# Pseudoparticle approach to strongly correlated systems

**Speaker:**Garry Goldstein

**When:**August 8, 2017 (Tue), 03:00PM to 04:00PM (add to my calendar)

**Location:**SCI SCI 328

*This event is part of the Condensed Matter Theory Seminar Series. *

In the ﬁrst part we present a slave-particle meanﬁeld study of the mixed boson+fermion quantum dimer model introduced by Punk, Allais, and Sachdev [PNAS 112, 9552 (2015)] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge e fermion pockets whose total area is equal to the hole doping p, for a range of parameters consistent with the t−J model for high temperature superconductivity. Here we ﬁnd that the dimers are unstable to d-wave superconductivity at low temperatures. The region of the phase diagram with d-wave rather than s-wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone.

In the second part we present an approach for studying systems with hard constraints such that certain positive semideﬁnite operators must vanish. The diﬃculty with mean-ﬁeld treatments of such cases is that imposing that the constraint is zero only in average is problematic for a quantity that is always non-negative. We reformulate the hard constraints by adding an auxiliary system such that some of the states to be projected out from the total system are at ﬁnite negative energy and the rest at ﬁnite positive energy, we dubbed this method the soft constraint. This auxiliary system comes with an extra coupling that we are free to vary and that parametrizes a whole family of mean-ﬁeld theories. We argue that this variational-type parameter for the family of mean-ﬁeld theories should be ﬁxed by matching a given experimental observation, with the quality of the resulting mean-ﬁeld approximation measured by how it ﬁts other data. We test these ideas in the well-understood single-impurity Kondo problem, where we ﬁx the parameter via the TK (Kondo temperature) obtained from the magnetic susceptibility value, and score the quality of the approximation by its predicted Wilson ratio. We also study a continuum version of the soft constraint method. To show its usefulness we study the Laughlin fractional quantum Hall states at ﬁlling fraction ν = 1 2m+1. We produce the Landau Ginzburg Cherns Simons theory for hard core bosons(arising in this formulation of the Laughlin functions0 for these ﬁlling fractions. We handle the hard core constraint explicitly and show that to leading order it is equivalent to a theory of soft core bosons with an eﬀective density density interaction between the particles of the form of a Coulomb interaction coming from the electrons in the original theory and an eﬀective interaction coming from the hard core constraint that can be tuned by hand which we denote by λ(q,ω). We show that we can use this eﬀective interaction to reproduce the known spectra of both inter Landau level and intra Landau level neutral excitations for the Laughlin states as well as the energy gap to charged excitations and the electromagnetic response tensor.