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In this paper, we propose a modified Density Matrix Renormalization Group(DMRG) algorithm to preferentially select minimum entropy states (minimallyentangled states) in finite systems with asymptotic ground state degeneracy.The algorithm adds a "quench" process to the conventional DMRG method, whichmimics the decoherence of physical systems, and collapses non-locally entangledstates such as Schr\"odinger cats. We show that the method works forrepresentative models with ground state degeneracy arising from eithertopological order or spontaneous discrete symmetry breaking. In the minimalentropy states thus obtained, properties associated with thermodynamic limit,such as topological entanglement entropy and magnetic order parameters, can beobtained directly and efficiently.

Collapsing Schr\"odinger Cats in the Density Matrix Renormalization Group