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arXiv · 2403.17242

The c-d conjecture

José I. Latorre·Germán Sierra
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Abstract

We conjecture a relation between the local dimension $d$ of a local nearest-neighbor critical Hamiltonian in one spatial dimension and the maximum central charge, $c_{\text{max}}$, that it can yield. Specifically, we propose that $c_{\text{max}} \leq d-1$, establishing a link between the short-distance lattice realization of a model and its emerging long-distance entanglement properties. This inequality can be viewed as a general form of a $c$-theorem establishing the reduction of effective degrees of freedom between the UV lattice and the IR conformal field theory. We support this conjecture with numerous examples.

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José I. Latorre, Germán Sierra. 2024-03-25. The c-d conjecture. https://doi.org/10.1088/1742-5468%2Fad8f2d

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