A scaling hypothesis for projected entangled-pair states

• URL: http://arxiv.org/abs/2102.03143v3
• Date: Fri, 11 Nov 2022 14:54:20 GMT
• Title: A scaling hypothesis for projected entangled-pair states
• Authors: Bram Vanhecke, Juraj Hasik, Frank Verstraete, Laurens Vanderstraeten
• Abstract summary: We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly-correlated systems. We use the effective correlation length $chi$ for inducing a collapse of data points, $f(D,chi)=f(xi(D,chi))$, for arbitrary values of $D$ and the environment bond dimension $chi$. We test our hypothesis on the critical 3-D dimer model, the 3-D classical Ising model, and the 2-D quantum Heisenberg model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\chi$ for inducing a collapse of data points, $f(D,\chi)=f(\xi(D,\chi))$, for arbitrary values of $D$ and the environment bond dimension $\chi$. As such we circumvent the need for extrapolations in $\chi$ 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-$\chi$ 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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