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See all on WikipediaSymmetry-protected topological order - Wikipedia
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 … See more
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 … See more
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 … See more
SPT states are short-range entangled while topologically ordered states are long-range entangled. Both intrinsic topological order, … See more
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 See more
Wikipedia text under CC-BY-SA license Topological order - Wikipedia
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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Topological insulator - Wikipedia
WEBAll topological insulators have at least U(1) symmetry from particle number conservation, and often have time-reversal symmetry from the absence of a magnetic field. In this …
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[1106.4772] Symmetry protected topological orders and the group ...
WEBJun 23, 2011 · Symmetry protected topological orders and the group cohomology of their symmetry group. Symmetry protected topological (SPT) phases are gapped short …
WEBSymmetry protected topological phases are gapped phases with certain global symmetry (time reversal, charge conjugation, discrete ZN symmetry, spatial symmetry etc.). The …
Symmetry-Protected Topological Orders in Interacting …
WEBDec 21, 2012 · Topological insulators (TIs) are characterized by boundary states that are protected by time-reversal symmetry. A systematic study of this, and other symmetry-protected states, is possible in …
WEBIn this lecture, we are going to introduce some prototypical models with gapped topological order, symmetry protected topological order, and fracton order. In particular, we are …
Sub-symmetry-protected topological states | Nature Physics
WEBApr 17, 2023 · A hallmark of symmetry-protected topological phases are topological boundary states, which are immune to perturbations that respect the protecting …
What is the difference between symmetry protected topological …
WEBThe difference between these two would be: Topological order could endure any perturbations (as long as it's not too big), while SPT order could only endure …
Symmetry Protected Topological Order in Open Quantum Systems
WEBDec 8, 2021 · We systematically investigate the robustness of symmetry protected topological (SPT) order in open quantum systems by studying the evolution of string …
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