Rényi entropy perspective on topological order in classical toric code models

Topological entanglement Rényi entropy and reduced density matrix structure.

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordere...

Entanglement and topological entropy of the toric code at finite temperature

We calculate exactly the von Neumann and topological entropies of the toric code as a function of system size and temperature. We do so for systems with infinite energy scale separation between magnetic and electric excitations, so that the magnetic closed loop structure is fully preserved while the electric loop structure is tampered with by thermally excited electric charges. We find that the...

Interplay of topological order and spin glassiness in the toric code under random magnetic fields

Dimitris I. Tsomokos,1 Tobias J. Osborne,1,2 and Claudio Castelnovo3 1Department of Mathematics, Royal Holloway, University of London, Egham TW20 0EX, United Kingdom 2Wissenschaftskolleg zu Berlin, Wallotstraße 19, D-14193 Berlin, Germany 3Rudolf Peierls Centre for Theoretical Physics and Worcester College, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom (Received 29 December...

On the Conditional Rényi Entropy

On Rényi entropy power inequalities

This paper is a follow-up of a recent work by Bobkov and Chistyakov, obtaining some improved Rényi entropy power inequalities (R-EPIs) for sums of independent random vectors. The first improvement relies on the same bounding techniques used in the former work, while the second significant improvement relies on additional interesting properties from matrix theory. The improvements obtained by th...