Abstract
We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL) in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.
4 More- Received 21 October 2016
DOI:https://doi.org/10.1103/PhysRevX.6.041070
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Topological phases of matter are systems that look boring almost everywhere but have interesting properties at the surfaces that would be impossible if not for the existence of the underlying material. Some of these phases are “chiral,” featuring unidirectional transport of quantities such as electron charge around the edge. We pose the following question: Can chiral phases exist in settings where neither charge nor energy is conserved? Since those nonconserved properties can just appear and disappear, they cannot be pumped around the system, and the usual description of chiral phases fails. We find that, nonetheless, chiral phases are tenable in such systems. Instead of charge or energy, quantum information is pumped around the edges.
We developed a theoretical framework in which we can describe chiral phases in a two-dimensional system of bosons—subatomic particles, such as photons, that can occupy a single quantum state. While the main focus of our study is bosons, we find that this can be extended to some systems of fermions, which are subatomic particles (such as electrons), that cannot occupy the same quantum state. We describe a possible experimental setup in which bosonic atoms are cooled to low temperatures and loaded onto a 2D lattice with lasers. If our description of chiral phases is valid, then particle numbers will remain stable in the bulk of the setup while those at the edge will rotate about the center.
While the age of quantum computing is still a ways off, one-way transport of quantum information could be used to distribute quantum entanglement, a universal resource for any quantum communication protocol.