This series consists of talks in the area of Condensed Matter.
Topological phases are quantum
phases that can not be described by any local order parameter.
We study the spectrum of the amplitude mode, the analog
of the Higgs mode in high energy physics, for the d-density wave (DDW) state
proposed to describe the anomalous phenomenology of the pseudogap phase of the
high Tc cuprates. Even though the state breaks translational symmetry by a
lattice spacing and is described by a particle-hole singlet order parameter at
the wave vector q = Q = (pi, pi), remarkably, we find that the amplitude mode
spectrum can have peaks at both q = (0, 0) and q = Q = (pi , pi). In general,
The search for Majorana zero-modes in condensed matter
system has attract increasing research interests recently. Looking for Majorna
zero-mode is actually looking for topologically protected ground state
degeneracy. The topological degeneracies on closed manifolds have been used to
discover/define topological order in many-body systems, which contain
excitations with fractional statistics. In this talk, I will present our recent
work on new types of topological degeneracy induced by condensing anyons along
Near a critical
point, the equilibrium relaxation time of a system diverges and any change of control parameters leads to non-equilibrium behavior. The Kibble-Zurek (KZ) problem is to determine
the evolution of the system when the change is slow. In this talk, I will introduce a non-equilibrium scaling limit in which these evolutions are universal and define a KZ universality classification with exponents and scaling functions. I will illustrate the physics accessible in this
In this talk I will review some existing experimental
methods, as well as a few recent theoretical proposals, to tune the
interactions in a number of low-dimensional systems exhibiting the fractional
quantum Hall effect (FQHE). The materials in question include GaAs wide quantum
wells and multilayer graphene, where the tunability of the electron-electron
interactions can be achieved via modifying the band structure, dielectric
environment of the sample, by tilting the magnetic field or varying the mass
Fractional Chern insulators (FCIs) are topologically
ordered states of interacting fermions that share their universal properties
with fractional quantum Hall states in Landau levels. FCIs have been found
numerically in a variety of two-dimensional lattice models upon partially
filling an almost dispersionless band with nontrivial topological character
with repulsively interacting fermions. I will show how FCIs emerge in bands
with Chern number C=1 and C=2 and in Z_2 topological insulators, where the
We consider quantum phase transitions out of topological
Mott insulators in which the ground state of the fractionalized excitations
(fermionic spinons) is topologically non-trivial. The spinons in topological
Mott insulators are coupled to an emergent compact U(1) gauge field with a
so-called "axion" term. We study the confinement transitions from the
topological Mott insulator to broken symmetry phases, which may occur via the
condensation of dyons. Dyons carry both "electric" and
In this talk I will describe my work characterizing
quantum entanglement in systems with a Fermi surface. This class includes everything from Fermi
liquids to exotic spin liquids in frustrated magnets and perhaps even
holographic systems. I review my
original scaling argument and then describe in detail a number of new precise
results on entanglement in Fermi liquids.
I will also discuss recent quantum Monte Carlo calculations of Renyi
entropies and will argue that we now have a rather complete agreement between
Most applications of the density matrix renormalization
group (DMRG) have been to lattice models with short range interactions. But
recent developments in DMRG technology open the door to studying continuum
systems with long-range interactions in one dimension (1d). One key motivation
is simulating cold atom experiments, where it is possible to engineer
Hamiltonians of precisely this type.
We have been applying DMRG in the 1d continuum with
another