Comment on "Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems"
This is a comment on arXiv:1402.6767 (2014) by Y. Imura, T. Okubo, S. Morita, and K. Okunishi.
cond-mat.stat-mech↗
arXiv subjects
Ching Hua Lee
Publications and source records attributed to Ching Hua Lee.
Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems
We examine the snapshot entropy of general fractal images defined by their singular values. Remarkably, the singular values for a large class of fractals are in exact correspondence with the entanglement spectrum of free fermions in one dimension. These fermions allow for a holographic interpretation of the logarithmic scaling of the snapshot entropy, which is in agreement with the Calabrese-Cardy formula. However, the coarse-grained entropy exhibits a linear scaling due to the degeneracy of the spectrum, in contrast with the logarithmic scaling behavior in one-dimensional quantum near-critical systems.
cond-mat.stat-mech↗
Non-integer optical modes in a Möbius-ring resonator
In-plane polarized light experiences a non-trivial topological evolution as it propagates resonantly in a Möbius ring resonator. The resultant geometric phase varies continuously when changing the light ellipticity, which leads to constructive interference for a non-integer number of wavelengths, and therefore to the occurrence of an arbitrary fractional number of optical modes. The geometric phase in Möbius-ring resonators is topologically robust and implies excellent intrinsic fault-tolerance.
physics.optics↗
Pseudopotential Formalism for Fractional Chern Insulators
Recently, generalizations of fractional quantum Hall (FQH) states known as fractional quantum anomalous Hall or, equivalently, fractional Chern insulators states have been realized in lattice models. Ideal wavefunctions such as the Laughlin wavefunction, as well as the corresponding trial Hamiltonians for which the former are exact ground states, have been vital to characterizing FQH phases. The Wannier function representation of fractional Chern insulators proposed in [X.-L. Qi, Phys. Rev. Lett., 126803] defines an approach to generalize these concepts to fractional Chern insulators. In this paper, we apply the Wannier function representation to develop a systematic pseudopotential formalism for fractional Chern insulators. The family of pseudopotential Hamiltonians is defined as the set of projectors onto asymptotic relative angular momentum components which forms an orthogonal basis of two-body Hamiltonians with magnetic translation symmetry. This approach serves both as an expansion tool for interactions and as a definition of positive semidefinite Hamiltonians for which the ideal fractional Chern insulator wavefunctions are exact nullspace modes. We compare the short-range two-body pseudopotential expansion of various fractional Chern insulator models at one-third filling in phase regimes where a Laughlin-type ground state is expected to be realized. We also discuss the effect of inhomogeneous Berry curvature which leads to components of the Hamiltonian that cannot be expanded into pseudopotentials, and elaborate on their role in determining low energy theories for fractional Chern insulators. Finally, we generalize our Chern pseudopotential approach to interactions involving more than two bodies with the goal of facilitating the identification of non-Abelian fractional Chern insulators.
cond-mat.str-el↗
Multistable binary decision making on networks
We propose a simple model for a binary decision making process on a graph, motivated by modeling social decision making with cooperative individuals. The model is similar to a random field Ising model or fiber bundle model, but with key differences on heterogeneous networks. For many types of disorder and interactions between the nodes, we predict discontinuous phase transitions with mean field theory which are largely independent of network structure. We show how these phase transitions can also be understood by studying microscopic avalanches, and describe how network structure enhances fluctuations in the distribution of avalanches. We suggest theoretically the existence of a "glassy" spectrum of equilibria associated with a typical phase, even on infinite graphs, so long as the first moment of the degree distribution is finite. This behavior implies that the model is robust against noise below a certain scale, and also that phase transitions can switch from discontinuous to continuous on networks with too few edges. Numerical simulations suggest that our theory is accurate.
physics.soc-ph↗
N=8 Supergravity 4-point Amplitudes
We present the explicit expressions in N=8 supergravity for the bosonic 4-particle tree and 1-loop amplitudes including vectors and scalars. We also present the candidate 4-point UV divergences in a form of helicity amplitudes, corresponding to 3-loop manifestly N=8 supersymmetric and Lorentz covariant counterterm. This may shed some light on the 3-loop finiteness of N=8 SG and on a conjectured higher loop finiteness. We perform a supersymmetric deformation to complex momentum of the 4-point generating function including higher-loop counterterms and the 1-loop UV finite amplitudes. Using the explicit form of the scalar part of the 3-loop counterterm and of the 1-loop UV finite scalar 4-point amplitudes we find that they both have an unbroken E7 symmetry. We derive from E7 symmetry the low-energy theorem for the 1-loop n-point amplitudes.
hep-th↗