Journal ArticleDOI
Exact analysis of an interacting bose gas. i. the general solution and the ground state
Elliott H. Lieb,Werner Liniger +1 more
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In this paper, the ground-state energy as a function of γ was derived for all γ, except γ = 0, and it was shown that Bogoliubov's perturbation theory is valid when γ is small.Abstract:
A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the solutions of a transcendental equation. The problem has one nontrivial coupling constant, γ. When γ is small, Bogoliubov’s perturbation theory is seen to be valid. In this paper, we explicitly calculate the ground-state energy as a function of γ and show that it is analytic for all γ, except γ=0. In Part II, we discuss the excitation spectrum and show that it is most convenient to regard it as a double spectrum—not one as is ordinarily supposed.read more
Citations
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Entanglement between particle partitions in itinerant many-particle states
TL;DR: In this paper, particle-partitioning entanglement for itinerant many-particle systems is defined as "entanglement between two subsets of particles making up the system".
Journal ArticleDOI
On Bethe vectors in \( \mathfrak{g}{\mathfrak{l}}_3 \) -invariant integrable models
TL;DR: In this article, the authors considered quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing a constant -invariant R-matrix and proved that the vectors constructed by this method are semi-on-shell Bethe vectors for arbitrary values of Bethe parameters.
Journal ArticleDOI
On integrable directed polymer models on the square lattice
TL;DR: In this article, a two-parameter family of integrable directed polymer models with random weights on the square lattice is presented, called the Inverse-Beta polymer.
Journal ArticleDOI
Exact results of the ground state and excitation properties of a two-component interacting Bose system
TL;DR: In this article, the ground state and low-lying excitations of a Bose system with repulsive δ-function interaction in the presence of an SU(2) intrinsic degree of freedom on the basis of the coordinate Bethe ansatz were determined by both numerical and analytical methods.
Journal ArticleDOI
Form factors of local operators in a one-dimensional two-component Bose gas
TL;DR: In this paper, the authors consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schr\"odinger operator of free spinless particle.
References
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Journal ArticleDOI
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
TL;DR: In this article, a rigorous one-one correspondence between one-dimensional systems of bosons and spinless fermions is established, subject only to the restriction that the interaction has an impenetrable core.
Journal ArticleDOI
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
TL;DR: In this paper, the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum was carried out and it was shown that the elementary excitations are most naturally thought of as a double spectrum, not a single one.
Journal ArticleDOI
Linear antiferromagnetic chain with anisotropic coupling
TL;DR: In this article, the exact solution for a linear chain of spin atoms coupled together by the anisotropic Hamiltonian was given for the antiferromagnetic ground state and comparison was made with a variational method.
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