Session M66: Fractons: from symmetry and fractionalisation to dynamics and realisations

Fracton topological order via quantum elasticity duality

I will discuss a recent discovery that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor and to a coupled-vector gauge theories, thereby providing a concrete realization of the “fracton order” phenomenon. The disclinations and dislocations respectively map onto charges and dipoles of these gauge theories. The fractionalized mobility of fractons matches the constrained dynamics of lattice topological defects. These dualities lead to predictions fractonic phases, and phase transitions to their descendants, that are duals of the commensurate crystal, supersolid, smectic, and hexatic liquid crystals. Extensions of this duality to generalized elasticity theories provide a route to discovery of new fractonic models and their potential experimental realizations.

Michael Pretko, Leo Radzihovsky, "Fracton-Elasticity Duality", Phys. Rev. Lett. 120, 195301 (2018);
"Symmetry Enriched Fracton Phases from Supersolid Duality", Phys. Rev. Lett. 121, 235301 (2018).
Leo Radzihovsky, Michael Hermele, "Fractons from vector gauge theory", arXiv:1905.06951   

Non-Abelian Fracton Order: a TQFT perspective

Fracton phases exhibit striking behaviour which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm. In this talk, I will discuss progress towards understanding fracton order from the perspective of TQFTs, focusing primarily on non-Abelian fracton models, which host non-Abelian particles with restricted mobility in three spatial dimensions. In particular, I will present topological defect networks – networks of topological defects embedded in stratified 3+1D TQFTs – as a new, unified framework for describing gapped fracton orders.   

Fractons: The Road to Reality

In this talk, I will give an overview of progress towards connecting the field of fractons with experiments. I will begin with a brief introduction to fractons, describing some of the models and phenomenology encountered in the field. I will then describe some advances in proposed spin models realizing fracton behavior, along with some experimental diagnostics which are useful for detecting fractons. Finally, I will discuss several new platforms for realizing fracton physics, such as hole-doped antiferromagnets and electric circuits.   

Rank-2 Coulomb Spin Liquids from Classical Spins

Coulomb spin liquids are well studied spin liquid states exhibiting emergent electromagnetism, having a coarse-grained description corresponding to Maxwell's laws. It has recently been appreciated that even more exotic scenarios are possible, realizing generalizations of electromagnetism with rank-2 electric and magnetic fields. These are of particular interest since the emergent charges of the rank-2 electromagnetism can be fractons, with fundamentally constrained mobility.

In this talk I will describe an approach to finding simple, bilinear models, for classical spins which realize rank-2 Coulomb phases at low temperature [1,2]. Such models provide access to rank-2 Coulomb phase physics in a setting amenable to efficient numerical study and also suggest directions to look for rank-2 Coulomb phases in experiment.

Remarkably, we find that a traceless, vector-charged, rank-2 Coulomb phase can be generated by perturbing a simple Heisenberg model on the pyrochlore lattice with breathing anisotropy and weak Dzyalozhinskii-Moriya interactions [2]. This enables us to identify Yb-based breathing pyrochlores as potential candidate systems and to make explicit predictions for how the rank-2 Coulomb phase would manifest itself in experiment.


[1] O. Benton, L. D.C. Jaubert, H. Yan and N. Shannon, Nature Commun. 7, 11572 (2016)
[2] H. Yan, O. Benton, L. D.C. Jaubert and N. Shannon, arXiv:1902.10934
  

Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians

We show that the combination of charge and dipole conservation---characteristic of fracton systems---leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total Sz) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value. The absence of thermalization is identified as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local Sz basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including four-site terms and find that this perturbation leads to a weak fragmentation: the system still has exponentially many invariant subspaces, but they are no longer sufficient to avoid thermalization for typical initial states. More generally, for any finite range of interactions, the system still exhibits non-thermal eigenstates appearing throughout the entire spectrum.