Related papers: Parafermionic derivation of Andrews-type multiple …
Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice $\mathbb{Z}_4$…
Topological phases of matter remain a focus of interest due to their unique properties -- fractionalisation, ground state degeneracy, and exotic excitations. While some of these properties can occur in systems of free fermions, their…
Parafermions are emergent quasi-particles which generalize Majorana fermions and possess intriguing anyonic properties. The theoretical investigation of effective models hosting them is gaining considerable importance in view of present-day…
We construct all fundamental modules for the two parameter quantum affine algebra of type $A$ using a combinatorial model of Young diagrams. In particular we also give a fermionic realization of the two-parameter quantum affine algebra.
A general formula for the grand canonical partition function for a para Fermi system of any order and of any number of levels is derived.
We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the…
A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda $\tau$-functions of hypergeometric type, which…
We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.
In this paper, we explore a new type of global symmetries$-$the fermionic higher-form symmetries. They are generated by topological operators with fermionic parameter, which act on fermionic extended objects. We present a set of field…
An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutators of the respective matrices. The procedure is shown to…
The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
We generalize recent matrix-based factorization theorems for Lambert series generating functions generating the coefficients $(f \ast 1)(n)$ for some arithmetic function $f$. Our new factorization theorems provide analogs to these…
The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we…
We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both…
We formulate a $\mathbb{Z}_k$-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising…
The anomalous bilinear commutation relations satisfied by the components of the Green's ansatz for paraparticles are shown to derive from the comultiplication of the paraboson or parafermion algebra. The same provides a generalization of…
We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are over projective Schur functions $Q_\alpha$ for strict partitions $\alpha$. We…
A geometric understanding of the origin of mass hierarchy among the standard model fermions have been addressed in a multiple warped spacetime. We show that the requirement of $10^{16}$ order warping between the Planck and the visible…