Abelian and non-abelian symmetries in infinite projected entangled pair states

Abstract

We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions $D=10$ in the square lattice Heisenberg model at computational effort comparable to calculations at $D=6$ without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.

18 pages, submitted to SciPost Physics

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• Time-evolution methods for matrix-product states
• Review on novel methods for lattice gauge theories
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• Time-dependent study of disordered models with infinite projected entangled pair states
• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Efficient and Flexible Approach to Simulate Low-Dimensional Quantum Lattice Models with Large Local Hilbert Spaces
• A programming guide for tensor networks with global $SU(2)$ symmetry
• A beginner's guide to non-abelian iPEPS for correlated fermions
• Optimal sampling of dynamical large deviations via matrix product states
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Quantum Quench and Charge Oscillations in the SU(3) Hubbard Model: a Test of Time Evolving Block Decimation with general non-Abelian Symmetries
• The Three-Legged Tree Tensor Networks with SU(2)- and molecular point group symmetry
• Benchmarking global $SU(2)$ symmetry in 2d tensor network algorithms
• iPEPS study of spin symmetry in the doped $t$-$J$ model
• The seniority quantum number in Tensor Network States