# Calculation of norms of Bethe wave functions

@article{Korepin1982CalculationON, title={Calculation of norms of Bethe wave functions}, author={Vladimir E. Korepin}, journal={Communications in Mathematical Physics}, year={1982}, volume={86}, pages={391-418} }

A class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered. Eigenfunctions of the Hamiltonians are known for these models. Norms of these eigenfunctions in the finite box are calculated in the present paper. These models include in particular the quantum nonlinear Schrödinger equation and the HeisenbergXXZ model.

## 615 Citations

Dressing equations for correlation functions

- Physics
- 1986

Correlation functions of two-dimensional integrable models of quantum field theory and statistical physics are investigated. Dressing equations for the correlation functions are obtained in a model…

Norms of Bethe wave functions for the nonlinear Schrödinger model of spin‐1/2 particles

- Physics
- 1990

A formula for scalar products of Bethe wave functions in the nonlinear Schrodinger model of spin‐ (1)/(2) particles is proposed. It is shown, in addition, that one can replace conjugate states by…

FORM FACTORS IN THE FINITE VOLUME

- Physics
- 1999

We study exactly solvable models of quantum statistical mechanics. Our main example is the Quantum nonlinear Schrodinger equation. This model can be solved by algebraic Bethe Ansatz. We are…

Dual field formulation of quantum integrable models

- Mathematics, Physics
- 1987

Equal time correlators are studied in completely integrable models. The main example is the quantum non-linear Schrödinger equation. Introduction of an auxiliary Fock space permits us to represent…

Correlation functions of integrable models: A description of the ABACUS algorithm

- Physics
- 2009

Recent developments in the theory of integrable models have provided the means of calculating dynamical correlation functions of some important observables in systems such as Heisenberg spin chains…

Quantum projectors and local operators in lattice integrable models

- Mathematics
- 2003

In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for one-dimensional quantum integrable models, especially for the lattice versions of…

The quantum inverse scattering method approach to correlation functions

- Physics
- 1984

The inverse scattering method approach is developed for calculation of correlation functions in completely integrable quantum models with theR-matrix of XXX-type. These models include the…

The algebraic Bethe ansatz and quantum integrable systems

- Mathematics, Physics
- 2007

Methods are considered for applying an algebra with bilinear commutation relations to the theory of quantum integrable systems. This survey describes most of the results obtained in this area over…

Norms of bound states

- Mathematics
- 1988

The formula for the norms of the Bethe wave functions in the form of a Jacobian plays an important role in the computation of the correlation functions. In the present paper this formula is…

Solution of the quantum inverse problem

- Physics, Mathematics
- 1999

We derive a formula that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula is a quantum analogue of the…

## References

SHOWING 1-10 OF 17 REFERENCES

The lattice quantum Sine-Gordon model

- Physics
- 1981

The integrable statistical physics model on the rectangular two-dimensional lattice which we call ‘the L-model’ is constructed. This model generates the integrable quantum sine-Gordon model on the…

Bose Gas in One Dimension. I. The Closure Property of the Scattering Wavefunctions

- Physics
- 1971

We verify the closure relation of a continuum basis of Lieb's wavefunctions, describing the scattering states of identical bosons interacting via a δ‐function potential in one dimension.

One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System

- Physics
- 1966

Bethe's hypothesis is proved for the ground state of a one-dimensional cyclic chain of anisotropic nearest-neighbor spin-spin interactions. The proof holds for any fixed number of down spins.

Spontaneous staggered polarization of theF-model

- Physics
- 1973

The “order parameter” of the two-dimensionalF-model, namely the spontaneous staggered polarizationP0, is derived exactly. At the critical temperatureP0 has an essential singularity, bothP0 and all…

Exact Solution of the Problem of the Entropy of Two-Dimensional Ice

- Physics, Chemistry
- 1967

At low temperatures ice has a residual entropy caused, presumably, by an indeterminacy of the crystal structure. The oxygen atoms constitute a periodic crystal lattice that is hydrogen bonded. The…

Solvable eight-vertex model on an arbitrary planar lattice

- PhysicsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- 1978

Any planar set of intersecting straight lines forms a four-coordinated graph, or ‘lattice’, provided no three lines intersect at a point. For any such lattice an eight-vertex model can be…

Study of Exactly Soluble One-Dimensional N-Body Problems

- Physics
- 1964

In this paper it is shown that several cases of one‐dimensional N‐body problems are exactly soluble. The first case describes the motion of three one‐dimensional particles of arbitrary mass which…

Zur Theorie der Metalle

- Physics
- 1931

ZusammenfassungEs wird eine Methode angegeben, um die Eigenfunktionen nullter und Eigenwerte erster Näherung (im Sinne des Approximationsverfahrens von London und Heitler) für ein „eindimensionales…

Phys

- Rev. D 23, 417-4i9
- 1981