Finite correlation length scaling with infinite projected entangled-pair states

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Corboz, Philippe and Czarnic, Piotr and Kapteijns, Geert and Tagliacozzo, Luca (2018) Finite correlation length scaling with infinite projected entangled-pair states. Physical Review X, 8 (3). 031031. ISSN 2160-3308 (https://doi.org/10.1103/PhysRevX.8.031031)

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Abstract

We show how to accurately study 2D quantum critical phenomena using infinite projected entangled-pair states (iPEPS). We identify the presence of a finite correlation length in the optimal iPEPS approximation to Lorentz-invariant critical states which we use to perform a finite correlation-length scaling (FCLS) analysis to determine critical exponents. This is analogous to the one-dimensional (1D) finite entanglement scaling with infinite matrix product states. We provide arguments why this approach is also valid in 2D by identifying a class of states that despite obeying the area law of entanglement seems hard to describe with iPEPS. We apply these ideas to interacting spinless fermions on a honeycomb lattice and obtain critical exponents which are in agreement with Quantum Monte Carlo results. Furthermore, we introduce a new scheme to locate the critical point without the need of computing higher order moments of the order parameter. Finally, we also show how to obtain an improved estimate of the order parameter in gapless systems, with the 2D Heisenberg model as an example.

ORCID iDs

Corboz, Philippe, Czarnic, Piotr, Kapteijns, Geert and Tagliacozzo, Luca ORCID logoORCID: https://orcid.org/0000-0002-5858-1587;
  • Item type:Article
    ID code:64672
    Dates:
    Date
    Event
    30 July 2018
    Published
    22 June 2018
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:04 Jul 2018 10:14
    Last modified:18 Dec 2024 01:22
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/64672
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