92 research outputs found
Topological phases with generalized global symmetries
We present simple lattice realizations of symmetry-protected topological
(SPT) phases with -form global symmetries where charged excitations have
spatial dimensions. Specifically, we construct space-dimensional models
supported on a -colorable graph by using a family of unitary phase
gates, known as multi-qubit control- gates in quantum information community.
In our construction, charged excitations of different dimensionality may
coexist and form a short-range entangled state which is protected by symmetry
operators of different dimensionality. Non-triviality of proposed models, in a
sense of quantum circuit complexity, is confirmed by studying protected
boundary modes, gauged models and corresponding gapped domain walls. We also
comment on applications of our construction to quantum error-correcting codes,
and discuss corresponding fault-tolerant logical gates.Comment: 32 pages, 17 figures, single column (v2, corrected minor mistakes and
typos, to appear in PRB
Exotic topological order in fractal spin liquids
We present a large class of three-dimensional spin models that possess
topological order with stability against local perturbations, but are beyond
description of topological quantum field theory. Conventional topological spin
liquids, on a formal level, may be viewed as condensation of string-like
extended objects with discrete gauge symmetries, being at fixed points with
continuous scale symmetries. In contrast, ground states of fractal spin liquids
are condensation of highly-fluctuating fractal objects with certain algebraic
symmetries, corresponding to limit cycles under real-space renormalization
group transformations which naturally arise from discrete scale symmetries of
underlying fractal geometries. A particular class of three-dimensional models
proposed in this paper may potentially saturate quantum information storage
capacity for local spin systems.Comment: 18 pages, 10 figure
Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory
We examine two proposals for marginally self-correcting quantum memory, the
cubic code by Haah and the welded code by Michnicki. In particular, we prove
explicitly that they are absent of topological order above zero temperature, as
their Gibbs ensembles can be prepared via a short-depth quantum circuit from
classical ensembles. Our proof technique naturally gives rise to the notion of
free energy associated with excitations. Further, we develop a framework for an
ergodic decomposition of Davies generators in CSS codes which enables formal
reduction to simpler classical memory problems. We then show that memory time
in the welded code is doubly exponential in inverse temperature via the Peierls
argument. These results introduce further connections between thermal
topological order and self-correction from the viewpoint of free energy and
quantum circuit depth.Comment: 19 pages, 18 figure
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