https://doi.org/10.1007/s100510070092
Exactly solvable toy model for the pseudogap state
Institut für Theoretische Physik, Universität Göttingen,
Bunsenstrasse 9, 37073 Göttingen, Germany
Received:
15
March
2000
Published online: 15 October 2000
We present an
exactly solvable toy model which describes the emergence of a pseudogap
in an electronic system
due to a fluctuating off-diagonal order parameter.
In one dimension our model reduces to the
fluctuating gap model (FGM)
with a gap 
that is constrained to be of the form
,
where A and Q are random variables.
The FGM was
introduced by Lee, Rice and
Anderson [Phys. Rev. Lett. 31, 462 (1973)]
to study fluctuation effects in Peierls chains.
We show that their perturbative results for the average
density of states are exact for our toy model if we assume
a Lorentzian probability distribution for Q and ignore
amplitude fluctuations.
More generally, choosing the probability distributions of
A and Q such
that the average of 
vanishes and its covariance is
,
we study the combined effect of phase and amplitude fluctuations
on the low-energy properties of Peierls chains.
We explicitly calculate the average density of states, the
localization length, the average single-particle Green's function, and
the real part of the average conductivity.
In our model phase fluctuations generate delocalized
states at the Fermi energy, which give rise to a
finite Drude peak in the conductivity.
We also find that the interplay between phase and amplitude
fluctuations leads to a weak logarithmic singularity
in the single-particle spectral function at the bare quasi-particle energies.
In higher dimensions our model
might be relevant to describe the
pseudogap state in the underdoped cuprate superconductors.
PACS: 71.23.-k – Electronic structure of disordered solids / 02.50.Ey – Stochastic processes / 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
