The c-d Conjecture: A Bridge Between Lattice Systems and Conformal Field Theory"

In this talk, we will present a conjecture that explores a relationship between the local dimension d of a critical nearest-neighbor Hamiltonian in one spatial dimension and the maximum central charge, cmax​, it can produce. Specifically, we propose that cmax ≤ d−1, which establishes a connection between the short-distance lattice structure of a model and its long-distance entanglement properties. This inequality can be understood as a generalized form of a c-theorem, demonstrating a reduction in effective degrees of freedom from the UV lattice to the IR conformal field theory. We will illustrate this conjecture with multiple examples and provide theoretical justification to support it. This is joint work with José Ignacio Latorre, as presented in the preprint "The c-d conjecture", arXiv:2403.17242.