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Common mathematical theory can have profound applications in understanding real materials. The intrinsic connection between aperiodic orders observed in the Fibonacci sequence, Penrose tiling, and quasicrystals is a well-known example.…
We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely…
To a phenomenological core described by the Generalized Coherent State Model a set of interacting particles are coupled. Among the particle-core states one identifies a finite set which have the property that the angular momenta carried by…
In recent years, a lot of effort has been devoted to the quest for experimental realizations of Kitaev interactions in spin systems. Recently, many materials have been synthesized which seem to realize extended Kitaev models, where Kitaev…
Recently a new class of technicolor models are proposed, using technifermions of symmetric second-rank tensor. In the models, one can make reasonable estimates of physical quantities like the Higgs mass and the size of oblique corrections,…
We derive a set of genuine multi-mode entanglement criteria for second moments of the quadrature operators. The criteria have a common form of the uncertainty relation between sums of variances of position and momentum quadrature…
Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of…
We discuss the supersymmetric standard model from the perspective that the up and down Higgs supermultiplets are composite states. We show that a Higgs multiplet in which the scalar states are bound states of two squarks and the…
We construct a simple theory in which the fine-tuning of the standard model is significantly reduced. Radiative corrections to the quadratic part of the scalar potential are constrained to be symmetric under a global U(4) x U(4)' symmetry…
We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two and three-dimensional lattices.…
Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography. In this direction, many people have tried to construct aperiodic tilings that are built from a…
We discuss the consequences of the chiral doubling scenario for baryons built of heavy and light quarks. In particular, we use the soliton description for baryons, demonstrating why each heavy-light baryon should be accompanied by the…
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…
The problem of constructing a limit series of Penrose type partitions of a two-dimensional sphere is solved, which makes it possible to model quasicrystals possessing a point icosahedral group symmetry Ih. Images of polyhedron models are…
We employ a novel algorithm using a quasi-exact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin glass model with…
Using the density matrix renormalization group, we study the possibility of real space checkerboard patterns arising as the ground states of the t-J model. We find that checkerboards with a commensurate (pi,pi) background are not low energy…
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending…
Expanding the library of self-assembled superstructures provides insight into the behavior of atomic crystals and supports the development of materials with mesoscale order. Here we build upon recent findings of soft matter quasicrystals…
Theoretical investigations of the pentaquark states which were recently discovered provide important information on their nature and structure. It is necessary to study the spectroscopic parameters like masses and residues of particles…
The nature of the five-fold surface of Al(70)Pd(21)Mn(9) has been investigated using scanning tunneling microscopy. From high resolution images of the terraces, a tiling of the surface has been constructed using pentagonal prototiles. This…