SKM 2021 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 19: Transport (joint session TT/DY)

DY 19.5: Vortrag

Freitag, 1. Oktober 2021, 14:30–14:45, H6

Thermal fluctuations of two-dimensional crystalline membranes: a scale-invariant but nonconformal field theory — •Achille Mauri and Mikhail I. Katsnelson — Radboud University, Institute for Molecules and Materials, Nijmegen, The Netherlands

Statistical fluctuations of two-dimensional membranes have been the subject of extensive investigations, from string theories to biological and condensed matter systems such as graphene and other atomically-thin 2D materials. In the case of solid layers subject to vanishing external tension, the interplay of thermal fluctuations and anharmonic phonon-phonon interactions gives rise to a crucial renormalization of the elastic constants: as a result, the long-wavelength behavior of phonon fluctuations is scale-invariant and it is controlled by an interacting fixed point of the renormalization group (RG). In this contribution, we argue that, in contrast with several other field-theories, the emergent dilatation symmetry is not enhanced to the full conformal invariance. We analyze in particular, the structure of the energy-momentum tensor T_{µ ν} within an є-expansion, after extension of the problem from the physical dimension D = 2 to a non-integer dimensionality D = 4 − є. The trace T_{µ µ} reduces, at the fixed point, to the total divergence of a non-trivial virial current, implying the absence conformal invariance.