Three-dimensional spin-orbital liquids | Paper Citation Record

Observation 56adaa66-fb23-4cb5-907b-74e5bc67f598 · outbound

This paper cites III C— can have on the low-energy behavior of the SOL.

Three-dimensional spin-orbital liquids III C— can have on the low-energy behavior of the SOL

Reference 1

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Observation 44a3d745-4d15-44b1-8553-b8c5a348b7d2 · outbound

This paper cites Doing a Fourier transform and combining all the Majoranas into a single spinorψ ψ(k) = (cx k,1,.

Three-dimensional spin-orbital liquids Doing a Fourier transform and combining all the Majoranas into a single spinorψ ψ(k) = (cx k,1,

Reference 2

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Observation b09cfc38-e6e0-4cbb-85ba-a517bc2d8c6a · outbound

This paper cites It can be visualized as a square-octagon lattice, where the squares are replaced by co-rotating spirals, see Fig.

Three-dimensional spin-orbital liquids It can be visualized as a square-octagon lattice, where the squares are replaced by co-rotating spirals, see Fig

Reference 3

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Observation d00f1146-9389-42c7-8f31-ce531fd00f81 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 4

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Observation 471308de-f2ec-4417-8587-6687216738ba · outbound

This paper cites This requires a finite perturbation strength.

Three-dimensional spin-orbital liquids This requires a finite perturbation strength

Reference 5

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Observation 7e6a93e2-cca1-4285-90f8-d9bdc7b788b9 · outbound

This paper cites (49) The lattice with our choice of unit cell and lattice trans- lation vectors is illustrated in Fig.

Three-dimensional spin-orbital liquids (49) The lattice with our choice of unit cell and lattice trans- lation vectors is illustrated in Fig

Reference 6

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Observation 3cf04a4b-9687-4587-84e0-3cbb5098bf15 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 7

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Observation 220e0e24-a78a-4cd4-8a2e-15f8801c8ab8 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 8

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Observation 1716b84f-3a81-486e-87ff-32e8f215dda4 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 9

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Observation 21edf861-cece-4730-b940-df64060ffe9f · outbound

This paper cites Overview table of possible SOL behavior on the four-coordinated lattices under perturbations.

Three-dimensional spin-orbital liquids Overview table of possible SOL behavior on the four-coordinated lattices under perturbations

Reference 10

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Observation 29fc4e9b-45b9-4fc8-9d92-71894ba97a80 · outbound

This paper cites As we did for the three-coordinated lattices, we can apply a Fourier transform and combine all the Majoranas into a single spinorψ ψ(k) = (cx k,1,.

Three-dimensional spin-orbital liquids As we did for the three-coordinated lattices, we can apply a Fourier transform and combine all the Majoranas into a single spinorψ ψ(k) = (cx k,1,

Reference 11

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Observation cd69ad1d-73cf-4559-b7d3-b1b95bf05184 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 12

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Observation 1ea2114e-60cf-4ecc-ba5d-e1e22afc8fb8 · outbound

This paper cites Baskaran, S.

Three-dimensional spin-orbital liquids Baskaran, S

Reference 13

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Observation ffe476d7-6862-470d-80b7-353322035492 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 14

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Observation 7e05ce8f-7a5e-4053-919e-cb9efb595e27 · outbound

This paper cites The chiral square-octagon has two symmetry- inequivalent bonds.

Three-dimensional spin-orbital liquids The chiral square-octagon has two symmetry- inequivalent bonds

Reference 15

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Observation bcbaf46c-fb2d-4ed2-96be-eaff32f125df · outbound

This paper cites The resulting lattice is again bipartite.

Three-dimensional spin-orbital liquids The resulting lattice is again bipartite

Reference 16

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Observation 0ae54c4a-a692-4af0-9031-f5dde6914fac · outbound

This paper cites These are not all independent, as we have three volume constraints per unit cell.

Three-dimensional spin-orbital liquids These are not all independent, as we have three volume constraints per unit cell

Reference 17

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Observation c0edae98-aa0c-4f14-8c3f-1f9fdfd06e0b · outbound

This paper cites representative lattices.

Three-dimensional spin-orbital liquids representative lattices

Reference 18

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Observation 407ec5db-98b7-482c-8ef7-c62779eb5257 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 19

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Observation 9693da7f-8723-4759-ba99-942d050680a6 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 20

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Observation cab6ec27-25a7-4586-bfd5-3a402a0385a5 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.502133Z

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Observation e902cbd3-418c-49a0-90b9-f7a8bf0e2313 · outbound

This paper cites Lieb’s theorem does not apply to the chiral square-octagon lattice, as it lacks mirror planes.

Three-dimensional spin-orbital liquids Lieb’s theorem does not apply to the chiral square-octagon lattice, as it lacks mirror planes

Reference 22

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Observation bb24d9b9-58bd-4842-be89-f3e66a9eddfd · outbound

This paper cites Thus, Lieb’s theorem suggests that the ground state has flux zero.

Three-dimensional spin-orbital liquids Thus, Lieb’s theorem suggests that the ground state has flux zero

Reference 23

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Observation 3d3c2443-6b4e-47f0-bca7-c712edc0e1e6 · outbound

This paper cites Four loops of length 6 can be visualized as transversing once around the square-spiral and moving back via the zig-zag chain to the starting point.

Three-dimensional spin-orbital liquids Four loops of length 6 can be visualized as transversing once around the square-spiral and moving back via the zig-zag chain to the starting point

Reference 24

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Observation 23fd0089-3096-43ae-9eb8-5034f0a48714 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 25

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Observation f8d7a4eb-4b50-45a3-85f0-4e5f596c6f67 · outbound

This paper cites Chulliparambil, L.

Three-dimensional spin-orbital liquids Chulliparambil, L

Reference 26

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Observation 3abe1b3f-b1bf-4558-856b-dcb44975fa54 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 27

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Observation eea80d0e-24fe-4f45-8776-50a92a4df809 · outbound

This paper cites Wen, Quantum orders and symmetric spin liquids, Physical Review B65, 165113 (2002).

Three-dimensional spin-orbital liquids Wen, Quantum orders and symmetric spin liquids, Physical Review B65, 165113 (2002)

Reference 28

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Observation 2614c59a-8f3d-48f2-bc34-d9194bbf3064 · outbound

This paper cites The lattice vectors are given by a1 = (1,0,0),a 2 = (0,1,0),a 3 = (0,0, 1√ 2 ),(67) which yields the following reciprocal vectors q1 = (2π,0,0),q 2 = (0,2π,0),q 3 = (0,0,2 √ 2π).

Three-dimensional spin-orbital liquids The lattice vectors are given by a1 = (1,0,0),a 2 = (0,1,0),a 3 = (0,0, 1√ 2 ),(67) which yields the following reciprocal vectors q1 = (2π,0,0),q 2 = (0,2π,0),q 3 = (0,0,2 √ 2π)

Reference 29

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Observation e0080c6a-9c69-468a-8a8e-9d72d89a18b6 · outbound

This paper cites Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010).

Three-dimensional spin-orbital liquids Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

Reference 30

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Observation d9d73bb1-8ae1-48b7-aeaf-425f2147cbcf · outbound

This paper cites Broholm, R.

Three-dimensional spin-orbital liquids Broholm, R

Reference 31

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Observation 4b960a0b-f3c3-403f-8891-05d7914b6f9d · outbound

This paper cites Knolle and R.

Three-dimensional spin-orbital liquids Knolle and R

Reference 32

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Observation da8ba7d8-3a2e-4ee7-bd96-5fb5db42d4ba · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 33

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Observation 824b851f-d011-4d4a-ad82-239e32769e5e · outbound

This paper cites Savary and L.

Three-dimensional spin-orbital liquids Savary and L

Reference 34

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Observation 50cc7f7b-4b2d-4783-aac0-16bcc1f691e3 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 35

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Observation 9dd053c3-b69a-492d-b264-8ce83194b901 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 36

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Observation 1fc8be1e-2d20-4d42-8e57-b55e5ddf05c3 · outbound

This paper cites Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics321, 2 (2006).

Three-dimensional spin-orbital liquids Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics321, 2 (2006)

Reference 37

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Observation 8c03c3c7-08d6-4fde-a7b7-233deca0c544 · outbound

This paper cites Moessner and S.

Three-dimensional spin-orbital liquids Moessner and S

Reference 38

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Observation 2a864047-2aa2-4c23-b569-6d2eed916868 · outbound

This paper cites Knolle, D.

Three-dimensional spin-orbital liquids Knolle, D

Reference 39

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Observation 91bb4a4e-2b39-40ac-bf37-3a2a4b3105c6 · outbound

This paper cites Raman Scattering Signatures of Kitaev Spin Liquids in A$_2$ IrO$_3$ Iridates.

Three-dimensional spin-orbital liquids Raman Scattering Signatures of Kitaev Spin Liquids in A$_2$ IrO$_3$ Iridates

Reference 40

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Observation 98cdfe20-ab91-461f-9618-81efb4756932 · outbound

This paper cites Kanega, T.

Three-dimensional spin-orbital liquids Kanega, T

Reference 41

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Observation 0dca3d15-ca41-495c-8d73-4558d1a4c295 · outbound

This paper cites An exact chiral spin liquid with non-Abelian anyons.

Three-dimensional spin-orbital liquids An exact chiral spin liquid with non-Abelian anyons

Reference 42

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Observation fda94407-9436-468f-a8e9-d7e5b36ff5aa · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 43

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Observation 65b86fec-54e7-4483-91df-e896bbf0c60d · outbound

This paper cites Mandal and N.

Three-dimensional spin-orbital liquids Mandal and N

Reference 44

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Observation 66625ed1-94e4-48b3-a393-165876c8bfd9 · outbound

This paper cites Hermanns and S.

Three-dimensional spin-orbital liquids Hermanns and S

Reference 45

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Observation a3aea956-5aef-4dfd-a984-50aa33783b8a · outbound

This paper cites O’Brien, M.

Three-dimensional spin-orbital liquids O’Brien, M

Reference 46

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Observation 91826c3a-c633-4f90-ae3f-3f0f09da4ca5 · outbound

This paper cites Eschmann, P.

Three-dimensional spin-orbital liquids Eschmann, P

Reference 47

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Observation ce6eca3f-8060-465c-9571-8c2fb41e89b8 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 48

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Observation cc7d1bf1-1b3f-4a7e-a66e-33d46530cc9d · outbound

This paper cites Yao, S.-C.

Three-dimensional spin-orbital liquids Yao, S.-C

Reference 49

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Observation 6fa74d33-7673-43b6-9187-3d90dfe45b13 · outbound

This paper cites Ryu, Three-dimensional topological phase on the dia- mond lattice, Physical Review B79, 075124 (2009).

Three-dimensional spin-orbital liquids Ryu, Three-dimensional topological phase on the dia- mond lattice, Physical Review B79, 075124 (2009)

Reference 50

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Observation 486bbfcb-ccd9-4bf3-bba9-11c6889a4dc9 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 51

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Observation fec086fe-ab51-4105-aaa4-15e3b3feee41 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 52

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Observation 9b655eca-1f48-40d0-82bf-379634dba2b5 · outbound

This paper cites Nakai, S.

Three-dimensional spin-orbital liquids Nakai, S

Reference 53

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Observation f2895545-476b-4baf-a696-bc6f233496c6 · outbound

This paper cites Wang and A.

Three-dimensional spin-orbital liquids Wang and A

Reference 54

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Observation 0b30fd0c-aa2b-4ace-ab2e-574c56fa3d73 · outbound

This paper cites Corboz, M.

Three-dimensional spin-orbital liquids Corboz, M

Reference 55

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Observation 525fe933-6b61-4129-8af7-d8fd1b029d4b · outbound

This paper cites Chulliparambil, U.

Three-dimensional spin-orbital liquids Chulliparambil, U

Reference 56

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Observation 8b2e492e-a294-4a15-986b-416619e765d1 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 57

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Observation c95e2da6-7c1a-48ab-8148-565bc7d7f542 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 58

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Observation 0fef1905-e988-45ff-a5bc-b8e41e55048c · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 59

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Observation 0d273cab-7430-4086-af3d-ba3f796f306a · outbound

This paper cites Eschmann, P.

Three-dimensional spin-orbital liquids Eschmann, P

Reference 60

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Observation d9f1e6f7-8d48-4061-9f95-184f708b1d88 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 61

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Observation 06b69912-4640-4dcd-b962-a0eb1b53f09f · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 62

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Observation ed2a7a30-fa67-4616-ae40-6e5ffcb6b671 · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 63

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Observation 8b361eb0-4bd5-49cd-8b51-916586d32f7e · outbound

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Three-dimensional spin-orbital liquids Unresolved cited work

Reference 64

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Observation 4bff645f-6696-48ef-a994-b96d2c4ca462 · outbound

This paper cites In the Majorana representation, this changes the symmetry class to DIII, yielding aZ 2 invariant in two dimensions and aZinvari- ant in three dimensions.

Three-dimensional spin-orbital liquids In the Majorana representation, this changes the symmetry class to DIII, yielding aZ 2 invariant in two dimensions and aZinvari- ant in three dimensions

Reference 65

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Observation 8d829f05-2fe2-4a59-a5a2-29c8f12b1211 · outbound

This paper cites Chaloupka and G.

Three-dimensional spin-orbital liquids Chaloupka and G

Reference 66

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Observation a266cc04-4b27-4db8-a562-58fcdbe077a8 · outbound

This paper cites Khaliullin and S.

Three-dimensional spin-orbital liquids Khaliullin and S

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.688962Z

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Observation 5c6c8168-2357-4d43-9e7b-773ddb5cc25a · outbound

This paper cites Kimchi and A.

Three-dimensional spin-orbital liquids Kimchi and A

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.693131Z

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Observation 0af06b0b-2789-4bbf-b863-584053409d9e · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.697028Z

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Observation eea09adc-07fd-4020-9a87-e684e619852c · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.700937Z

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Observation ae2dc271-43f7-4557-83ef-69b0d68c134f · outbound

This paper cites Bradlyn, J.

Three-dimensional spin-orbital liquids Bradlyn, J

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.704798Z

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Observation 37abe924-08c6-45d2-bbe7-340add0dc7c2 · outbound

This paper cites Kimchi, J.

Three-dimensional spin-orbital liquids Kimchi, J

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.708696Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 836fd985-5cdf-4b95-910e-e47c638fb656 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.712394Z

Source-reported events for the cited work

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Observation 3584ccb0-1dd5-4d0c-84ae-7159dc0c2902 · outbound

This paper cites Takayama, A.

Three-dimensional spin-orbital liquids Takayama, A

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.716040Z

Source-reported events for the cited work

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Observation f25e793d-7474-4334-855e-1df790aced06 · outbound

This paper cites Takagi, T.

Three-dimensional spin-orbital liquids Takagi, T

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.719816Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 556254aa-df44-46ec-8859-0edc0ecb467a · outbound

This paper cites Without loss of gen- erality, we will set the coupling constants identical for both types.

Three-dimensional spin-orbital liquids Without loss of gen- erality, we will set the coupling constants identical for both types

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.724010Z

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Observation f0b2c453-7ec7-4fc2-8a08-ff13eebdac98 · outbound

This paper cites Rather, the low-energy features originate from the presence of 6 chargeless zero-modes on the ring, with a very flat, but non-zero dispersion connecting them.

Three-dimensional spin-orbital liquids Rather, the low-energy features originate from the presence of 6 chargeless zero-modes on the ring, with a very flat, but non-zero dispersion connecting them

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.728325Z

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Observation 557743cd-35ea-40bc-a841-ed550463906b · outbound

This paper cites O’keeffe and N.

Three-dimensional spin-orbital liquids O’keeffe and N

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.732225Z

Source-reported events for the cited work

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Observation 75d813f1-90b1-4b5e-9611-f8fe0e6e8b11 · outbound

This paper cites an unresolved cited work.

Three-dimensional spin-orbital liquids Unresolved cited work

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.736069Z

Source-reported events for the cited work

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Observation 7a2a4da7-6986-4981-bf68-924dccb47842 · outbound

This paper cites The latter are of no use in Lieb’s theorem.

Three-dimensional spin-orbital liquids The latter are of no use in Lieb’s theorem

Reference 80

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.739882Z

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Observation 464c95f1-f23e-4398-b51d-bf811fda5d5a · outbound

This paper cites Hermanns, S.

Three-dimensional spin-orbital liquids Hermanns, S

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.744023Z

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Observation b27b1660-9d52-4374-a6e6-33bfba6d4920 · outbound

This paper cites Momma and F.

Three-dimensional spin-orbital liquids Momma and F

Reference 82

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.748071Z

Source-reported events for the cited work

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Observation 92c9a95b-30b5-42bd-8e7b-d17af713e5cb · outbound

This paper cites Danisch and J.

Three-dimensional spin-orbital liquids Danisch and J

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-03T03:55:01.752804Z

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