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Exact thermodynamics of the Hubbard chain: free energy and correlation lengths
Institution: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. Institute of Manufacturing Management, Faculty of Manufacturing Technologies with the seat in Prešov, Technical University of Košice, Bayerova 1, 08001 Prešov, Slovakia;2. Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 04001 Košice, Slovakia;3. Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Svientsitskii Street 1, 79011 L''viv, Ukraine;1. Angewandte Physik-Sensorik, BTU Cottbus, Konrad Wachsmann Allee 17, 03046 Cottbus, Germany;2. Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany;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
Abstract:We study the one-dimensional Hubbard model at finite temperatures in the quantum transfer matrix approach. The eigenvalue equations of this matrix are obtained by a nested Bethe ansatz. The largest and next-largest eigenvalues yield the free energy as well as the correlation lengths of the system. An equivalent set of four integral equations is derived from the Bethe ansatz equations. The limit of Trotter-Suzuki number N → ∞ is taken analytically. For half-filling the final equations are studied in the low-temperature limit yielding analytic expressions for the free energy and spin-spin correlation length. Numerical results are presented for intermediate temperatures.
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