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Completeness of the Bethe Ansatz on Weyl Alcoves [PDF]
Letters in Mathematical Physics, 2009 We prove the completeness of the Bethe ansatz eigenfunctions of the Laplacian on a Weyl alcove with repulsive boundary condition at the walls. For the root system of type A this amounts to the result of Dorlas of the completeness of the Bethe ansatz eigenfunctions of the quantum Bose gas on the circle with repulsive delta-function interaction.
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Confirmation of the Asymptotic Bethe Ansatz
Physical Review Letters, 1995We show that the asymptotic Bethe ansatz gives the exact zero temperature values of all the integrals of motion for the classical one-dimensional system interacting by an inverse-sinh-squared pair potential, in the thermodynamic limit. It is remarkable that the asymptotic Bethe ansatz, using only the scattering data for finite numbers of particles in ...
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2015
The algebraic Bethe Ansatz method for quantum integrable models was proposed by the Leningrad Group [1, 2, 3, 4, 5, 6, 7] in the late 1970s, based on YBE. This method was then generalized to open boundary integrable systems by Sklyanin [8] in 1988, through developing an equation accounting for the integrable boundaries.
Yupeng Wang +3 more
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The algebraic Bethe Ansatz method for quantum integrable models was proposed by the Leningrad Group [1, 2, 3, 4, 5, 6, 7] in the late 1970s, based on YBE. This method was then generalized to open boundary integrable systems by Sklyanin [8] in 1988, through developing an equation accounting for the integrable boundaries.
Yupeng Wang +3 more
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Journal of Physics A: Mathematical and General, 1987
The partition function of a finite Z-invariant six-vertex lattice model (with a prescribed arrow configuration at the boundary) is given. The expression is of the same type that occurs in the Bethe ansatz, but there are no 'wavenumber' equations to solve.
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The partition function of a finite Z-invariant six-vertex lattice model (with a prescribed arrow configuration at the boundary) is given. The expression is of the same type that occurs in the Bethe ansatz, but there are no 'wavenumber' equations to solve.
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2020
Abstract The Thermodynamic Bethe Ansatz (TBA) allows us to study finite size and finite temperature effects of an integrable model. This chapter investigates the integral equations that determine the free energy and gives their physical interpretation.
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Abstract The Thermodynamic Bethe Ansatz (TBA) allows us to study finite size and finite temperature effects of an integrable model. This chapter investigates the integral equations that determine the free energy and gives their physical interpretation.
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2017
The Algebraic Bethe Ansatz (ABA) approach is essentially a second quantization of the coordinate one we used so far. It uses the Yang-Baxter algebra of the transfer matrix to generate the wavefunctions by applying certain operators (which can be interpreted as quasi-particle creation operators) to a reference state (known as the pseudo-vacuum).
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The Algebraic Bethe Ansatz (ABA) approach is essentially a second quantization of the coordinate one we used so far. It uses the Yang-Baxter algebra of the transfer matrix to generate the wavefunctions by applying certain operators (which can be interpreted as quasi-particle creation operators) to a reference state (known as the pseudo-vacuum).
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2009
Abstract The thermodynamics of a quantum field theory in an infinite volume can be determined by its S-matrix. This idea, originally proposed by R. Dashen, S.K. Ma, and H.J. Berstein, has been widely used to study the thermal properties of the integrable field theories in (1 + 1) dimensions. The reason consists of the particularly simple
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Abstract The thermodynamics of a quantum field theory in an infinite volume can be determined by its S-matrix. This idea, originally proposed by R. Dashen, S.K. Ma, and H.J. Berstein, has been widely used to study the thermal properties of the integrable field theories in (1 + 1) dimensions. The reason consists of the particularly simple
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Introduction to the coordinate-space bethe ansatz and to the treatment of bethe ansatz equations
2008The Bethe Ansatz is a method, by which the diagonalization of certain 1D many particle Hamiltonians can be reduced to the solving of a set of nonlinear algebraic equations, the so called Bethe Ansatz equations. This method is presented through the diagonalization of the Heisenberg chain and the δ-gas of spin 1/2 Fermions.
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Heun operator of Lie type and the modified algebraic Bethe ansatz
Journal of Mathematical Physics, 2021Pierre-Antoine Bernard +2 more
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Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions
Nuclear Physics B, 2013Junpeng Cao, Wen-Li Yang, Yupeng Wang
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