Gapless Topological Phases and Symmetry-Enriched Quantum Criticality

By R. Verresen, Ryan Thorngren, N. G. Jones, Frank Pollmann. Physical Review X, 2019

139 citations recorded by the source corpus.

We introduce topological invariants for critical bosonic and fermionic chains. More generally, the symmetry properties of operators in the low-energy conformal field theory (CFT) provide discrete invariants, establishing the notion of symmetry-enriched quantum criticality. For nonlocal operators, these invariants are topological and imply the presence of localized edge modes. Depending on the symmetry, the finite-size splitting of this topological degeneracy can be exponential or algebraic in system size. An example of the former is given by tuning the spin-1 Heisenberg chain to an Ising phase. An example of the latter arises between the gapped Ising and cluster phases: this symmetry-enriched Ising CFT has an edge mode with finite-size splitting $\sim 1/L^{14}$. More generally, our formalism unifies various examples previously studied in the literature. Similar to gapped symmetry-protected topological phases, a given CFT can split into several distinct symmetry-enriched CFTs. This raises the question of classification, to which we give a partial answer---including a complete characterization of symmetry-enriched Ising CFTs.

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

View Paper: https://www.semanticscholar.org/paper/66e9c5a898bdf491fbf05d9804c059a9568c0251

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. Yifan Wang
2. Ryan Thorngren
3. D. Gaiotto

In Condensed Matter Physics

1. Yifan Wang
2. Ryan Thorngren

Citations in the corpus

• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, background): “flip and as one of the symmetry generators in this SPT, we obtain a variation of Ising(2) which we call Ising after [52], where this theory was studied as a possible topologically enriched critical point.”