Fracton topological order via coupled layers

By Han Ma, E. Lake, Xie Chen, M. Hermele. 2017

152 citations recorded by the source corpus.

In this work, we develop a coupled layer construction of fracton topological orders in d=3 spatial dimensions. These topological phases have subextensive topological ground-state degeneracy and possess excitations whose movement is restricted in interesting ways. Our coupled layer approach is used to construct several different fracton topological phases, both from stacked layers of simple d=2 topological phases and from stacks of d=3 fracton topological phases. This perspective allows us to shed light on the physics of the X-cube model recently introduced by Vijay, Haah, and Fu, which we demonstrate can be obtained as the strong-coupling limit of a coupled three-dimensional stack of toric codes. We also construct two new models of fracton topological order: a semionic generalization of the X-cube model, and a model obtained by coupling together four interpenetrating X-cube models, which we dub the ‘four color cube model”. The couplings considered lead to fracton topological orders via mechanisms we dub “p-string condensation” and “p-membrane condensation”, in which strings or membranes built from particle excitations are driven to condense. This allows the fusion properties, braiding statistics, and ground-state degeneracy of the phases we construct to be easily studied in terms of more familiar degrees of freedom. Our work raises the possibility of studying fracton topological phases from within the framework of topological quantum field theory, which may be useful for obtaining a more complete understanding of such phases.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/99eef2d9040601df6a101a2ecc480232f2db9ecb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. M. Pretko
2. R. Nandkishore
3. A. Gromov
4. M. Hermele
5. Yizhi You
6. Xie Chen
7. Andrew Lucas
8. S. Pai

In Condensed Matter Physics

1. M. Pretko
2. A. Gromov
3. R. Nandkishore
4. M. Hermele
5. Xie Chen
6. S. Pai
7. Yizhi You
8. Andrew Lucas

Citations in the corpus

• Fractons (2018, methodology): “It has been shown that some gapped fracton phases, in particular the phase of the Xcube model, can be obtained by coupling together two dimensional layers of Z2 toric codes [17, 18].”
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids (2016, background): “e theories is much the same as in a rank 1 U(1) spin liquid, and no further comments are necessary. On the other hand, consider a delta function source for the scalar charge theory: @ i@ jE ij = (r) (21) The scaling of the electric eld now behaves as: E~ij(q) ˘ 1 q2 (22) Eij(r) = Z d3qE~ij(q)eiq~~r ”
• Localization in Fractonic Random Circuits (2018, background): “Parallel to the developments in quantum dynamics, recent years have also witnessed an explosion of interest in fracton phases of quantum matter [26–45] - for a review, see [46].”
• Fracton hydrodynamics (2020, background): “[37] Han Ma, Ethan Lake, Xie Chen, and Michael Hermele,”
• Fracton phases of matter (2020, methodology): “[30] Han Ma, Ethan Lake, Xie Chen, and Michael Hermele, “Fracton topological order via coupled layers,” Phys.”