Measuring universal correlation functions in one dimension

Andrey Zheludev (Eidgenössische Technische Hochschule Zürich, Switzerland)

Magnetic materials have always been the models of choice for studying critical phenomena. One dimensional spin systems in particular host a number of very interesting and fundamentally important quantum critical states. The latter can in many cases be understood through a mapping of the spin Hamiltonian on that of interacting Fermions. This correspondence enables exact theoretical predictions not only fro the critical exponents, but also for scaling functions of both thermodynamic properties and correlations. Moreover, these exponents and scaling functions turn out to be partially or even completely universal, in that they are independent of any microscopic details of the underlying spin Hamiltonian. This, in turn, allows for a quantitative comparison of experimental results to exact theory without almost any knowledge about the material under study!

Theoretically, the problem of interaction Fermions in one dimension is an old one and has been fully resolved over two decades ago.
Nevertheless, many of these predictions could not be properly verified experimentally. It has only become possible quite recently, thanks to breakthroughs in the synthesis of new materials, new high resolution neutron spectroscopy techniques and new numerical methods.
In my talk I will describe two examples of such recent studies in magnetized spin ladder materials. One is that of the so-called attractive Tomonaga-Lutinger spin liquid (a quantum critical state of attractive Fermions that has a dynamical exponent z=1). The other deals with "zero-scale-factor" universality at a quantum phase transition with z=2. In both cases we used neutron spectroscopy to directly measure the scaling of temporal correlation functions for a direct comparison with exact analytical results.

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