For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
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For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
A discretization-plus-coarse-graining scheme turns continuous-space interacting particles into a tensor-network-representable lattice model, enabling partition-function calculations for the 2D hard-disk problem.
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
TNPA uses tensor-network contractions only in a reliable temperature window to seed population annealing, with an effective-sample-size diagnostic to pick the switch-over temperature.
citing papers explorer
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Algorithmic Locality via Provable Convergence in Quantum Tensor Networks
For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
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Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
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Statistical mechanics in continuous space with tensor network methods
A discretization-plus-coarse-graining scheme turns continuous-space interacting particles into a tensor-network-representable lattice model, enabling partition-function calculations for the 2D hard-disk problem.
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Symmetry breaking phases and transitions in an Ising fusion category lattice model
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
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Tensor-Network Population Annealing
TNPA uses tensor-network contractions only in a reliable temperature window to seed population annealing, with an effective-sample-size diagnostic to pick the switch-over temperature.