arXiv:1905.00082 · International Journal of Modern Physics E

Symmetries of Hamiltonians describing systems with arbitrary spins

Michael J. Cervia, Amol V. Patwardhan, A. B. Balantekin

Published May 1, 2019• 9 citations

Abstract

We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial relationships between the operator invariants, or equivalently, between eigenvalues of those invariants.

DOI: 10.1142/s0218301319500320

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arXiv:1905.00082 · International Journal of Modern Physics E

Symmetries of Hamiltonians describing systems with arbitrary spins

Michael J. Cervia, Amol V. Patwardhan, A. B. Balantekin

Published May 1, 2019• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1142/s0218301319500320

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q

is a root of unity. We start by solving the six-vertex model with fixed boundary conditions (FBC) that guarantee exact

SU(2)_q

invariance on the lattice. The algebra of the Yang-Baxter (YB) and

SU(2)_q

generators turns to close. The infinite spectral parameter limit of the YB generators yields {\bf cleanly} the

SU(2)_q

generators. The Bethe Ansatz states constructed for FBC are shown to be {\bf highest weights} of

SU(2)_q

. The higher level Bethe Ansatz equations (BAE, describing the physical excitations) are explicitly derived for FBC. We then solve the RSOS(

p

) models on the light--cone lattice with fixed boundary conditions by disentangling the type II representations of

SU(2)_q

, at

q=e^{iπ/p}

, from the full SOS spectrum obtained through Algebraic Bethe Ansatz. The RSOS states are those with quantum spin $J

Exact solution of the

SU_{q}(n)

invariant quantum spin chains

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the

A_{n-1}

vertex model with fixed open boundary conditions and the corresponding

SU_{q}(n)

invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.