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It seems like everyone studies quantum spin liquids in either 2D or 3D. Can not there be quantum spin liquids in 1D?

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  • $\begingroup$ Depends on your definition of "quantum spin liquid". $\endgroup$ – Norbert Schuch Oct 16 at 16:59
  • $\begingroup$ @NorbertSchuch in my perspective, QSL is a state which keeps fluctuating even at T = 0 and it has very high degree of entanglement. $\endgroup$ – Luqman Saleem Oct 16 at 17:37
  • $\begingroup$ From that definition, perhaps you would consider the spin-1/2 (or 3/5, 5/2, ...) Heisenberg chain to be a spin liquid? It does not have spin order at T=0, and it has entanglement that grows logarithmically with the entanglement cut. $\endgroup$ – Seth Whitsitt Oct 16 at 18:07
  • $\begingroup$ @SethWhitsitt Maybe "gapped" in another criterion? $\endgroup$ – Norbert Schuch Oct 16 at 21:22
  • $\begingroup$ @LuqmanSaleem What about the AKLT chain? -- Note that we generally expect any gapped system to have the same (area-law) amount of entanglement, unless you are talking about the prefactor! $\endgroup$ – Norbert Schuch Oct 16 at 21:23

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