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  • Letter
  • Open Access

Exact solution to the quantum and classical dimer models on the spectre aperiodic monotiling

Shobhna Singh1,2 and Felix Flicker2

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Phys. Rev. B 109, L220303 – Published 18 June, 2024

DOI: https://doi.org/10.1103/PhysRevB.109.L220303

Abstract

The decades-long search for a shape that tiles the plane only aperiodically under translations and rotations recently ended with the discovery of the “spectre” aperiodic monotile. In this setting we study the dimer model, in which dimers are placed along tile edges such that each vertex meets precisely one dimer. The complexity of the tiling combines with the dimer constraint to allow an exact solution to the model. The partition function is Z=2Nmystic+1 where Nmystic is the number of “mystic” tiles. We exactly solve the quantum dimer (Rokhsar-Kivelson) model in the same setting by identifying an eigenbasis at all interaction strengths V/t. We find that test monomers, once created, can be infinitely separated at zero energy cost for all V/t, constituting a deconfined phase in a (2+1)-dimensional bipartite quantum dimer model.

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Phys. Rev. B 109, L220303– Published 18 June, 2024
  • Received 2 October 2023
  • Revised 23 May 2024
  • Accepted 3 June 2024
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