Size-Driven Quantum Phase Transitions

TL;DR

This paper introduces a size-driven quantum phase transition model where the ground state properties change drastically at a certain system size, challenging the extrapolation from finite to infinite systems.

Contribution

It presents a novel size-driven phase transition model with a local Hamiltonian that exhibits different ground states below and above a threshold size, which grows faster than any computable function.

Findings

Ground state changes from classical to topologically degenerate at threshold size

Threshold size grows faster than any computable function with local spin dimension

Model is thermally robust, suggesting experimental observability

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.