String-net liquid: Difference between revisions

Revision as of 12:02, 12 January 2024

Revision as of 17:23, 27 March 2025

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[[Z2 spin liquid]] obtained using [[slave-particle approach]] may be the first theoretical example of string-net liquid.<ref name="Read Sachdev pp. 1773–1776">{{cite journal | last1=Read | first1=N. | last2=Sachdev | first2=Subir | title=Large-Nexpansion for frustrated quantum antiferromagnets | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=66 | issue=13 | date=1 March 1991 | issn=0031-9007 | doi=10.1103/physrevlett.66.1773 | pages=1773–1776 | pmid=10043303| bibcode=1991PhRvL..66.1773R }}</ref><ref>[[Xiao-Gang Wen]], Mean Field Theory of Spin Liquid States with Finite Energy Gaps and Topological Orders, [http://link.aps.org/doi/10.1103/PhysRevB.44.2664 Phys. Rev. B44, 2664 (1991)].</ref>

===The toricToric code===

The [[toric code]] is a two-dimensional spin-lattice that acts as a quantum error-correcting code. It is defined on a two-dimensional lattice with [[torus|toric]] [[boundary conditions]] with a spin-1/2 on each link. It can be shown that the ground-state of the standard toric code Hamiltonian is an ''equal-weight superposition'' of closed-string states.<ref name=kitaevlaumann>{{Cite arXiv|last=Kitaev|first=Alexei, Y.|author2=Chris Laumann |title=Topological phases and quantum computation|date=2009|eprint=0904.2771|class=cond-mat.mes-hall}}</ref> Such a ground-state is an example of a string-net condensate<ref>{{Cite journal|journal=Physical Review A|volume=85|issue=6|page=062328|doi=10.1103/PhysRevA.85.062328|last=Morimae|first=Tomoyuki|title=Quantum computational tensor network on string-net condensate|date=2012|arxiv=1012.1000|bibcode = 2012PhRvA..85f2328M |s2cid=118522495}}</ref> which has the same [[topological order]]

as the Z2 spin liquid above.