This series consists of talks in the area of Condensed Matter.
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
In Dicke Superradiance, a collection of 2-level atoms
interacting with a single boson mode acquires, through quantum coherence, an
enhanced emission property and a rich dynamics. We suggest possibility of Dicke
superradiance in a BCS superconductor. The necessary 2-level atoms are
identified with Anderson pseudo spins seeing
a self consistent mean field in k-space.
A way to couple these 2-level bose atoms to an external boson mode and
create a novel non equilibrium superradiant superconductivity
An exciting new prospect in condensed matter physics is
the possibility of realizing fractional quantum Hall
states in simple lattice models without a large external magnetic
field, which are called fractional Chern insulators. A fundamental question is whether qualitatively new
states can be realized on the lattice as compared with ordinary
fractional quantum Hall states. Here we propose new symmetry-enriched topological
states, topological nematic states, which are a dramatic consequence of
Topological gauge theories and group cohomology
Robbert Dijkgraaf and Edward Witten
Braiding statistics approach to symmetry-protected topological phases
Michael Levin, Zheng-Cheng Gu
Anderson localization - quantum suppression of carrier
diffusion due to disorders - is a basic notion of modern condensed matter
physics. Here I will talk about a novel localization phenomenon totally
contrary to this common wisdom. Strikingly, it is purely of strong interaction
origin and occurs without the assistance of disorders. Specifically, by
combined numerical (density matrix renormalization group) method and analytic
analysis, we show that a single hole injected in a quantum antiferromagnetic
In this talk, I will present our recent work on the
effect of thermal fluctuations on the topological stability of chiral p-wave
superconductors. We consider two models of superconductors: spinless and
spinful with a focus on topological properties and Majorana zero-energy modes.
We show that proliferation of vortex-antivortex pairs above the
Kosterlitz-Thouless temperature T_KT drives the transition from a thermal Quantum
Hall insulator to a thermal metal/insulator, and dramatically modifies the
It has been known for some time that
a system with a filled band will have an integer quantum Hall conductance equal
to its Chern number, a toplogical index associated with the band. While this is
true for a system in a magnetic field with filled Landau Levels, even a system
in zero external field can exhibit the QHE if its band has a Chern number. I
review this issue and discuss a more recent question of whether a partially
filled Chern band can exhibit the Fractional QHE. I describe the work done with
What information can be determined about a state given
just the ground state wave function?
Quantum ground states, speaking intuitively, contain
fluctuations between many of the configurations one might want to understand.
The information about them can be organized by introducing an imaginary system,
dubbed the entanglement Hamiltonian.
What light does the dynamics of this Hamiltonian (a
precise version of the notion of "zero point motion") shed on the