Fermionic representations of integrable lattice systems

Abstract

We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter equation and to express the corresponding $L$-matrix and the generators of symmetries in terms of Fermi operators. We illustrate our approach through a number of examples. Our main example is the algebraic Bethe ansatz solution of the Hubbard model in the infinite coupling limit.

minor changes, typos corrected

References in corpus (3)

• The su(N) XX model
• Algebraic Solution of the Hubbard Model on the Infinite Interval
• SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model

Cited by in corpus (30)

• Solution of the quantum inverse problem
• Baxter's Q-operators for supersymmetric spin chains
• Yang-Baxter integrable Lindblad equations
• Algebraic Bethe ansatz for the gl(1|2) generalized model and Lieb-Wu equations
• Integrable impurities for an open fermion chain
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Integrable Chain Model with Additional Staggered Model Parameter
• Algebraic Bethe ansatz for the gl(1$|$2) generalized model II: the three gradings
• Real-Time Evolution in the Hubbard Model with Infinite Repulsion
• Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-S
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Results on the symmetries of integrable fermionic models on chains
• Quantum Inverse Scattering Method with anyonic grading
• Integrable Ladder t-J Model with Staggered Shift of the Spectral Parameter
• On the quantization of continuous non-ultralocal integrable systems
• Non-diagonal boundary conditions for gl(1|1) super spin chains
• An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
• Fermionization and Hubbard Models
• Integrable theories and generalized graded Maillet algebras
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Lattice path integral approach to the one-dimensional Kondo model
• Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
• Truncation identities for the small polaron fusion hierarchy
• Bethe Ansatz solution of the small polaron with nondiagonal boundary terms
• Weak ergodicity breaking with isolated integrable sectors
• A range three elliptic deformation of the Hubbard model
• New series of multi-parametric solutions to GYBE: quantum gates and integrability
• Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains
• Explicit R-matrices for inhomogeneous 3D chiral Potts models: Integrability and the action formulation for
• Non-additive fusion, Hubbard models and non-locality