A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions

We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund and Rommer [1], we separate the Hilbert space of the system into subspaces with different momentum. This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation. Surprisingly, many branches of the dispersion relation are approximated to a very good precision. We benchmark the accuracy of the algorithm by comparison with the exact solutions of the quantum Ising and the antiferromagnetic Heisenberg spin-1/2 model.Comment: 13 pages, 11 figures, 5 table

Intra-sector mobility and psecific inputs in tax-incidence theory

In a simple three-factor-two-final-good formulation (two factors immobile and sector-specific), a well-known result under competitive and full-employment assumptions is that a partial tax on the mobile factor in either industry hurts that factor everywhere. It can be reversed, however, when the taxed activity uses a sector-specific input produced in the other sector. The model becomes asymmetrical: the same tax often yields different results, depending on where it is levied and the nature and cross-sector linkages of various inputs. Their respective roles in determining tax- incidence are discussed in a series of plausible settings, each 3 x 2, involving primary and produced inputs and intra-sector mobility of some sector-specific factors. Cross-sector linkages of produced inputs, more than any other element, drive the new results which are often similar to those in models with all mobile factors

On Kostant's partial order on hyperbolic elements

We study Kostant's partial order on the elements of a semisimple Lie group in relations with the finite dimensional representations. In particular, we prove the converse statement of [3, Theorem 6.1] on hyperbolic elements.Comment: 7 page