I understand the definition of a gapped spin liquid: it's a gapped, topologically ordered spin state - i.e. there does not exist a local unitary transformation that takes it to a product state in finite time. I know this is a notoriously difficult question, but what is the precise definition of a gapless spin liquid? The previous definition no longer works, because almost all gapless states are local unitary inequivalent to a product state.
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2$\begingroup$ You do not need to ask for the definition of a gapless spin liquid. You may just provide your own definition, since the so called non-trivial gapless spin liquid has not been defined. $\endgroup$– Xiao-Gang WenCommented Jul 9, 2016 at 22:26
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$\begingroup$ Why do you claim that "all gapless states are local unitary inequivalent to a product state?" $\endgroup$– user32229Commented Nov 14, 2016 at 1:05
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$\begingroup$ gapless states are many states near the ground state(s), but a product state is just one state. How do you compare the two by Local-Unitary-Trans? $\endgroup$– user32229Commented Nov 14, 2016 at 1:06
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$\begingroup$ @mysteriousness I meant gapless ground states. $\endgroup$– tparkerCommented Nov 14, 2016 at 5:26
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1$\begingroup$ @tparker I think a good working definition (at least it fits all examples I know) is: at low energies its effective/universal description is that of a deconfined phase of a massless gauge theory. The 'gauge theory' aspect will results in a local gauge constraint such that the elementary excitations are fractional (e.g., carry gauge charge), and 'deconfined' refers to idea that separating two such fractionalized particles only requires a finite amount of energy. (Note that this definition does not assume the gauge field is gapless such that it also applies to the Kitaev honeycomb model.) $\endgroup$– Ruben VerresenCommented Feb 7, 2021 at 16:24
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