Have you ever had a dream, Neo, that you seemed so sure it was real? But if were unable to wake up from that dream, how would you tell the difference between the dream world & the real world?
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EntanglementCFTFrom F. Pollmann, S. Mukerjee, A. M. Turner, and J. E. Moore, Phys. Rev. Lett. 102, 255701 (2009) (ArXiv link https://arxiv.org/abs/0812.2903v2), the central charge at a critical point can be determined from the scaling of the entropy or correlation length with respect to the number of states. Near (but not at) a critical point, the entanglement scales with the correlation length as {$$S = \frac{c}{6} \log \xi + a$$} where {$c$} is the central charge, and {$a$} is some nonuniversal boundary term. This is not a bad way to determine {$c$} for an iMPS. An MPS is driven off criticality by the finite basis size; the correlation length is cutoff by {$$\xi \propto m^\kappa$$} Hence this gives a relation for an MPS, {$$S = \frac{c \kappa}{6} \log m + \mbox{const}$$} Pollmann et al showed, making use of the CalibreseLefevre result for the distribution of the reduced density matrix spectra (Phys Rev A 78, 032329 (2008)), that this leads to a connection between correlation exponent {$\kappa$} and central charge {$c$}, {$$ \kappa \simeq \frac{6}{c + \sqrt{12c}} $$}
