Draft:The c-d conjecture

Submission declined on 1 May 2024 by Theroadislong (talk).

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Declined by Theroadislong 29 days ago. Last edited by Citation bot 28 days ago. Reviewer: Inform author.

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In an arXiv preprint^[1], José Ignacio Latorre and Germán Sierra made the following conjecture about the upper bound of the central charge for one-dimensional quantum critical lattice Hamiltonians with nearest-neighbor interactions:

If the local Hilbert space dimension of the lattice model is $d$ , the maximal central charge that the model can reach is $c_{\mathrm {max} }=d-1$ .

Intuitions edit

Examples edit

The currently known examples are consistent with this conjecture.

The upper bound is saturated for the SU( $n$ ) Uimin-Lai-Sutherland model^[2]^[3], whose low-energy effective theory is the SU( $n$ ) level 1 Wess-Zumino-Witten model^[4]. The local Hilbert space dimension of the lattice model is $d=n$ , and the SU( $n$ ) level 1 Wess-Zumino-Witten model has central charge $c=n-1$ .

References edit

^ Latorre, José I.; Sierra, Germán (2024). "The c-d conjecture". arXiv:2403.17242. {{cite journal}}: Cite journal requires |journal= (help)
^ Lai, C. K. (1974-10-01). "Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics". Journal of Mathematical Physics. 15 (10): 1675–1676. Bibcode:1974JMP....15.1675L. doi:10.1063/1.1666522. ISSN 0022-2488.
^ Sutherland, Bill (1975-11-01). "Model for a multicomponent quantum system". Physical Review B. 12 (9): 3795–3805. Bibcode:1975PhRvB..12.3795S. doi:10.1103/PhysRevB.12.3795.
^ Affleck, Ian (December 1988). "Critical behaviour of SU(n) quantum chains and topological non-linear σ-models". Nuclear Physics B. 305 (4): 582–596. Bibcode:1988NuPhB.305..582A. doi:10.1016/0550-3213(88)90117-4. ISSN 0550-3213.

[1] Latorre, José I.; Sierra, Germán (2024). "The c-d conjecture". arXiv:2403.17242. {{cite journal}}: Cite journal requires |journal= (help)

[2] Lai, C. K. (1974-10-01). "Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics". Journal of Mathematical Physics. 15 (10): 1675–1676. Bibcode:1974JMP....15.1675L. doi:10.1063/1.1666522. ISSN 0022-2488.

[3] Sutherland, Bill (1975-11-01). "Model for a multicomponent quantum system". Physical Review B. 12 (9): 3795–3805. Bibcode:1975PhRvB..12.3795S. doi:10.1103/PhysRevB.12.3795.

[4] Affleck, Ian (December 1988). "Critical behaviour of SU(n) quantum chains and topological non-linear σ-models". Nuclear Physics B. 305 (4): 582–596. Bibcode:1988NuPhB.305..582A. doi:10.1016/0550-3213(88)90117-4. ISSN 0550-3213.

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