### Abstract

Language | English |
---|---|

Article number | 031031 |

Number of pages | 10 |

Journal | Physical Review X |

Volume | 8 |

Issue number | 3 |

Early online date | 30 Jul 2018 |

DOIs | |

Publication status | E-pub ahead of print - 30 Jul 2018 |

### Fingerprint

### Keywords

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

### Cite this

*Physical Review X*,

*8*(3), [031031]. https://doi.org/10.1103/PhysRevX.8.031031

}

*Physical Review X*, vol. 8, no. 3, 031031. https://doi.org/10.1103/PhysRevX.8.031031

**Finite correlation length scaling with infinite projected entangled-pair states.** / Corboz, Philippe; Czarnic, Piotr; Kapteijns, Geert; Tagliacozzo, Luca.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Finite correlation length scaling with infinite projected entangled-pair states

AU - Corboz, Philippe

AU - Czarnic, Piotr

AU - Kapteijns, Geert

AU - Tagliacozzo, Luca

PY - 2018/7/30

Y1 - 2018/7/30

N2 - 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.

AB - 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.

KW - infinite projected entangled-pair states

KW - iPEPS

KW - Lorentz-invariant critical states

KW - FCLS

KW - two-dimensional

UR - https://journals.aps.org/prx/

U2 - 10.1103/PhysRevX.8.031031

DO - 10.1103/PhysRevX.8.031031

M3 - Article

VL - 8

JO - Physical Review X

T2 - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 3

M1 - 031031

ER -