Slave boson mean field theories for quantum dimers
This event is part of the Condensed Matter Theory Seminar Series.
Abstract: We present a slave boson mean field analysis of the Quantum Dimer Model. We present a generic approach to produce slave boson formulations of quantum dimer models. We study mean fields as well as quantum fluctuations beyond them - using a variety of Hubbard Stratonovich transformations. We study dimer models on square, cubic and triangular lattices and we reproduce parts of their phase diagrams (which were previously known only numerically or through partial mappings to the transverse field Ising model). We show that the mean field supports several dimer liquids and solids. Furthermore we show that dimer models are equivalent to either U(1)xU(1), U(1)xZ2 or Z4 gauge theories which may or may not be in the confining phase depending on the parameters of the dimer model. We show that the projective symmetry group (PSG) classification applies to dimer models. In particular we show that the Algebraic PSG for a dimer model is equivalent to the Algebraic PSG of a bosonic spin liquid with the same IGG (Invariant Gauge Group). We present a large N limit for these dimer model (where the number of dimer species - N - becomes large) and show that the meanfield analysis becomes exact in this limit. We also present a large S (semiclassical limit where the number of dimers per link becomes large) for the dimer models. Preliminary results on the slave boson mean field for the Kagome and hexagonal lattices is also presented. A slave boson formulation and mean field of the dimer model doped with bosonic holes is also presented; large N and large S extensions are derived. Motivated by the high Tc problem we also study the case when there is a mixture of fermionic and bosonic dimers (with the fermions representing the doped holes and the bosons representing valence bonds between the spins). We find that there are four fermion pockets located at (+/-Pi/2, +/-Pi/2) with the total area enclosed by the pockets equal to the fermion doping. We find that the dimers are unstable to d-wave superconductivity at low temperatures. A slave fermion meanfield is also presented for the square and hexagonal lattice quantum dimer models. Preliminary results on a slave boson formulation and analysis of a related model: quantum spin ice