Spin-fermion mappings for even Hamiltonian operators

Abstract

We revisit the Jordan-Wigner transformation, showing that --rather than a non-local isomorphism between different fermionic and spin Hamiltonian operators-- it can be viewed in terms of local identities relating different realizations of projection operators. The construction works for arbitrary dimension of the ambient lattice, as well as of the on-site vector space, generalizing Jordan-Wigner's result. It provides direct mapping of local quantum spin problems into local fermionic problems (and viceversa), under the (rather physical) requirement that the latter are described by Hamiltonian's which are even products of fermionic operators. As an application, we specialize to mappings between constrained-fermions models and spin 1 models on chains, obtaining in particular some new integrable spin Hamiltonian, and the corresponding ground state energies.

arXiv comment7 pages, ReVTeX file, no figures

References in corpus (5)

• Generalized Jordan-Wigner Transformations
• Algebraic Approach to Interacting Quantum Systems
• Spin Gap and Superconductivity in the One-Dimensional t-J Model with Coulomb Repulsion
• Results on the symmetries of integrable fermionic models on chains
• Band and filling controlled transitions in exactly solved electronic models

Cited by in corpus (5)

• The Bond-Algebraic Approach to Dualities
• The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice
• Dynamics and Control of a Quasi-1D Spin System
• Entanglement in extended Hubbard models and quantum phase transitions
• Quantized Brans Dicke Theory: Phase Transition and Strong Coupling (Large $\omega$) Limit & General Relativity