Tailoring non-compact spin chains

Boundary Effects in Non-uniform Spin Chains

We give an explicit comparison of eigenvalues and eigenvectors of XY Hamiltonians of an open linear spin-1/2 chain and a closed spin-1/2 ring with periodic in space coefficients. It is shown that the Hamiltonian of a k-periodic chain with nk − 1 sites has (n − 1)k multiplicity one eigenvalues which are eigenvalues of multiplicity two for a Hamiltonian of a k-periodic ring with 2kn sites. For th...

Spin Networks for Non-Compact Groups

Spin networks are natural generalization of Wilson loops functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables. Physically the restriction to compact gauge group is enough for the study of Yang-mills theories, however it is well known that non-compact groups naturally ari...

On the Gauged Non-compact Spin System

We examine classical and quantum aspects of the planar non-compact spin system coupled with Chern-Simons gauge field in the presence of background charge. We first define our classical spin system as non-relativistic non-linear sigma model in which the order parameter spin takes value in the non-compact manifold M = SU(1, 1)/U(1). Although the naive model does not allow any finite energy self d...

Universality relations in non-solvable quantum spin chains

We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models.

Field-Induced Disorder Point in Non-Collinear Ising Spin Chains