Boundary conditions for integrable quantum systems

@article{Sklyanin1988BoundaryCF,
  title={Boundary conditions for integrable quantum systems},
  author={Evgeny K. Sklyanin},
  journal={Journal of Physics A},
  year={1988},
  volume={21},
  pages={2375-2389}
}
  • E. Sklyanin
  • Published 21 May 1988
  • Physics, Mathematics
  • Journal of Physics A
A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open quantum chains with appropriate boundary terms in the Hamiltonian. The general considerations are applied to the XXZ and XYZ models, the nonlinear Schrodinger equation and Toda chain. 

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References

SHOWING 1-10 OF 15 REFERENCES

On perturbations of the periodic Toda lattice

A class of Hamiltonian systems including perturbations of the periodic Toda lattice and homogeneous cosmological models is studied. Separatrix approximation of oscillation regimes in these systems

Pauli principle for one-dimensional bosons and the algebraic bethe ansatz

For the construction of the physical vacuum in exactly solvable one-dimensional models of interacting bosons it is important that the momenta of all the particles be different. We give a formal proof

Dynamical charges in the quantized renormalized massive Thirring model

Hubbard chain with reflecting ends

The one-dimensional Hubbard model bounded by infinitely high potential walls is exactly diagonalised by Bethe-Yang ansatz techniques. The 'surface' energy is studied for the half-filled band and in

Surface exponents of the quantum XXZ, Ashkin-Teller and Potts models

Eigenspectra of the critical quantum Ashkin-Teller and Potts chains with free boundaries can be obtained from that of the XXZ chain with free boundaries and a complex surface field. By deriving and

Boundary Energy of a Bose Gas in One Dimension

By the superposition of Bethe's wave functions, using the Lieb's solution for the system of identical bosons interacting in one dimension via a $\ensuremath{\delta}$-function potential, we construct

One-dimensional anisotropic Heisenberg chain