The quantum inverse scattering method for Hubbard-like models |
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| Institution: | 1. Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands;2. Universidade Federal de Sao Carlos, Departamento de Fisica, C.P. 676, 13560 São Carlos, Brazil;1. Materials Research Laboratory, Department of Physics, Faculty of Basic and Applied Sciences (FBAS), International Islamic University (IIU) Islamabad 44000, Pakistan;2. Materials Science Laboratory, Department of Physics, Quaid-i-Azam University, Islamabad 45320, Pakistan;1. National Research University Higher School of Economics, Russian Federation;2. Skolkovo Institute of Science and Technology, 143026 Moscow, Russian Federation;3. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991 Moscow, Russian Federation;4. ITEP, B. Cheremushkinskaya 25, Moscow 117218, Russian Federation;5. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, Moscow Region 141700, Russian Federation;1. Moscow Institute of Physics and Technology, Inststitutskii per. 9, Dolgoprudny, Moscow region, 141700, Russian Federation;2. ITEP, B.Cheremushkinskaya 25, Moscow 117218, Russian Federation;3. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russian Federation;4. Skolkovo Institute of Science and Technology, 143026 Moscow, Russian Federation;5. National Research University Higher School of Economics, Russian Federation;6. Institute of Biochemical Physics of Russian Academy of Sciences, Kosygina str. 4, 119334, Moscow, Russian Federation;1. The Ruppin Academic Center, Emeq Hefer 40250, Israel;2. The Hadassah Institute, Jerusalem 91010, Israel |
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| Abstract: | This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of the classical “covering” Hubbard model within the algebraic Bethe ansatz framework. The fundamental commutation rules exhibit a hidden 6-vertex symmetry which plays a crucial role in the whole algebraic construction. Next we apply this formalism to study the SU(2) highest weights properties of the eigenvectors and the solution of a related coupled spin model with twisted boundary conditions. The machinery developed in this paper is applicable to many other models, and as an example we present the algebraic solution of the Bariev XY coupled model. |
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