相关论文: Topological Obstruction in Block-spin Transformati…

We show that the indices of certain twisted Dirac operators vanish on a $Spin$-manifold $M$ of positive sectional curvature if the symmetry rank of $M$ is $\geq 2$ or if the symmetry rank is one and $M$ is two connected. We also give…

When reflected from an interface, a laser beam generally drifts and tilts away from the path predicted by ray optics, an intriguing consequence of its finite transverse extent. Such beam shifts manifest more dramatically for structured…

The Dirac fermion with linear dispersion in the kagom\'e lattice governs the low-energy physics of different valleys at two inequivalent corners of hexagonal Brillouin zone. The effective Hamiltonian based on the cyclic permutation symmetry…

We investigate the vortex lattice configuration in a rotating spin orbit-coupled spin-2 Bose-Einstein condensate confined in a quasi-two-dimensional harmonic trap. By considering the interplay between rotation frequency, spin-orbit…

We pursue the idea of constructing higher spin fields as solutions to twisted Dirac operators. As general results we find that twisted prenormally hyperbolic first order operators (such as the Dirac operator) on globally hyperbolic…

We propose a lattice formulation of the Arf-Brown-Kervaire (ABK) invariant which takes values in $\mathbb{Z}_8$. Compared to the standard $\mathbb{Z}$-valued index, the ABK invariant is more involved in that it arises in Majorana fermion…

We study the phase diagram of spin-one polar condensates in a two dimensional optical lattice with magnetic anisotropy. We show that the topological binding of vorticity to nematic disclinations allows for a rich variety of phase…

One-dimensional tight-binding lattice, single site of which possesses harmonically vibrating level is studied. The states of non-interacting electrons incident with fixed energy from infinity are considered. It is shown that at definite…

Topological invariants and their associated anomalies have played a crucial role in understanding low-energy phenomena in quantum field theories. In lattice gauge theory, the standard $\mathbb{Z}$-valued Atiyah-Singer index is formulated…

In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores…

Based on the algebraic theory of signal processing, we recursively decompose the discrete sine transform of first kind (DST-I) into small orthogonal block operations. Using a diagrammatic language, we then second-quantize this decomposition…

Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in…

We study the vortex pinning effect on the vortex lattice structure of the rotating two-component Bose-Einstein condensates (BECs) in the presence of impurities or disorder by numerically solving the time-dependent coupled Gross-Pitaevskii…

The isotropic S=1/2 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak…

We use the overlap formalism to define a topological index on the lattice. We study the spectral flow of the hermitian Wilson-Dirac operator and identify zero crossings with topological objects. We determine the topological susceptibility…

Gyroscopic metamaterials --- mechanical structures composed of interacting spinning tops --- have recently been found to support one-way topological edge excitations. In these structures, the time reversal symmetry breaking that enables…

Lattice QCD using fermions whose Dirac operator obeys the Ginsparg-Wilson relation, is perhaps the best known formulation of QCD with a finite cutoff. It reproduces all the low energy QCD phenomenology associated with chiral symmetry at…

It has been understood that short range interactions can reduce the classification of topological superconductors in all dimensions. In this paper we demonstrate by explicit calculations that when the topological phase transition between…

We numerically evaluate the one-loop counterterms for the four-dimensional Wess-Zumino model formulated on the lattice using Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus…

We consider the N=1 supersymmetric kink on a circle, i.e., on a finite interval with boundary or transition conditions which are locally invisible. For Majorana fermions, the single-particle Dirac Hamiltonian as a differential operator…