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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TLDR
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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Edge States: Topological Insulators, Superconductors and QCD Chiral Bags
TL;DR: In this article, the dynamics of the magnetic field in a superconducting phase is described by an effective massive bosonic field theory, and the boundary conditions of the electromagnetic fields are predetermined by physics.
Journal ArticleDOI
The nonlinear Schrodinger model as a special continuum limit of the anisotropic Heisenberg model
TL;DR: In this paper, a mapping of the anisotropic spin-1/2 Heisenberg model in the limit Delta to 1 onto the non-linear Schrodinger model (a gas of bosons with delta function interactions) is given.
Journal ArticleDOI
Symmetry resolved entanglement in integrable field theories via form factor bootstrap
TL;DR: In this paper, the authors considered the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies.
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Log-gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
TL;DR: In this article, the integer moments of a discrete directed polymer (DP) on a square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights are studied using a transfer matrix formulation, which appears as a generalization of the Lieb-Liniger quantum mechanics of bosons to discrete time and space.
Journal ArticleDOI
Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
TL;DR: In this article, a Bethe ansatz-based method was proposed to derive the long-distance asymptotic behavior at finite temperature of the density-density correlation function in the interacting one-dimensional Bose gas.
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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