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Symmetry-protected topological (SPT) order is a kind of order in zero-temperature quantum-mechanical states of matter that have a symmetry and a finite energy gap. To derive the results in a most-invariant way, renormalization group methods are used (leading to equivalence classes corresponding to certain fixed … 展开
1. The boundary effective theory of a non-trivial SPT state always has pure gauge anomaly or mixed gauge-gravity anomaly for the symmetry group. As a result, the boundary of a SPT state is … 展开
Using the notion of quantum entanglement, one obtains the following general picture of gapped phases at zero temperature. All gapped zero-temperature phases can be divided into two classes: long-range entangled phases (ie phases with intrinsic topological order 展开
SPT states are short-range entangled while topologically ordered states are long-range entangled. Both intrinsic topological order, and … 展开
The first example of SPT order is the Haldane phase of odd-integer spin chain. It is a SPT phase protected by SO(3) spin rotation symmetry. Note that Haldane phases of even-integer-spin chain do not have SPT order. A more well known example of SPT order is the 展开
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The materials described by Landau symmetry-breaking theory have had a substantial impact on technology. For example, ferromagnetic materials that break spin rotation symmetry can be used as the media of digital information storage. A hard drive made of ferromagnetic materials can store gigabytes of information. Liquid crystals that break the rotational symmetry of molecules find wide application in display technology. Crystals that break translation symmetry lead to well defined electronic bands
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AKLT model | Wikipedia
网页[2] [3] [4] [5] It has also served as a useful example for such concepts as valence bond solid order, symmetry-protected topological order [6] [7] [8] [9] and matrix product state …
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Symmetry protected topological orders and the group …
网页2013年4月4日 · Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$. They can all be smoothly connected to …
[1106.4772] Symmetry protected topological orders and the group ...
网页2011年6月23日 · Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to …
Realizing the symmetry-protected Haldane phase in Fermi ... | Nature
网页2022年6月1日 · We show this by measuring both topological and trivial string order parameters. An instructive way to engineer the Haldane phase in systems of spin-1/2 …
Intertwined topological phases induced by emergent symmetry …
网页2019年6月19日 · Emergent symmetry protection: we represent qualitatively a ground-state manifold, where different quantum phases are characterized by their symmetry and …
Symmetry Protected Topological Order in Open Quantum Systems
网页2021年12月8日 · We systematically investigate the robustness of symmetry protected topological (SPT) order in open quantum systems by studying the evolution of string …
Symmetry Protected Topological phases of Quantum Matter
网页2014年5月15日 · We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal …
Gapless Symmetry-Protected Topological Order | Physical Review …
网页2017年11月29日 · We present a general theoretical framework for describing a class of strongly interacting gapless systems with topological properties. Our construction …
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