dimer (changes) in nLab

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Contents

Idea

In solid state physics and quantum many-body physics, and specifically in the context of topological phases of matter, by a dimer one means an edge a→ba \to b in some graph that models a given physical system.

Typically this goes along with some prescription for what is to be associated with/modeled by this dimer.

For example a Majorana dimer encodes an pair of entangled qbits (“spins”). In Majorana dimer codes these dimers arrange as the chords of a chord diagram, see at holographic entanglement entropy the section Chord diagra, diagram, representation.

References

Survey:

• Richard Kenyon, Andrei Okounkov, What is… a dimer?, Notices of the AMS, Vol. 52 No 3 (2005) (pdf)

• Richard Kenyon, An introduction to the dimer model (arXiv:math/0310326)

• Subir Sachdev, Quantum dimer model

Original articles:

As a model for superconductivity:

• Daniel S. Rokhsar and Steven A. Kivelson, Superconductivity and the Quantum Hard-Core Dimer Gas, Phys. Rev. Lett. 61, 2376 – Published 14 November 1988 (arXiv:10.1103/PhysRevLett.61.2376)