Emergent Phases of Quantum Matter in Strongly Correlated Mott Insulators
- Author(s): Iaconis, Jason John
- Advisor(s): Balents, Leon
- et al.
Strongly correlated electron systems have the potential to host very exotic
phases of matter. In order to have relevance to real materials, this exotic
physics often must emerge from relatively simple models. The quantum
wavefunctions which describe such phases may bear little resemblance to the
original microscopic models. In these cases a variety of complex analytic
tools often must be supplemented with controlled numerical calculations to
fully understand the essential behavior of these models. In this dissertation,
we study such quantum phases of matter and their relationship to real materials.
We focus on three main problems. First, we explore the relationship between
strong spin-orbit coupling and spin liquid physics by studying a very general
model on the triangular lattice where spin-orbit coupling leads to the presence
of highly anisotropic interactions. We use variational Monte Carlo to study both
U(1) quantum spin liquid states and ordered ones, via the Gutzwiller projected
fermion construction. We thereby obtain the ground state phase diagram in this
phase space. We furthermore consider effects beyond the Gutzwiller wavefunctions
for the spinon Fermi surface quantum spin liquid, which are of particular
importance when spin-orbit coupling is present.
Second we show that the interplay between a high density two-dimensional electron
gas and localized electrons in a neighboring Mott insulator leads to kinetic
magnetism unique to the Mott/band insulator interface. Our study is based upon
a bilayer Hubbard model at $U=\infty$ with a potential difference between the
two layers. We combine analytic results with DMRG simulations to show that
magnetism, and especially kinetic ferromagnetism, is greatly enhanced relative by the
proximity of the two subsystems.
Third we study the effect of interactions on the properties of a model 2D
topological Kondo insulator phase. We introduce a model Hamiltonian which we
believe captures the essential physics of the different competing phases.
Perhaps the most dramatic example of many-body physics in symmetry protected
topological phases is the existence of exotic gapless edge states. We comment on
the potentially dramatic effects that interactions can have on such edge states.