# Size-Driven Quantum Phase Transitions. (arXiv:1512.05687v3 [quant-ph] UPDATED)

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.