Finite correlation length scaling with infinite projected entangled-pair states

Philippe Corboz, Piotr Czarnic, Geert Kapteijns, Luca Tagliacozzo

Research output: Contribution to journalArticle

11 Citations (Scopus)

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.
LanguageEnglish
Article number031031
Number of pages10
JournalPhysical Review X
Volume8
Issue number3
Early online date30 Jul 2018
DOIs
Publication statusE-pub ahead of print - 30 Jul 2018

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exponents
scaling
critical point
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estimates
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approximation

Keywords

  • infinite projected entangled-pair states
  • iPEPS
  • Lorentz-invariant critical states
  • FCLS
  • two-dimensional

Cite this

Corboz, Philippe ; Czarnic, Piotr ; Kapteijns, Geert ; Tagliacozzo, Luca. / Finite correlation length scaling with infinite projected entangled-pair states. In: Physical Review X. 2018 ; Vol. 8, No. 3.
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Finite correlation length scaling with infinite projected entangled-pair states. / Corboz, Philippe; Czarnic, Piotr; Kapteijns, Geert; Tagliacozzo, Luca.

In: Physical Review X, Vol. 8, No. 3, 031031, 30.07.2018.

Research output: Contribution to journalArticle

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