相关论文: Dirac Operator Zero-modes on a Torus

We provide an argument based on flux insertion to show that certain superconductors with a non-trivial topological invariant have protected zero modes in their vortex cores. This argument has the flavor of a two dimensional index theorem…

A recently constructed model for low lying excitations in bilayer graphene exhibits mid-gap, zero energy modes in its Dirac-like spectrum, when a scalar order parameter takes a vortex profile. We show that these modes persist when the…

Model wave functions constructed from (1+1)D conformal field theory (CFT) have played a vital role in studying chiral topologically ordered systems. There usually exist multiple degenerate ground states when such states are placed on the…

Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern-Simons action admits only certain quantized values for gauge fields that lead to zero modes of the…

The zero modes of closed strings on a torus --the torus coordinates plus dual coordinates conjugate to winding number-- parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be…

The classical and quantum aspects of the Schwinger model on the torus are considered. First we find explicitly all zero modes of the Dirac operator in the topological sectors with nontrivial Chern index and is spectrum. In the second part…

Using chiral decomposition, we are able to find analytically the zero modes and the conditions for such modes to exist in the Kitaev ladder model and superconducting nanowires with Dresselhaus spin-orbit coupling. As a result, we are able…

We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…

Spectral triples over noncommutative principal $\T^n$-bundles are studied, extending recent results about the noncommutative geometry of principal U(1)-bundles. We relate the noncommutative geometry of the total space of the bundle with the…

The spectrum and degeneracies of the Dirac operator are analysed on compact coset spaces when there is a non-zero homogeneous background gauge field which is compatible with the symmetries of the space, in particular when the gauge field is…

The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain…

We consider magnetic fields on $\mathbb{R}^3$ which are parallel to a conformal Killing field. When the latter generates a simple rotation we show that a Weyl-Dirac operator with such a magnetic field cannot have a zero mode. In particular…

We give a proof of the index theorem of lattice Wilson--Dirac operators, which states that the index of a twisted Dirac operator on the standard torus is described in terms of the corresponding lattice Wilson--Dirac operator. Our proof is…

At magic twisted angles, Dirac cones in twisted bilayer graphene (TBG) can evolve into flat bands, serving as a critical playground for the study of strongly correlated physics. When chiral symmetry is introduced, rigorous mathematical…

We find and classify possible equivariant spin structures with Dirac operators on the noncommutative torus, proving that similarly as in the classical case the spectrum of the Dirac operator depends on the spin structure.

We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our…

We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove…

In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two dimensional compact manifold $S^2$ as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes…

We calculate the low-lying eigenmodes of the Neuberger overlap-Dirac operator for $4d$ compact lattice QED in the quenched approximation. In the strong coupling phase we find exact zero-modes, quite similar as in non-Abelian lattice QCD.…

We calculate the index of the Dirac operator defined on the q-deformed fuzzy sphere. The index of the Dirac operator is related to its net chiral zero modes and thus to the trace of the chirality operator. We show that for the q-deformed…