# 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} }

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.

## 1,307 Citations

### Classical and quantum integrable systems with boundaries

- Mathematics, Physics
- 1999

We study two-dimensional classically integrable field theory with independent boundary conditions at each end, and obtain three possible generating functions for integrals of motion when this model…

### New solutions to the reflection equation and the projecting method

- Physics
- 1999

New integrable boundary conditions for integrable quantum systems can be constructed by tuning of scattering phases due to reflection at a boundary and an adjacent impurity and subsequent projection…

### Boundary transfer matrices and boundary quantum KZ equations

- Physics, Mathematics
- 2014

A simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an…

### Integrable open-boundary conditions for the q-deformed extended Hubbard model

- Physics
- 1999

Integrable open-boundary condition for the q-deformed Essler-Korepin-Schoutens extended Hubbard model of strongly correlated electrons, are studied in the framework of the boundary quantum inverse…

### The reconstruction of local quantum operators for the boundary XXZ spin-½ Heisenberg chain

- Physics
- 2000

The method of the reconstruction of local quantum operators in terms of the elements of the quantum monodromy matrix is applied to the XXZ spin-½ Heisenberg chain with integrable boundary conditions.

### Quantum spin chain with `soliton non-preserving' boundary conditions

- Mathematics
- 2000

We consider the case of an integrable quantum spin chain with `soliton non-preserving' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain…

### Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

- Physics, Mathematics
- 1995

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them in the framework of the quantum inverse scattering method. The quasi-exactly…

### OPEN T-J CHAIN WITH BOUNDARY IMPURITIES

- Physics
- 1999

We study integrable boundary conditions for the supersymmetric t-J model of correlated electrons which arise when combining static scattering potentials with dynamical impurities carrying an internal…

## References

SHOWING 1-10 OF 15 REFERENCES

### On perturbations of the periodic Toda lattice

- Mathematics, Physics
- 1976

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…

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

- Physics
- 1987

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

- Physics
- 1971

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…

### Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

- Mathematics, Physics
- 1979

### Aq-difference analogue of U(g) and the Yang-Baxter equation

- Mathematics
- 1985

Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced. Its structure and representations are studied in the simplest case g=sl(2). It is then applied…