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.
Highlights
In recent years there has been a very active development of tensor network variational ansätze for describing strongly correlated quantum many-body systems [1,2,3,4,5]
We have demonstrated the usefulness and applicability of finite correlation length scaling in two dimensions based on infinite projected entangled-pair states (iPEPS) by determining the critical exponents and critical point of an interacting spinless fermion model on a honeycomb lattice
We introduced a new approach to determine the critical point based on the derivative of the order parameter, which does not require the computation of higher-order moments of the order parameter or extrapolations of the effective correlation length in χ, making it a useful approach for 2D tensor network calculations
Summary
In recent years there has been a very active development of tensor network variational ansätze for describing strongly correlated quantum many-body systems [1,2,3,4,5]. The situation in 2D seems different because unlike in 1D there exist critical states with an area law [35,36,37,38,39,40,41] and there are known examples of exact critical infinite projected entangled-pair states (iPEPS) with a finite D [40,42] The latter include 2D classical states [43] and ground states of generalized Rokhsar-Kivelson (RK) Hamiltonians at their critical point. The linear dispersion is the footprint of an enhanced emerging symmetry, where energy and momentum (or space and time) play a very similar role and these critical points are called Lorentz-invariant critical points For such a critical point there are no known examples of a finite-D iPEPS that exactly represents the critical state [51,52,53].
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