Spectrum of a spin chain with inverse square exchange
TLDR
The spectrum of a one-dimensional chain of SU(n) spins positioned at the static equilibrium positions of the particles in the corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied in this article.Abstract:
The spectrum of a one-dimensional chain of SU(n) spins positioned at the static equilibrium positions of the particles in the corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied. As in the translationally invariant Haldane-Shastry model the spectrum is found to exhibit a very simple structure containing highly degenerate 'super-multiplets'. The algebra underlying this structure is identified and several sets of raising and lowering operators are given explicitly. On the basis of this algebra and numerical studies the authors give the complete spectrum and thermodynamics of the SU(2) system.read more
Citations
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Journal ArticleDOI
The physics and mathematics of Calogero particles
TL;DR: A review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains can be found in this article, with a focus on spin chains.
Journal ArticleDOI
Exact spectrum of SU(n) spin chain with inverse square exchange
TL;DR: In this article, the spectrum and partition function of a nonuniform spin chain with long-range interactions are derived, and the partition function takes the form of a q-deformed polynomial.
Book ChapterDOI
Generalized Statistics in One Dimension
TL;DR: An exposition of the different definitions and approaches to quantum statistics is given in this article, with emphasis in one-dimensional situations, and the Calogero model, matrix model and spin chain models constitute specific realizations.
Journal ArticleDOI
Supersymmetric Calogero–Moser–Sutherland models and Jack superpolynomials
TL;DR: In this article, a supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model is presented, which decomposes triangularly in terms of the symmetric monomial superfunctions.
Journal ArticleDOI
Yangian symmetry and Virasoro character in a lattice spin system with long-range interactions
TL;DR: In this paper, the symmetry of lattice su(n ) spin systems with inverse square exchange was investigated and it was shown that both systems have yangian symmetry for a finite number of sites.
References
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Solution of the One‐Dimensional N‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
TL;DR: In this paper, the quantum-mechanical problems of N 1-dimensional equal particles of mass m interacting pairwise via quadratic (harmonical) and/or inverse (centrifugal) potentials is solved.
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Solution of a three-body problem in one-dimension
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Exact Results for a Quantum Many-Body Problem in One Dimension
TL;DR: In this paper, a system of either fermions or bosons interacting in one dimension by a two-body potential with periodic boundary conditions was investigated, and expressions for the one-particle density matrix at zero temperature and particular (nontrivial) values of the coupling constant $g, as a determinant of order $N\ifmmode\times\else\texttimes\fi{}N$ were presented.
Journal ArticleDOI
Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-(1/2 antiferromagnetic Heisenberg chain with 1/r2 exchange.
TL;DR: In this article, a set of Jastrow wave functions comprises exact eigenstates of a family of S = 1/2$ antiferromagnetic chains with exchange, and the full set of energy levels of this model is obtained; the spectrum exhibits remarkable ''supermultiplet'' degeneracies suggesting the existence of a hidden continuous symmetry.
Journal ArticleDOI
Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions.
TL;DR: The S=½ Heisenberg Hamiltonian H = ½ N - 1Σn = 1NΣm = 1 Jn σM · σm+n with Jn=J0/sin2 (nπ/N), is shown to have a simple singlet ground state in the form of a Jastrow function.