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.

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• The emergence of gapless quantum spin liquid from deconfined quantum critical point
• Variational methods for contracting projected entangled-pair states
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Quantum criticality with emergent symmetry in the extended Shastry-Sutherland model
• Generating function for projected entangled-pair states
• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• Efficient calculation of three-dimensional tensor networks
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states
• Tensor networks and efficient descriptions of classical data
• Finite-Entanglement Scaling of 2D Metals
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Efficient optimization of variational tensor-network approach to three-dimensional statistical systems
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Variational optimization of projected entangled-pair states on the triangular lattice
• Equivalence of residual entropy of hexagonal and cubic ices from tensor network methods