Related papers: Jordan-Wigner transformations for tree structures
Mapping spins to fermions via the Jordan-Wigner (JW) transformation can render mean-field (Hartree-Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is…
Recently it has been shown that the quantum spin-1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [\cite{JW1}], and 2D [\cite{JW2}] as well. In this paper, using the…
We introduce Majorana Propagation, an algorithmic framework for the classical simulation of Fermionic circuits. Inspired by Pauli Propagation, Majorana Propagation operates by applying successive truncations throughout the Heisenberg…
Hybrid quantum systems that combine discrete-variable (DV) and continuous-variable (CV) architectures represent a promising direction in quantum information science. However, transferring concepts, information and states between such…
A novel approach, the fermion-spin transformation to implement the charge-spin separation, is developed to study the low-dimensional $t$-$J$ model. In this approach, the charge and spin degrees of freedom of the physical electron are…
We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a…
We investigate a non-equilibrium reaction-diffusion model and equivalent ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The exact energy spectrum and the n-point hole correlations are considered with the help of…
We study a generalization of the Wigner function to arbitrary tuples of hermitian operators. We show that for any collection of hermitian operators A1...An , and any quantum state there is a unique joint distribution on R^n, with the…
Spin chains with two Ising symmetries are the Jordan-Wigner duals of one-dimensional interacting fermions with particle-hole and time-reversal symmetry. From earlier works on Majorana chains, it is known that this class of models has 10…
A method to perform bosonization of a fermionic theory in (1+1) dimensions in a path integral framework is developed. The method relies exclusively on the path integral property of allowing variable shifts, and does not depend on the…
In the present paper, we propose a mean field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean field level that ladders with even number legs open a energy gap in…
We describe a scheme to exchange fermion parity between two pairs of Majorana bound states mediated by coupling with a centralized quantum dot. We specifically formulate such a scheme for Majorana bound states nucleated in the Josephson…
As part of the intense effort towards identifying platforms in which Majorana bound states can be realized and manipulated to perform qubit operations, we propose a topological Josephson junction architecture that achieves these…
We consider quantum error-correcting subsystem codes whose gauge generators realize a translation-invariant, free-fermion-solvable spin model. In this setting, errors are suppressed by a Hamiltonian whose terms are the gauge generators of…
We propose an easy-to-build easy-to-detect scheme for realizing Majorana fermions at the ends of a chain of magnetic atoms on the surface of a superconductor. Model calculations show that such chains can be easily tuned between trivial and…
We propose a scheme to braid Majorana zero modes (MZMs) through steering the spin degree of freedom, without moving, measuring, or more generically fusing the modes. For a spinful Majorana system, we show that braiding two MZMs is achieved…
Using fiber bundle theory and conformal mappings, we continuously select a point from the interior of Jordan domains in Riemannian surfaces. This selection can be made equivariant under isometries, and take on prescribed values such as the…
In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the…
We establish an exact mapping between identical particles in one dimension with arbitrary exchange statistics, including bosons, anyons and fermions, provided they share the same scattering length. This boson-anyon-fermion mapping…
We study in this work the ground state entanglement properties of finite XX spin-1/2 chains with random couplings, using Jordan-Wigner transformation. We divide the system into two parts and study reduced density matrices (RDMs) of its…