### Garry Goldstein

###
(University of Cambridge)

## Quantum Dimers

In this talk we review the slave boson meanfield formulation
of the fermion+boson quantum dimer model for the pseudogap phase of the
high temperature superconductors. We show that in the presence of weak
slowly varying external magnetic and electric fields the fermionic
dimers undergo semiclassical motion in the external field. As a result
in the presence of magnetic fields strong enough to destroy
superconductivity the dimers undergo quantum oscillations. Indeed they
satisfy Onsager quantization for their orbits and Lifshtiz-Kosevich
formula for the amplitude of oscillations. We also compute the
effective charges of the dimers in the presence of external magnetic
fields as a function of temperature. We show that the effective
magnetic charge changes sign from negative −e at low temperature to
positive +e at high temperature. This leads to a change of the sign of
the Hall coefficient as a function of temperature. We also compute the
magnetoresistance as a function of the external field and temperature
within a linearized Boltzmann equation approximation for the fermionic
dimers. Furthermore we further show that the dimers undergo a Lifshitz
transition as a function of doping with a van Hove singularity
appearing at the Fermi surface near optimal doping ∼ 20%. Indeed the
van Hove singularity leads to a divergence of the density of states and
as such an optimum Tc. We study the interplay of nematic fluctuations
and the van Hove singularity both of which occur near optimal doping.
We show that the van Hove singularity modifies the critical properties
of the QCP (quantum critical point) for nematic fluctuations and that
the QCP may be described by Hertz Millis like theory with z = 4. This
allows us to calculate the critical exponents of the nematic
fluctuations and to show that the fermionic dimers have non-Fermi
liquid behavior near the QCP with the self energy diverging ∼
ω3/4 near the QCP.