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...American English|date=January 2019}}{{Short description|Effect in quantum mechanics where conductivity acquires quantized values ...ll insulators (also called Chern insulators).<ref>{{cite arXiv|title = The quantum anomalous Hall effect|eprint= 1508.07106|date = 2015-08-28|first1 = Chao-Xi ...

...mmetry group |url=https://www.semanticscholar.org/paper/Symmetry-protected-topological-orders-and-the-group-Chen-Gu/f9494cc87731130f5e0b974541bf5e057dd64226 |jour Broadly speaking, the application of categorical models to topological systems comes from the fact that the objects the categories describe some s ...

...ies and modular tensor categories to the [[algebraic theory of topological quantum information]], this theorem has found various uses within [[mathematical ph == Interpretation in terms of topological quantum field theory == ...

{{Short description|Quantum computational theorem on problem complexity}} ...olas P. |last3=Nirkhe |first3=Chinmay |chapter=NLTS Hamiltonians from Good Quantum Codes |date=2023-06-02 |title=Proceedings of the 55th Annual ACM Symposium ...

...s P.|last3=Spitters|first3=Bas|date=2009-10-01|title=A Topos for Algebraic Quantum Theory|journal=[[Communications in Mathematical Physics]]|language=en|volum === Ringed topos of a topological space === ...

...can English|date=January 2019}}{{Short description|Phenomenon in many-body quantum systems ...n| last2=Niu | first2=Q. | title=Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann ...

{{Short description|Quantum-mechanical phenomenon}} ...://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/Topological%20phases/a-c%20effect%20expts/Cimmino_PRL_1989.pdf | issue=4 | pmid=1004105 ...

...iated to the [[Reshetikhin–Turaev invariant|Reshetikhin–Turaev topological quantum field theory]] associated to <math>\mathcal{C}</math>.<ref name=":113">{{Ci ...mathcal{C}</math>, where in both these formulas <math>d_{A}</math> are the quantum dimensions of the simple objects. ...

...invariant]]s such as the [[Berry phase]] and [[Chern number]]s as in the [[Quantum Hall effect]]. {{See also|Heisenberg model (quantum)|l1=Heisenberg model}} ...

.... Freedman |author5=S. Das Sarma |title=Non-Abelian Anyons and Topological Quantum Computation |journal=Reviews of Modern Physics |date=28 March 2008 |volume= ...quantum state. These multiple states provide a [[Hilbert space]] on which quantum computation can be done. ...

...t2=Wei|last3=Chitra|first3=R.|title=Generating quantum multicriticality in topological insulators by periodic driving|journal=Physical Review B|year=2020|volume=1 ...l). The vertical red lines depict topological phase boundaries. Across the topological phase transitions, the Berry connection diverges and flips sign around the ...

{{Short description|Phenomenon in quantum mechanics}} ...uents. One of the earliest and most prominent examples is the [[fractional quantum Hall effect]], where the constituent particles are [[electrons]] but the qu ...

...s geometric formulation of [[classical field theory]] and [[non-autonomous mechanics]] including: ...''48''' (2007) 082104; {{arXiv|quant-ph/0703266}}.</ref> [[non-autonomous mechanics]] on [[fiber bundle]]s over <math>\mathbb R</math> ...

{{Short description|Model for topological superconductors in physics}} ...t=Kitaev |first=A Yu |date=2001-10-01 |title=Unpaired Majorana fermions in quantum wires |url=https://iopscience.iop.org/article/10.1070/1063-7869/44/10S/S29 ...

...It is the inspiration for cluster algorithms used in [[Quantum Monte Carlo|quantum monte carlo]] simulations. ...dx.doi.org/10.1016/0378-4371%2892%2990145-G|journal=Physica A: Statistical Mechanics and Its Applications|language=en|volume=183|issue=3|pages=249–254|doi=10.10 ...

{{Short description|Simple model of topological insulator}} ...de=1979PhRvL..42.1698S |issn=0031-9007}}</ref> It is a [[quantum mechanics|quantum mechanical]] [[tight binding]] approach, that describes the hopping of [[Sp ...

...es the [[magnetic moment]] of an [[electron]] directly in the [[Lagrangian mechanics|Lagrangian]].<ref>{{Cite web |title=Minimal Coupling - an overview {{!}} Sc In [[Cartesian coordinates]], the [[Lagrangian mechanics#Electromagnetism|Lagrangian]] of a non-relativistic classical particle in a ...

...otential barrier. Vacuum instantons carry a [[Winding number|winding]] (or topological) number, the other configurations do not. Periodic instantons were discover ...st1=J.-Q.|last2=Müller-Kirsten|first2=H. J. W.|title=Nonvacuum bounces and quantum tunneling at finite energy|journal=Physical Review D|volume=50|issue=10|yea ...

...st1=Liang |last1=Kong |first2=Zhi-Hao |last2=Zhang |title=An invitation to topological orders and category theory |date=2022-05-11}}</ref> [[Category:Topological quantum mechanics]] ...

{{Short description|Black hole solution in 2+1 dimensional topological gravity}} ...nd [[Jorge Zanelli]], is a [[black hole]] solution for [[(2+1)-dimensional topological gravity]] with a negative [[cosmological constant]]{{clarify|what is the si ...