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
state is sufficient to determine the quasiparticle charges, topological spins,
quantum dimensions, chiral central charge, and Hall viscosity of the phase.
Then I will show how to introduce localized quasiparticles of fixed topological
charge. By pinning a pair of quasiparticles and dragging them into contact, we
can directly measure the force curve of their interaction.
Advanced LIGO (aLIGO) and Advanced Virgo (AdV) are kilometer-scale
gravitational wave (GW) detectors that are expected to yield the first
direct observations of gravitational waves. I will describe the
currently projected schedule, sensitivity, and sky
localization accuracy for the GW detector network in the next decade.
The general boundary formulation (GBF) is an atemporal, but spacetime local formulation of quantum theory. Usually it is presented in terms of the amplitude formalism, which, in the presence of a background time, recovers the pure state formalism of the standard formulation of quantum theory. After reviewing the essentials of the amplitude formalism I will introduce a new "positive formalism", which recovers instead a mixed state formalism. This allows to define general quantum operations within the GBF and opens it to quantum information theory. Moreover, the transition to the positive formalism eliminates operationally irrelevant structure, making the extraction of measurement probabilities more direct. As a consequence, the probability interpretation takes on a remarkably simple and compelling form. I shall describe implications of the positive formalism, both for our understanding of quantum theory and for the practical formulation of quantum theories. I also observe a certain convergence with Lucien Hardy's operator tensor formulation of quantum theory, on which I hope to comment
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.
However, at the Neel–VBS transition, we found that the
size of a single spinon is significantly greater than the bound-state in VBS,
which indicates that spinons are “soft” and shrink when bound state is formed.
Both spinon size and confinement length diverge as the critical point is
approached. We have also compared spinon statistics in J-Q model with bilayer
Heisenberg model and 1D spin chain. We conclude that the spinon deconfinement
is marginal in the lowest-energy state in the spin-1 sector, due to very weak
attractive spinon interactions. Deconfinement in the vicinity of the critical
point should occur at higher energies.
I consider a class of
simple classical systems which exhibit motion in their lowest-energy states and thus spontaneously break time-translation symmetry. Their Lagrangians have nonstandard kinetic terms and their Hamiltonians are multivalued functions of momentum, yet they are perfectly consistent and amenable to quantization. Field theoretical generalizations of these systems may have applications in condensed matter physics and cosmology.
The presence of additional light fields during inflation
can source isocurvature fluctuations, which can cause the curvature
perturbation $\zeta$, and its statistics to evolve on superhorizon scales. I
will demonstrate that if these fluctuations have not completely decayed before
the onset of perturbative reheating, then primordial observables such as the
level of non--Gaussianity can develop substantial reheating dependant
corrections. I will argue that for inflationary models where an adiabatic
condition is not reached before the relevant fields begin to decay, we must be
careful in our interpretation of any observational constraints that place
bounds on the statistics of $\zeta$.
Two types of topological phases have attracted a lot of
attention in condensed matter physics:
symmetry protected
topological(SPT) phases and topologically ordered phases.
On the one hand, SPT phases are protected by given global symmetries while
there is no topological order in the bulk. On the other hand, topologically
ordered phases do not require symmetry and feature topological ground state
degeneracy. In this talk, I present a
classification of phases with both topological orders and global symmetries,
equipped with local bosonic exactly solvable models. This classification, in
some sense, organizes previous pieces of understandings on SPT phases,
topological orders, symmetry fractionalizations, into a single framework.
Solution of the exactly solvable models and measurable consequences will be
discussed.
In
quantum information theory, random techniques have proven to be very useful.
For example, many questions related to the problem of the additivity of
entropies of quantum channels rely on fine properties of concentration of
measure.
In
this talk, I will show that very different techniques of random matrix theory
can complement quite efficiently more classical random techniques. I will spend
some time on discussing the Weingarten calculus approach, and the operator norm
approach. Both techniques have been initially used in free probability theory,
and I will give some new applications of these techniques to quantum
information theory.
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.
Several examples will be discussed, including high-temperature
quantum spin hall effect in LaAlO3/LaAuO3/LaAlO3 bilayer, correlation induced
topological phases in LaAlO3/LaNiO3/LaAlO3 multilayer, nearly flat topological
band with C=2 (C: Chern number) in SrIrO3 trilayer, and abelian/nonabelian
fractional quantum hall effects in the absence of Landau levels (fractional
Chern insulators). If time is allowed, I will also briefly introduce our work
on classifying wavefunctions of fractional Chern/topological insulators.
I
will discuss some basic notions in the theory of phonology (sound systems
in language). The sounds of a language are generally assumed to be
composed of smaller constituents, called features. The features that
make up a sound cannot be directly obtained from its pronunciation, but
rather must be inferred from the system of contrasts that are at play
in a particular language. How to determine which features are contrastive
presents a logical and empirical puzzle that may be interesting
to students of physics, who are accustomed to explaining observable events
in terms of hidden structures that cannot be directly observed.
In this talk I investigate the
"firewall argument", that claims that black hole horizons can
not be smooth.
Using
a holographic model of the black hole horizon as a quantum mechanical
membrane, I show how
to
recover the black hole interior as an emergent
smooth region of space-time. The reconstruction makes
use
of the formalism of quantum error correcting codes. I explain
why the horizon of very old black holes
appears
to be singular, and formulate a complementarity principle that resolves
this firewall paradox.