Entanglement and SU(n) symmetry in one-dimensional valence bond solid states

Here we evaluate the many-body entanglement properties of a generalized SU(n) valence bond solid state on a chain. Our results follow from a derivation of the transfer matrix of the system which, in combination with symmetry properties, allows for a new, elegant and straightforward evaluation of different entanglement measures. In particular, the geometric entanglement per block, correlation length, von Neumann and R\'enyi entropies of a block, localizable entanglement and entanglement length are obtained in a very simple way. All our results are in agreement with previous derivations for the SU(2) case.Comment: 4 pages, 2 figure

On the completeness of solutions of Bethe's equations

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of numbers of so-called singular (or exceptional) solutions. Using homotopy continuation methods, we find all such solutions of the Bethe equations for chains of length up to 14. The numbers of these solutions are in perfect agreement with the conjecture. We also discuss an indirect method of finding solutions of the Bethe equations by solving the Baxter T-Q equation. We briefly comment on implications for thermodynamical computations based on the string hypothesis.Comment: 17 pages; 85 tables provided as supplemental material; v2: clarifications and references added; v3: numerical results extended to N=14, M=

Off-farm Work, Technical Efficiency, and Production Risk: Empirical Evidence from a National Farmer Survey in Taiwan

The objective of this paper is to investigate the differences in yield production, production efficiency, and yield risk for farmers with and without off-farm work. Using a nationwide survey of Taiwanese rice farmers, we estimate a stochastic production frontier model accommodating the technical inefficiency and the production risk simultaneously. Applying the stochastic dominance criterion to rank the estimated technical efficiency and yield risk between professional farmers and farmers with off-farm jobs, our empirical analysis shows that off-farm work is significantly associated with lower technical efficiency. Additionally, farmers with off-farm work face higher production risks. Comparing the marginal effects of input uses on technical inefficiency and yield risk between these groups of farmers, we found a substantial heterogeneity of input uses between these two groups of farmers.Off-farm work, technical efficiency, production risk, Taiwan, Crop Production/Industries, Farm Management,

Singular solutions, repeated roots and completeness for higher-spin chains

We investigate the completeness of the solutions of the Bethe equations for the integrable spin-s isotropic (XXX) spin chain with periodic boundary conditions. Solutions containing the exact string i s, i (s-1), ..., -i(s-1), -is are singular. For s>1/2, there exist also "strange" solutions with repeated roots, which nevertheless are physical (i.e., correspond to eigenstates of the Hamiltonian). We derive conditions for the singular solutions and the solutions with repeated roots to be physical. We formulate a conjecture for the number of solutions with pairwise distinct roots in terms of the numbers of singular and strange solutions. Using homotopy continuation, we solve the Bethe equations numerically for s=1 and s=3/2 up to 8 sites, and find some support for the conjecture. We also exhibit several examples of strange solutions.Comment: 17 pages; many tables provided as supplemental material; v2: minor change

Precessionless spin transport wire confined in quasi-two-dimensional electron systems

We demonstrate that in an inversion-asymmetric two-dimensional electron system 2DES with both Rashba and Dresselhaus spin-orbit couplings taken into account, certain transport directions on which no spin precession occurs can be found when the injected spin is properly polarized. By analyzing the expectation value of spin with respect to the injected electron state on each space point in the 2DES, we further show that the adjacent regions with technically reachable widths along these directions exhibit nearly conserved spin. Hence a possible application in semiconductor spintronics, namely, precessionless spin transport wire, is proposed.Comment: 3 pages, 4 figures, to be appeared in Journal of Applied Physics, Proceedings of the 50th MMM Conferenc

Purchasing power parity in G-7 countries: Further evidence based on ADL test for threshold cointegration

This study applies a newly-developed Autoregressive Distributed Lag (ADL) test for threshold cointegration, proposed by Li and Lee (2010) to test the validity of long-run purchasing power parity (PPP) for G-7 countries over the January 1994 to April 2010. The empirical results indicate that PPP only holds true for Canada and France two countries. Our results have important policy implications for the G-7 countries under study.Purchasing Power Parity; G-7 Countries; ADL Test; Threshold Cointegration

Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity

We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of dimensions of irreducible representations of the Temperley-Lieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)_q-modules. These formulas include corrections that appear if two or more tilting modules are spectrum-degenerate. For the XX case (q=exp(i pi/2)), we give explicit formulas for the number of admissible solutions and degeneracies. We also consider the cases of generic q and the isotropic (q->1) limit. Numerical solutions of the Bethe equations up to N=8 are presented. Our results are consistent with the Bethe ansatz solution being complete.Comment: 34 pages; v2: reference added; v3: two more references added and minor correction