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Gapless Topological Phases and Symmetry-enriched Quantum Criticality by Verresen, Ruben; Thorngren, Ryan; Jones, Nick G.; Pollmann, Frank is a scholarly article available to read on EtoBox.

What is Gapless Topological Phases and Symmetry-enriched Quantum Criticality about?

We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants, establishing the notion of symmetry-enriched quantum criticality. The charges of nonlocal scaling operators, or more generally of symmetry defects, are topological and imply the presence of localized edge modes. We primarily focus on the $1+1d$ case where the edge has a topological degeneracy, whose finite-size splitting can be exponential or algebraic in system size depending on the involvement of additional gapped sectors. An example of the former is given by tuning the spin-1 Heisenberg chain to a symmetry-breaking 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 $\sim 1/L^{14}$. In addition to such new cases, 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

Author

Verresen, Ruben; Thorngren, Ryan; Jones, Nick G.; Pollmann, Frank

Published

2019

Language

EN