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