Size-Driven Quantum Phase Transitions

Abstract

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.

20 pages. Final version

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Cited by in corpus (16)

• Undecidability of the Spectral Gap (short version)
• Undecidability of the Spectral Gap in One Dimension
• Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
• The Complexity of Translationally-Invariant Spin Chains with Low Local Dimension
• Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice
• Geometrically confined thermal field theory: Finite size corrections and phase transitions
• Importance of the spectral gap in estimating ground-state energies
• Uncomputability of Phase Diagrams
• The Complexity of Translationally-Invariant Low-Dimensional Spin Lattices in 3D
• Undecidability of the Spectral Gap (full version)
• Bounding the finite-size error of quantum many-body dynamics simulations
• Undecidability in Physics: a Review
• Classifying Data with Local Hamiltonians
• Computing local properties in the trivial phase
• The Complexity of Approximating Critical Points of Quantum Phase Transitions
• Undecidability of the spectral gap in rotationally symmetric Hamiltonians