QUANTUM SUPERSPIN CHAINS

Towards a Theory of the Integer Quantum Hall Transition: From the Nonlinear Sigma Model to Superspin Chains

A careful study of the supersymmetric version of Pruisken’s nonlinear σ model for the integer quantum Hall effect is presented. The lattice regularized model is cast in Hamiltonian form by taking the anisotropic limit and interpreting the topological density as an alternating sum of Wess-Zumino terms. It is argued that the relevant large-scale physics of the model is preserved by projection of ...

Are there superspin glasses?

Approximate quantum Markov chains

This chapter reviews the concept of a Markov chain for random variables and then introduces a generalization to quantummechanical systems. We discuss the subtle differences between classical and quantumMarkov chains and point out difficulties that show up in the quantum case. Unlike the classical case that has been analyzed and understood well in the past, certain aspects of quantumMarkov chain...

Ising Quantum Chains

Le travail est désormais assuré d'avoir toute la bonne conscience de son côté : la propensionà la joie se nomme déjà " besoin de repos " et commencè a se ressentir comme un sujet de honte. [...] Oui, il se pourrait bien qu'on en vˆıntà ne point céderà un penchant pour la vita contemplativa (c'est-` a-dire pour aller se promener avec ses pensées et ses amis) sans mauvaise conscience et mépris de...

Quantum Markov Chains

A new approach to quantum Markov chains is presented. We first define a transition operation matrix (TOM) as a matrix whose entries are completely positive maps whose column sums form a quantum operation. A quantum Markov chain is defined to be a pair (G, E) where G is a directed graph and E = [Eij ] is a TOM whose entry Eij labels the edge from vertex j to vertex i. We think of the vertices of...