Related papers: Topological Obstruction in Block-spin Transformati…
A local transformation from fermionic operators to spin matrices is proposed and studied in this work. For this purpose, a system of fermions on a lattice is considered and one applies the scheme to replace the fermionic variables with spin…
In relativistic quantum field theory particles of half-integer spin must obey Fermi-Dirac statistics. Their quantum operators must anticommute at spacelike separation in contrast to commuting physical observables. We show that Fermi-Dirac…
We propose a novel, machine-learning-based framework for constructing lattice fermions using Physics-Informed Neural Networks (PINNs). Our approach treats the formulation of the Dirac operator as an optimization problem guided by physical…
The overlap hypercube fermion is constructed by inserting a lattice fermion with hypercubic couplings into the overlap formula. One obtains an exact Ginsparg-Wilson fermion, which is more complicated than the standard overlap fermion, but…
We observe interlaced square vortex lattices in rotating two-component dilute-gas Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a single-component BEC in an internal state $|1>$ of $^{87}$Rb atoms, we…
A remarkable feature of a lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson lattice Dirac operator does not possess topological zero modes for any…
In a recent article Hasenfratz and von Allmen have suggested a fixed point action for two flavors of Weyl fermions on the lattice with gauge group SU(2). The block-spin transformation they use maps the chiral and vector symmetries of the…
The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of two by two blocks. In each block the possible…
By examining rotating ferromagnetic spinor condensates through the perspective of large spin, we identify a novel type of topological point defects in the magnetization texture. These defects are not predicted by conventional homotopy…
We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case:…
The index, which is given in terms of the number of zero modes of the Dirac operator with definite chirality, plays a central role in various topological aspects of gauge theories. We investigate its properties in non-commutative geometry.…
A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically-nontrivial gauge backgrounds, it can reproduce correct axial anomaly for sufficiently smooth gauge…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
We address the problem of barrier tunneling in the two-dimensional T_3 lattice (dice lattice). In particular we focus on the low-energy, long-wavelength approximation for the Hamiltonian of the system, where the lattice can be described by…
We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with…
Spinor bosons offer conceptually simple picture of macroscopic quantum behavior of topological order-by-disorder: Paramagnetic state of two-component dipolar bosons in orbitally degenerate zig-zag lattice is unstable against infinitezimal…
A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t)…
Kondo lattice models have established themselves as an ideal platform for studying the interplay between topology and strong correlations such as in topological Kondo insulators or Weyl-Kondo semimetals. The nature of these systems requires…
To realize band structures with non-trivial topological properties in an optical lattice is an exciting topic in current studies on ultra cold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking…