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arXiv · 2102.03143

A scaling hypothesis for projected entangled-pair states

Bram Vanhecke·Juraj Hasik·Frank Verstraete·Laurens Vanderstraeten
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Abstract

We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly-correlated systems, allowing for reliable extrapolations of PEPS data with relatively small bond dimensions $D$. The key ingredient consists of using the effective correlation length $χ$ for inducing a collapse of data points, $f(D,χ)=f(ξ(D,χ))$, for arbitrary values of $D$ and the environment bond dimension $χ$. As such we circumvent the need for extrapolations in $χ$ and can use many distinct data points for a fixed value of $D$. Here, we need that the PEPS has been optimized using a fixed-$χ$ gradient method, which can be achieved using a novel tensor-network algorithm for finding fixed points of 2-D transfer matrices, or by using the formalism of backwards differentiation. We test our hypothesis on the critical 3-D dimer model, the 3-D classical Ising model, and the 2-D quantum Heisenberg model.

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Bram Vanhecke, Juraj Hasik, Frank Verstraete, Laurens Vanderstraeten. 2022-11-11. A scaling hypothesis for projected entangled-pair states. https://doi.org/10.1103/physrevlett.129.200601

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