Local Scale-Invariance in Disordered Systems

Michel Pleimling, Malte Henkel

Ferenc Pázmándi, R. T. Scalettar, Gergely T. Zimányi

Glen Evenbly, Philippe Corboz, Guifré Vidal

The multiscale entanglement renormalization ansatz (MERA) can be used, in its scale invariant version, to describe the ground state of a lattice system at a quantum-critical point. From the scale invariant MERA one can determine the local scaling operators of the model. Here we show that, in the presence of a global symmetry $\mathcal{G}$, it is also possible to determine a class of nonlocal scaling operators. Each operator consists, for a given group element $g∊\mathcal{G}$, of a semi-infinite string ${\ensuremath{\Gamma}}_{g}^{\ensuremath{\vartriangleleft}}$ with a local operator $\ensuremath{\varphi}$ attached to its open end. In the case of the quantum Ising model, $\mathcal{G}={\mathbb{Z}}_{2}$, they correspond to the disorder operator $\ensuremath{\mu}$, the fermionic operators $\ensuremath{\psi}$ and $\overline{\ensuremath{\psi}}$, and all their descendants. Together with the local scaling operators identity $\mathbb{I}$, spin $\ensuremath{\sigma}$, and energy $ϵ$, the fermionic and disorder scaling operators $\ensuremath{\psi}$, $\overline{\ensuremath{\psi}}$, and $\ensuremath{\mu}$ are the complete list of primary fields of the Ising CFT. Therefore the scale invariant MERA allows us to characterize all the conformal towers of this CFT.

T. R. Kirkpatrick, D. Belitz

Malte Henkel, Michel Pleimling

The ageing of the bond-disordered two-dimensional Ising model quenched to below its critical point is studied through the two-time autocorrelator and thermoremanent magnetization (TRM). The corresponding ageing exponents are determined. The form of the scaling function of the TRM is well described by the theory of local scale invariance.

A. MacKinnon