We introduce a spin chain based on finite-dimensional spin-1/2 SU(2) representations but with a non-hermitian `Hamiltonian and show, using mostly analytical techniques, that it is described at low energies by the SL(2,R)/U(1) Euclidian black hole Conformal Field Theory. This identification goes beyond the appearance of a non-compact spectrum: we are also able to determine the density of states, and show that it agrees with the formulas in [J. Math. Phys. 42, 2961 (2001)] and [JHEP 04, 014 (2002)], hence providing a direct `physical measurement of the associated reflection amplitude.
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