A scaling hypothesis for projected entangled-pair states

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.

References in corpus (4)

• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Scaling of entanglement support for Matrix Product States
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature

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