOS also results from fully disordered hopping on lattices of arbitrary topology; in this case, σ(ω) is incoherent [9].…”