Related papers: Something about spin-fermion connection
We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which allow us to extend the Jordan-Wigner…
Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. Taking into account a model with local fermionic modes, formally only the 'occupied' states |1> could be relevant for…
We consider the quantum kinetic-theory description for interacting massive spin-half fermions using the Wigner function formalism. We derive a general kinetic theory description assuming that the spin effects appear at the classical and…
In his seminal paper [1], Araki introduced an elegant extension of the Jordan-Wigner transformation which establishes a precise connection between quantum spin systems and Fermi lattice gases in one dimension in the so-called infinite…
We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form $\mathbb{Z}_2$ gauge theory with an unusual Gauss law. An important property of this map is that it…
The quantization of a massive spin $1/2$ field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-hermitian quantum field theory by the redefinition of the field dual and…
We consider a spin-1/2 XY chain in a transverse (z) field with multi-site interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan-Wigner transformation…
A three-particle spin-1/2 fermion problem with on-site repulsion and nearest-neighbor attraction is solved on the two-dimensional square lattice by discretizing a Schroedinger equation in momentum space. Energies of bound complexes (trions)…
We present a numerical self consistent variational approach based on the Jordan-Wigner transformation for two dimensional spin systems. We apply it to the study of the well known quantum (S=1/2) antiferromagnetic XXZ system as a function of…
We investigate a spin-1/2 antiferromagnetic chain with trimerized exchange couplings relevant to Na$_2$Cu$_3$Ge$_4$O$_{12}$. We show that the low-energy Hilbert space maps onto an effective Heisenberg chain of composite spin-1/2 trimer…
We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is…
It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase…
Spinor-valued one-forms (Rarita-Schwinger fields) are normally used in the context of supergravity, where they describe spin 3/2 particles (gravitinos). Indeed, when decomposed into irreducible representations of the Lorentz group such a…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
We use the Jordan-Wigner representation to study dynamic quantities for the spin-1/2 XX chain in a transverse magnetic field. We discuss in some detail the properties of the four-fermion excitation continuum which is probed by the dynamic…
The Casimir force between two perfectly reflecting parallel plates is considered. In a recent paper we presented generalised physical boundary conditions describing perfectly reflecting parallel plates. These boundary conditions are…
We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formulism. The chiral and spin kinetic equations can be derived from equations for Wigner functions. A general Wigner function has 16 components which…
Using the Jordan-Wigner fermionization in two dimensions we obtain the zz wave vector- and frequency-dependent structure factor for the spin-1/2 isotropic XY model on a spatially anisotropic square lattice. We use the obtained results to…
The present thesis is divided into three parts. In Part I we address a problem within Higher-Spin Gauge Theory in dimension three: namely, that of computing the asymptotic symmetry algebra of supersymmetric models, describing an infinite…