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We introduce a new spin-fermion mapping, for arbitrary spin $S$ generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for $S=1/2$. The mapping, valid for regular lattices in any…

Strongly Correlated Electrons · Physics 2009-10-31 C. D. Batista , G. Ortiz

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…

Mathematical Physics · Physics 2023-01-18 Walter H. Aschbacher

The Jordan-Wigner transformation is applied to study magnetic properties of the quantum spin-1/2 $XX$ model on the diamond chain. Generally, the Hamiltonian of this quantum spin system can be represented in terms of spinless fermions in the…

Strongly Correlated Electrons · Physics 2011-05-09 Taras Verkholyak , Jozef Strecka , Michal Jascur , Johannes Richter

A generalization of the Jordan-Wigner transformation to three (or higher) dimensions is constructed. The nonlocal mapping of spin to fermionic variables is expressed as a gauge transformation with topological charge equal to one. The…

Condensed Matter · Physics 2009-10-22 Luis Huerta , Jorge Zanelli

Inspired by recent developments generalizing Jordan-Wigner dualities to higher dimensions, we develop a framework of such dualities using an algebraic formalism for translation-invariant Hamiltonians proposed by Haah. We prove that given a…

Strongly Correlated Electrons · Physics 2020-06-19 Nathanan Tantivasadakarn

Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational…

Strongly Correlated Electrons · Physics 2022-10-19 Jannes Nys , Giuseppe Carleo

Recent work has highlighted that the strong correlation inherent in spin Hamiltonians can be effectively reduced by mapping spins to fermions via the Jordan-Wigner transformation (JW). The Hartree-Fock method is straightforward in the…

Strongly Correlated Electrons · Physics 2025-08-26 Shadan Ghassemi Tabrizi , Thomas M. Henderson , Thomas D. Kühne , Gustavo E. Scuseria

We analyse the control of Majorana zero-energy states by mapping the fermionic system onto a chain of Ising spins. Although the topological protection is lost for the Ising system, the mapping provides additional insight into the nature of…

Mesoscale and Nanoscale Physics · Physics 2017-11-08 Stefan Backens , Alexander Shnirman , Yuriy Makhlin , Yuval Gefen , Johan E. Mooij , Gerd Schön

In the paper nonlinear transformations of the Jordan-Wigner (JW) type are introduced in the form different from the ones known previously, for the purpose of expressing multi-index Pauli operators in terms of multi-index Fermi creation and…

Statistical Mechanics · Physics 2007-05-23 Martin S. Kochman'ski

Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of…

Quantum Physics · Physics 2022-10-11 Qing-Song Li , Huan-Yu Liu , Qingchun Wang , Yu-Chun Wu , Guo-Ping Guo

Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…

Quantum Physics · Physics 2014-07-09 Andrew J. Ferris

Using a global rotation by theta about the z-axis in the spin sector of the Jordan-Wigner transformation rotates Pauli matrices X and Y in the x-y-plane, while it adds a global complex phase to fermionic quantum states that have a fixed…

Quantum Physics · Physics 2026-01-01 Grant Davis , James K. Freericks

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…

Strongly Correlated Electrons · Physics 2019-12-25 Yu-An Chen , Anton Kapustin

A variety of analytical approaches have been developed for the study of quantum spin systems in two dimensions, the notable ones being spin-waves, slave boson/fermion parton constructions, and for lattices with one-to-one local…

Strongly Correlated Electrons · Physics 2023-08-09 Jagannath Das , Aman Kumar , Avijit Maity , Vikram Tripathi

The Jordan-Wigner map in 2D is as an exact lattice regularization of the 2 pi-flux attachment to a hard-core boson (or spin-1/2) leading to a composite-fermion particle. When the spin-1/2 model obeys ice rules this map preserves locality,…

Strongly Correlated Electrons · Physics 2024-07-22 Leonardo Goller , Inti Sodemann Villadiego

We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevancy of the fermionic picture for interpreting the neutron scattering…

Strongly Correlated Electrons · Physics 2007-05-23 Oleg Derzhko , Taras Krokhmalskii

The realization of Majorana zero modes is in the centre of intense theoretical and experimental investigations. Unfortunately, their exchange that can reveal their exotic statistics needs manipulations that are still beyond our experimental…

Quantum Physics · Physics 2016-10-26 Jin-Shi Xu , Kai Sun , Yong-Jian Han , Chuan-Feng Li , Jiannis K. Pachos , Guang-Can Guo

We explore the properties of the SO(3) Majorana representation of spin. Based on its non-local nature, it is shown that there is an equivalence between the SO(3) Majorana representation and the Jordan-Wigner transformation in one and two…

Strongly Correlated Electrons · Physics 2018-12-26 Jianlong Fu

Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. A characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit…

Quantum Physics · Physics 2023-10-25 Mitchell Chiew , Sergii Strelchuk

We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum…

Quantum Physics · Physics 2015-04-01 U. Las Heras , L. García-Álvarez , A. Mezzacapo , E. Solano , L. Lamata