322 research outputs found
Community detection in complex networks by dynamical simplex evolution
We benchmark the dynamical simplex evolution (DSE) method with several of the currently available algorithms to detect communities in complex networks by comparing correctly identified nodes for different levels of fuzziness of random networks composed of well-defined communities. The potential benefits of the DSE method to detect hierarchical substructures in complex networks are discussed
The "glass transition'' as a topological defect driven transition in a distribution of crystals and a prediction of a universal viscosity collapse
Topological defects are typically quantified relative to ordered backgrounds.
The importance of these defects to the understanding of physical phenomena
including diverse equilibrium melting transitions from low temperature ordered
to higher temperatures disordered systems (and vice versa) can hardly be
overstated. Amorphous materials such as glasses seem to constitute a
fundamental challenge to this paradigm. A long held dogma is that transitions
into and out of an amorphous glassy state are distinctly different from typical
equilibrium phase transitions and must call for radically different concepts.
In this work, we critique this belief. We examine systems that may be viewed as
simultaneous distribution of different ordinary equilibrium structures. In
particular, we focus on the analogs of melting (or freezing) transitions in
such distributed systems. The theory that we arrive at yields dynamical,
structural, and thermodynamic behaviors of glasses and supercooled fluids that,
for the properties tested thus far, are in qualitative and quantitative
agreement with experiment. We arrive at a prediction for the viscosity and
dielectric relaxations that is universally satisfied for all experimentally
measured supercooled liquids and glasses over 15 decades.Comment: 21 pages, 2 figure
Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
In this work, we illustrate how a Jordan-Wigner transformation combined with
symmetry considerations enables a direct solution of Kitaev's model on the
honeycomb lattice. We (i) express the p-wave type fermionic ground states of
this system in terms of the original spins, (ii) adduce that symmetry alone
dictates the existence of string and planar brane type correlators and their
composites, (iii) compute the value of such non-local correlators by employing
the Jordan-Wigner transformation, (iv) affirm that the spectrum is
inconsequential to the existence of topological quantum order and that such
information is encoded in the states themselves, and (v) express the anyonic
character of the excitations in this system and the local symmetries that it
harbors in terms of fermions.Comment: 14 pages, 7 figure
Microphase Separation and modulated phases in a Coulomb frustrated Ising ferromagnet
We study a 3-dimensional Ising model in which the tendency to order due to
short-range ferromagnetic interactions is frustrated by competing long-range
(Coulombic) interactions. Complete ferromagnetic ordering is impossible for any
nonzero value of the frustration parameter, but the system displays a variety
of phases characterized by periodically modulated structures. We have performed
extensive Monte-Carlo simulations which provide strong evidence that the
microphase separation transition between paramagnetic and modulated phases is a
fluctuation-induced first-order transition. Additional transitions to various
commensurate phases may also occur when further lowering the temperature.Comment: 6 pages, 4 figures, accepted in Europhys. Letter
Orbital Compass Model as an Itinerant Electron System
Two-dimensional orbital compass model is studied as an interacting itinerant
electron model. A Hubbard-type tight-binding model, from which the orbital
compass model is derived in the strong coupling limit, is identified. This
model is analyzed by the random-phase approximation (RPA) and the
self-consistent RPA methods from the weak coupling. Anisotropy for the orbital
fluctuation in the momentum space is qualitatively changed by the on-site
Coulomb interaction. This result is explained by the fact that the dominant
fluctuation is changed from the intra-band nesting to the inter-band one by
increasing the interaction.Comment: 7 pages, 8 figure
Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons
We present microscopic, multiple Landau level, (frustration-free and positive
semi-definite) parent Hamiltonians whose ground states, realizing different
quantum Hall fluids, are parton-like and whose excitations display either
Abelian or non-Abelian braiding statistics. We prove ground state energy
monotonicity theorems for systems with different particle numbers, demonstrate
S-duality in the case of toroidal geometry and establish an exact zero-energy
mode counting. The emergent Entangled Pauli Principle, introduced in Phys. Rev.
B 98, 161118(R) (2018) and which defines the "DNA" of the quantum Hall fluid,
is behind the exact determination of the topological characteristics of the
fluid, including charge and braiding statistics of excitations, and effective
edge theory descriptions. When the closed-shell condition is satisfied, the
densest (i.e., the highest density and lowest total angular momentum)
zero-energy mode is a unique parton state. As a corollary, it follows that the
Moore-Read Pfaffian and Read-Rezayi states (both of which may be expressed as
linear combinations of parton-like states) cannot be densest ground states of
two-body parent Hamiltonians. We conjecture, based on the algebra of
polynomials in holomormorphic and anti-holomorphic complex variables, that
parton-like states span the subspace of many-body wave functions with the
two-body -clustering property, that is, wave functions with th-order
coincidence plane zeroes. We illustrate our framework by presenting a parent
Hamiltonian whose excitations are rigorously proven to be Fibonacci anyons and
show how to extract the DNA of the fluid whose entanglement pattern manifests
in the form of a matrix product state.Comment: 49 pages, 17 figure
Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses
Recent decades have seen the discovery of numerous complex materials. At the
root of the complexity underlying many of these materials lies a large number
of possible contending atomic- and larger-scale configurations and the
intricate correlations between their constituents. For a detailed
understanding, there is a need for tools that enable the detection of pertinent
structures on all spatial and temporal scales. Towards this end, we suggest a
new method by invoking ideas from network analysis and information theory. Our
method efficiently identifies basic unit cells and topological defects in
systems with low disorder and may analyze general amorphous structures to
identify candidate natural structures where a clear definition of order is
lacking. This general unbiased detection of physical structure does not require
a guess as to which of the system properties should be deemed as important and
may constitute a natural point of departure for further analysis. The method
applies to both static and dynamic systems.Comment: (23 pages, 9 figures
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