Finite correlation length scaling with infinite projected entangled-pair states

TL;DR

This paper presents a method using infinite projected entangled-pair states (iPEPS) to accurately analyze 2D quantum critical phenomena by leveraging finite correlation length scaling, achieving results consistent with Quantum Monte Carlo.

Contribution

The paper introduces a finite correlation-length scaling approach with iPEPS for 2D critical states and demonstrates its effectiveness on fermionic and spin models.

Findings

Critical exponents agree with Quantum Monte Carlo results.

New scheme for locating critical points without higher order moments.

Improved order parameter estimates in gapless systems.

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.