Draft:The c-d conjecture

• Comment: See the comment Ldm1954 (talk) 21:40, 1 October 2024 (UTC)

• Comment: You have misunderstood what Wikipedia is about. It is not a newspaper, or a place for all information. Only well established science that has been around for a while qualifies. It does not matter if this is right or wrong, reprints are inappropriate. You will have to be patient and wait some years for the community to accept the idea. Ldm1954 (talk) 21:38, 1 October 2024 (UTC)

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In an arXiv preprint.., 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 $c_{\mathrm {max} }=d-1$.

Examples

The currently known examples are consistent with this conjecture.

The upper bound is saturated for the SU($n$) Uimin-Lai-Sutherland model, whose low-energy effective theory is the SU($n$) level 1 Wess-Zumino-Witten model. 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 $c=n-1$.

The Reshetikhin models are a family of integrable models with SO($n$) symmetric nearest-neighbor interactions. The local Hilbert space dimension of the Reshetikhin models is $d=n$, which transforms under the vector representation of SO($n$). These models are critical and their low-energy effective theory is the SO($n$) level 1 Wess-Zumino-Witten model with central charge $c=n/2$

The spin-$s$ XXX models are a family of integrable models with SU($2$) symmetric nearest-neighbor interactions. The local Hilbert space dimension of the spin-$s$ XXX models is $d=2s+1$, which transforms under the spin-$s$ irreducible representation of SU($2$). These models are critical and their low-energy effective theory is the SU($2$) level $2s$ Wess-Zumino-Witten model with central charge $c={\frac {3s}{s+1}}$.

The $Z_{Q}$ parafermion models are a family of integrable self-dual models with $Z_{Q}$ symmetric nearest-neighbor interactions. The local Hilbert space dimension of the $Z_{Q}$ parafermion models is $d=Q$. These models are critical and their low-energy effective theory is the $Z_{Q}$ parafermion conformal field theory with central charge $c={\frac {2(Q-1)}{Q+2}}$. For $Q=2$ and $3$, the models correspond to the critical Ising model and the critical $Z_{3}$ Potts model, respectively. For $Q=4$, the model corresponds to a special point of the critical Ashkin-Teller model