Size-Driven Quantum Phase Transitions

Understand

Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analysing a sequence of finite-size cases? We present a model for which such an approach gives completely misleading results: a translationally invariant, local Hamiltonian on a square lattice with open boundary conditions and constant spectral gap, which has a classical product ground state for all system sizes smaller than a particular threshold size, but a ground state with topological degeneracy for all system sizes larger than this threshold.

• Starting from a minimal case with spins of dimension 6 and threshold lattice size 15 x 15, we show that the latter grows faster than any computable function with increasing local spin dimension.
• The resulting effect may be viewed as a new type of quantum phase transition that is driven by the size of the system rather than by an external field or coupling strength.
• We prove that the construction is thermally robust, opening the possibility that these effects are accessible to experimental observation.