Spin chains

Sharoon Austin, Muhammad Qasim Khan, Maryam Mudassar +1 more

For spins chains to be useful for quantum information processing tasks, the interaction between the spin chain and its environment generally needs to be suppressed. In this paper, we propose the use of strong static and oscillating control fields in order to effectively remove the spin-chain-environment interaction. We find that our control fields can also effectively transform the spin-chain Hamiltonian. In particular, interaction terms which are absent in the original spin-chain Hamiltonian appear in the time-averaged effective Hamiltonian once the control fields are applied, implying that spin-spin interactions can be engineered via the application of static and oscillating control fields. This transformation of the spin chain can then potentially be used to improve the performance of the spin chain for quantum information processing tasks. For example, our control fields can be used to achieve almost perfect quantum state transfer across a spin chain even in the presence of noise. As another example, we show how the use of particular static and oscillating control fields not only suppresses the effect of the environment, but can also improve the generation of two-spin entanglement in the spin chain.

Charles Day

John B. Parkinson, DAMIAN J. J. FARNELL

Olalla A. Castro-Alvaredo, Jean Michel Maillet

We present determinant formulae for the form factors of spin operators of general integrable XXX Heisenberg spin chains for arbitrary (finite-dimensional) spin representations. The results apply to any 'mixed' spin chains, such as alternating spin chains, or to spin chains with magnetic impurities.

Jonas Fransson

D. Arnaudon, Nicolas Crampé, Anastasia Doikou +2 more

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a generic gl(n)-spin chain possessing on each site an arbitrary gl(n)-representation. For open spin chains, we use the classification of the reflection matrices to treat all the diagonal boundary cases. As a result, we obtain the Bethe equations in their full generality for closed and open spin chains. The classifications of finite dimensional irreducible representations for the Yangian (closed spin chains) and for the reflection algebras (open spin chains) are directly linked to the calculation of the transfer matrix eigenvalues. As examples, we recover the usual closed and open spin chains, we treat the alternating spin chains and the closed spin chain with impurity.