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Size-driven quantum phase transitions

Bausch, J; Cubitt, TS; Lucia, A; Perez-Garcia, D; Wolf, MM; (2018) Size-driven quantum phase transitions. Proceedings of the National Academy of Sciences of the United States of America , 115 (1) pp. 19-23. 10.1073/pnas.1705042114. Green open access

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Abstract

Can the properties of the thermodynamic limit of a many-body quantum system be extrapolated by analyzing a sequence of finite-size cases? We present models for which such an approach gives completely misleading results: translationally invariant, local Hamiltonians on a square lattice with open boundary conditions and constant spectral gap, which have 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 15×1515×15, we show that the latter grows faster than any computable function with increasing local spin dimension. The resulting effect may be viewed as a unique 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, showing that these effects are in principle accessible to experimental observation.

Type: Article
Title: Size-driven quantum phase transitions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1073/pnas.1705042114
Publisher version: http://doi.org/10.1073/pnas.1705042114
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Multidisciplinary Sciences, Science & Technology - Other Topics, quantum phase transition, condensed matter physics, finite-size effects, toric code, Wang tiling, LATTICE SYSTEMS, UNDECIDABILITY, NANOCRYSTALS, DEPENDENCE
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1557533
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