Emergence and topological order in classical and quantum systems

• Published in: Studies in History and Philosophy of Modern Physics Vol. 66; pp. 155 - 169
• Main Authors: McLeish, Tom, Pexton, Mark, Lancaster, Tom
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2019
• ISSN: 1355-2198; 1879-2502
• DOI: 10.1016/j.shpsb.2019.02.006

There has been growing interest in systems in condensed matter physics as a potential source of examples of both epistemic and ontological emergence. One of these case studies is the fractional quantum Hall state (FQHS). In the FQHS a system of electrons displays a type of holism due to a pattern of long-range quantum entanglement that some argue is emergent. Indeed, in general, quantum entanglement is sometimes cited as the best candidate for one form of ontological emergence. In this paper we argue that there are significant formal and physical parallels between the quantum FQHS and classical polymer systems. Both types of system cannot be explained simply by considering an aggregation of local microphysical properties alone, since important features of each are globally determined by topological features. As such, we argue that if the FQHS is a case of ontological emergence then it is not due to the quantum nature of the system and classical polymer systems are ontologically emergent as well. •The entangled polymer ring system is a candidate for showing strong emergence.•Emergent, topological degrees of freedom act decisively in this system.•This demonstrates possible ontological emergence, without quantum mechanics.•There is a mathematical correspondence with the fractional quantum Hall effect.