Inverse method for a generalized spin chain

Michael Fowler

Zhi-Ming Bai, Yaru Wang, Zhan Wei Xu +1 more

The free energy and Green function of the multi-coupled spin chain in low-energy theory are given by using the functional bosonization method. We deduce that 2 m coupled spinless chains ( m = 0,1,2,...), by using a series of unitary transformations, can be reduced to some uncoupled chains, but for other numbers of coupled spinless chains we need to solve a series of inverse matrices generally; for either case, the system can be formally separated into the charge and spin parts.

M R Davies, C K Harris, Robin B. Stinchcombe

Transfer matrix methods are used to obtain the partition function and correlation length of Ising chains at low temperatures. For the infinite-spin chain, asymptotically exact eigenvalues and eigenvectors are obtained from an iteration scheme, and from a secular equation method. It is also shown how the Ising chain for general spin S (including S to infinity ) may be treated using a 2*2 transfer matrix. For low temperatures (K identical to J/K B T>>1) the inverse correlation length, in units of the spin spacing, is xi -1 =4S e -2K +O(e -4K ) for finite S, and xi -1 =8K e -2K (ln 4K+ gamma +O((lnK)/K)) for infinite spin where gamma is Euler's constant.

Jill C. Bonner, Henk W. J. Blöte, Hans Beck +1 more

Oleg Derzhko, Taras Krokhmalskii, Joachim Stolze

P. P. Kulish

Diagonalization of integrable spin chain Hamiltonians by the quantum inverse scattering method gives rise to the connection with representation theory of different (quantum) algebras. Extending the Schur-Weyl duality between sl2 and the symmetric group SN from the case of the isotropic spin 1/2 chain (XXX-model) to a general spin chains related to the Temperley-Lieb algebra TLN(q) one finds a new quantum algebra Uq(n) with the representation ring equivalent to the sl2 one.