83,332 research outputs found
Statement of Bruce H. Simon Before the Commission on the Future of Worker-Management Relations
Testimony_Simon_022494.pdf: 204 downloads, before Oct. 1, 2020
Effect of Landau Level Mixing on Braiding Statistics
We examine the effect of Landau level mixing on the braiding statistics of
quasiparticles of abelian and nonabelian quantum Hall states. While path
dependent geometric phases can perturb the abelian part of the statistics, we
find that the nonabelian properties remain unchanged to an accuracy that is
exponentially small in the distance between quasiparticles.Comment: 4 page
Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
We perform numerical studies to determine if the fractional quantum Hall
state observed at filling nu=5/2 is the Moore-Read wavefunction or its particle
hole conjugate, the so-called AntiPfaffian. Using a truncated Hilbert space
approach we find that for realistic interactions, including Landau-level
mixing, the ground state remains fully polarized and the AntiPfaffian is
strongly favored.Comment: Main change is that the Anti-Pfaffian is favored instead of the
Pfaffian (caused by a sign error in the commutation relation of the dynamical
momenta). 4-plus pages, 3 figure
Spin-singlet Gaffnian wave function for fractional quantum Hall systems
We characterize in detail a wave function conceivable in fractional quantum
Hall systems where a spin or equivalent degree of freedom is present. This wave
function combines the properties of two previously proposed quantum Hall wave
functions, namely the non-Abelian spin-singlet state and the nonunitary
Gaffnian wave function. This is a spin-singlet generalization of the
spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In
this paper we present evidence demonstrating that the SSG corresponds to the
ground state of a certain local Hamiltonian, which we explicitly construct,
and, further, we provide a relatively simple analytic expression for the unique
ground-state wave functions, which we define as the zero energy eigenstates of
that local Hamiltonian. In addition, we have determined a certain nonunitary,
rational conformal field theory which provides an underlying description of the
SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit.
In order to verify our construction, we implement two recently proposed
techniques for the analysis of fractional quantum Hall trial states: The "spin
dressed squeezing algorithm", and the "generalized Pauli principle".Comment: 15 pages, 2 figures. Version 3 fixes a typographical error in the
Hamiltonian, Eq 3. Version 2 incorporates referee and editorial suggestions.
The original title "Putting a Spin on the Gaffnian" was deemed to be too
inappropriate for PR
Recommended from our members
Five seconds or sixty? Presentation time in expert memory
The template theory presented in Gobet and Simon (1996a, 1998) is based on the EPAM theory (Feigenbaum & Simon, 1984; Richman et al., 1995), including the numerical parameters that have been estimated in tests of the latter; and it therefore offers precise predictions for the timing of cognitive processes during the presentation and recall of chess positions. This paper describes the behavior of CHREST, a computer implementation of the template theory, in a task when the presentation time is systematically varied from one second to sixty seconds, on the recall of both game and random positions, and compares the model to human data. As predicted by the model, strong players are better than weak players with both types of positions. Their superiority with random positions is especially clear with long presentation times, but is also present after brief presentation times, although smaller in absolute value. CHREST accounts for the data, both qualitatively and quantitatively. Strong players’ superiority with random positions is explained by the large number of chunks they hold in LTM. Strong players’ high recall percentage with short presentation times is explained by the presence of templates, a special class of chunks. The model is compared to other theories of chess skill, which either cannot account for the superiority of Masters with random positions (models based on high-level descriptions and on levels of processing) or predict too strong a performance of Masters with random positions (long-term working memory)
Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
We show that all the bands of the Hofstadter model on the torus have an
exactly flat dispersion and Berry curvature when a special system size is
chosen. This result holds for any hopping and Chern number. Our analysis
therefore provides a simple rule for choosing a particularly advantageous
system size when designing a Hofstadter system whose size is controllable, like
a qubit lattice or an optical cavity array. The density operators projected
onto the flat bands obey exactly the Girvin-MacDonald-Platzman algebra, like
for Landau levels in the continuum in the case of , or obey its
straightforward generalization in the case of . This allows a mapping
between density-density interaction Hamiltonians for particles in the
Hofstatder model and in a continuum Landau level. By using the well-known
pseudopotential construction in the latter case, we obtain fractional Chern
insulator phases, the lattice counterpart of fractional quantum Hall phases,
that are exact zero-energy ground states of the Hofstadter model with certain
interactions. Finally, the addition of a harmonic trapping potential is shown
to lead to an appealingly symmetric description in which a new Hofstadter model
appears in momentum space.Comment: 15 pages, 8 figures; Published versio
- …