  It has been recently observed that the reduced density matrix of a
two-dimensional (2D) valence bond solid state can be mapped onto the thermal
density matrix of a 1D Heisenberg quantum spin chain. Motivated by the
observation, I propose a very simple phenomenological theory for this type of
correspondence based on a finite-temperature tensor network formalism recently
developed. I adress close relationship and sharp difference between the present
correspondence and multiscale entanglement renormalization ansatz in terms of
network geometry.
