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Entropy paradox in strongly correlated Fermi systems
A system of interacting, identical fermions described by standard Landau
Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if
the correlations grow sufficiently strong, as occurs at a quantum critical
point where the effective mass diverges. As yet, this phenomenon defies full
understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior
observed beyond the quantum critical point are still accessible within the
general framework of the Landau quasiparticle picture. Self-consistent
solutions of the coupled Landau equations for the quasiparticle momentum
distribution and quasiparticle energy spectrum are shown
to exist in two distinct classes, depending on coupling strength and on whether
the quasiparticle interaction is regular or singular at zero momentum transfer.
One class of solutions maintains the idempotency condition of
standard FL theory at zero temperature while adding pockets to the Fermi
surface. The other solutions are characterized by a swelling of the Fermi
surface and a flattening of the spectrum over a range of momenta
in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The
latter, non-idempotent solution is revealed by analysis of a Poincar\'e mapping
associated with the fundamental Landau equation connecting and
and validated by solution of a variational condition that yields
the symmetry-preserving ground state. Paradoxically, this extraordinary
solution carries the burden of a large temperature-dependent excess entropy
down to very low temperatures, threatening violation of the Nernst Theorem. It
is argued that certain low-temperature phase transitions offer effective
mechanisms for shedding the entropy excess. Available measurements in
heavy-fermion compounds provide concrete support for such a scenario.Comment: 34 pages, 6 figure
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