This series consists of talks in the area of Condensed Matter.
Since the quantum Hall effect, the notion of topological
phases of matter has been extended to those that are well-defined (or:
``protected'') in the presence of a certain set of
symmetries, and that exist in dimensions higher than two. In the (fractional)
quantum Hall effects (and in ``chiral'' topological phases in general),
Laughlin's thought experiment provides a key insight into their topological
characterization; it shows a close connection between topological phases and
quantum anomalies.
I will present a density-matrix renormalization group
(DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to
identify the conjectured spin liquid ground state. Exploiting SU(2) spin
symmetry, which allows us to keep up to 16,000 DMRG states, we consider
cylinders with circumferences up to 17 lattice spacings and find a spin liquid
ground state with an estimated per site energy of -0.4386(5), a spin gap of
0.13(1), very short-range decay in spin, dimer and chiral correlation functions
We construct in the K matrix formalism concrete examples
of symmetry enriched topological phases, namely intrinsically topological
phases with global symmetries. We focus on the Abelian and non-chiral
topological phases and demonstrate by our examples how the interplay between
the global symmetry and the fusion algebra of the anyons of a topologically
ordered system determines the existence of gapless edge modes protected by the
symmetry and that a (quasi)-group structure can be defined among these phases.
The density matrix renormalization group (DMRG), which
has proved so successful in one dimension, has been making the push into higher
dimensions, with the fractional quantum Hall (FQH) effect an important target.
I'll briefly explain how the infinite DMRG algorithm can be adapted to find the
degenerate ground states of a microscopic FQH Hamiltonian on an infinitely long
cylinder, then focus on two applications. To characterize the topological order
of the phase, I'll show that the bipartite entanglement spectrum of the ground
We have used a recently proposed quantum Monte Carlo
algorithm [1] to study spinons (emergent S = 1/2 excitations) in 2D
Resonating-Valence-Bond (RVB) spin liquids and in a J-Q model hosting a Neel –
Valence Bond Solid (VBS) phase transition at zero temperature [2]. We confirm
that spinons are well defined quasi-particles with finite intrinsic size in the
RVB spin liquid. The distance distribution between two spinons shows signatures
of deconfinement.
Two types of topological phases have attracted a lot of
attention in condensed matter physics:
symmetry protected
In this talk I will present our recent investigations on
possible topological phases in (111) heterostructures of transition metal
oxide. These (111) heterstructures are promising systems to realize many 2D
topological phases at high temperatures, even with strong correlations, which
is hard to be achieved in conventional materials.
Using quantum Monte Carlo simulations, we investigate the
finite-temperature phase diagram of hard-core bosons (XY model) in
Recent experiments in BEC
quantum magnets exhibit a dramatic evolution of
Topological phases are quantum
phases that can not be described by any local order parameter.