Exact diagonalisation of 1-d interacting spinless Fermions
Heiner Kohler
TL;DR
This paper develops a method to construct exact eigenfunctions for one-dimensional interacting spinless Fermion systems, enabling diagonalization of the many-body Hamiltonian and validating the asymptotic Bethe Ansatz for specific models.
Contribution
It introduces a novel formalism for exact diagonalization and eigenfunction construction in 1D interacting Fermionic systems, including proofs for the Calogero-Moser-Sutherland model.
Findings
Constructed an infinite set of exact eigenfunctions.
Diagonalized the many-body Hamiltonian explicitly.
Proved the correctness of the asymptotic Bethe Ansatz for the Calogero-Moser-Sutherland model.
Abstract
We acquire a method of constructing an infinite set of exact eigenfunctions of 1--d interacting spinless Fermionic systems. Creation and annihilation operators for the interacting system are found and thereby the many--body Hamiltonian is diagonalised. The formalism is applied to several examples. One example is the theory of Jack polynomials. For the Calogero-Moser-Sutherland Hamiltonian a direct proof is given that the asymptotic Bethe Ansatz is correct.
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