Quantum spin systems, fermi systems and group extensions

Ola Bratteli, Derek W. Robinson

P. Falco, V. Mastropietro

The phenomenon of Spin-Charge separation in non-Fermi liquids is well understood only in certain solvable d = 1 fermionic systems. In this paper we furnish the first example of asymptotic Spin-Charge separation in a d = 1 non solvable model. This goal is achieved using Renormalization Group approach combined with Ward-Identities and Schwinger-Dyson equations, corrected by the presence of a bandwidth cut-offs. Such methods, contrary to bosonization, could be in principle applied also to lattice or higher dimensional systems. 1 Introduction and Main results In recent years the properties of non-Fermi liquids have been extensively investigated, both from experimental and theoretical point of view. In particular, one of the most spectacular feature appearing in non-Fermi liquids is the phenomenon of Spin-Charge (SC) separation, which is surely relevant for the physics

Martin, Simon, Marcin Raczkowski, Fakher F. Assaad +1 more

A multichannel Kondo system, where a single quantum spin couples to multiple channels of an electronic bath, provides one of the simplest examples of a zero-dimensional non-Fermi liquid. It is natural to ask: what happens when an extensive number of such systems are coupled together? A simple renormalization group argument implies that in a chain of SU(N) multichannel quantum systems, where each spin is coupled to its own bath of K channels, the individual spins dynamically decouple at low energy when N>K, resulting in a 'sliding' non-Fermi liquid. Using Quantum Monte Carlo (QMC) simulations, we find evidences of a continuous, 'dimensionality-changing' phase transition out of this non-Fermi liquid into a valence-bond solid phase as the intersite coupling is increased. Remarkably, at the critical point, correlations exhibit a power-law behavior even along the direction in which the spins are coupled, indicating the breakdown of dynamical decoupling at the transition. We also develop an RG scheme to understand the universal aspects of this transition.

Harald Grosse, Victor Nikolaevich Popov

John B. Parkinson, DAMIAN J. J. FARNELL

Heide Narnhofer

We study the behaviour of continuous automorphism groups of quantum spin systems on the lattice. Whereas the shift is norm asymptotically abelian continuous automorphism groups can lead only to delocalization but not to norm asymptotic abelianess. As a consequence the shift does not allow a continuous extension.