Ferromagnetic Ordering of Energy Levels for $U_q(\mathfrak{sl}_2)$ Symmetric Spin Chains

Details Ferromagnetic Ordering of Energy Levels for $U_q(\mathfrak{sl}_2)$ Symmetric Spin Chains Ferromagnetic Ordering of Energy Levels for $U_q(\mathfrak{sl}_2)$ Symmetric Spin Chains

2011-05-26

arxiv.org/abs/1105.5264v1

Physics

Mathematical Physics

23 pages

Scientific paper

We consider the class of quantum spin chains with arbitrary $U_q(\mathfrak{sl}_2)$-invariant nearest neighbor interactions, sometimes called $\textrm{SU}_q(2)$ for the quantum deformation of $\textrm{SU}(2)$, for $q>0$. We derive sufficient conditions for the Hamiltonian to satisfy the property we call {\em Ferromagnetic Ordering of Energy Levels}. This is the property that the ground state energy restricted to a fixed total spin subspace is a decreasing function of the total spin. Using the Perron-Frobenius theorem, we show sufficient conditions are positivity of all interactions in the dual canonical basis of Lusztig. We characterize the cone of positive interactions, showing that it is a simplicial cone consisting of all non-positive linear combinations of "cascade operators," a special new basis of $U_q(\mathfrak{sl}_2)$ intertwiners we define. We also state applications to interacting particle processes.

Affiliated with

Also associated with

No associations

Rating

Ferromagnetic Ordering of Energy Levels for $U_q(\mathfrak{sl}_2)$ Symmetric Spin Chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ferromagnetic Ordering of Energy Levels for $U_q(\mathfrak{sl}_2)$ Symmetric Spin Chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ferromagnetic Ordering of Energy Levels for $U_q(\mathfrak{sl}_2)$ Symmetric Spin Chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-217906