SciPost Physics Lecture Notes

SciPost Phys. Lect. Notes 25 (2021) · published 25 February 2021

• doi: 10.21468/SciPostPhysLectNotes.25
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Abstract

Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network (TN) ansatz. Special focus is put on (i) a gentle introduction of the diagrammatic TN representations forming the basis for deriving the complex numerical algorithm, and (ii) the technical advance of fully exploiting non-abelian symmetries for fermionic iPEPS treatments of multi-band lattice models. The exploitation of non-abelian symmetries substantially increases the performance of the algorithm, enabling the treatment of fermionic systems up to a bond dimension $D=24$ on a square lattice. A variety of complex two-dimensional (2D) models thus become numerically accessible. Here, we present first promising results for two types of multi-band Hubbard models, one with $2$ bands of spinful fermions of $\mathrm{SU}(2)_\mathrm{spin} \otimes \mathrm{SU}(2)_\mathrm{orb}$ symmetry, the other with $3$ flavors of spinless fermions of $\mathrm{SU}(3)_\mathrm{flavor}$ symmetry.

• Ponsioen et al., Superconducting stripes in the hole-doped three-band Hubbard model
  Phys. Rev. B 108, 205154 (2023) [Crossref]
• Schmoll et al., Tensor network study of the spin- 12 Heisenberg antiferromagnet on the shuriken lattice
  Phys. Rev. B 107, 064406 (2023) [Crossref]
• Mayer, Non-local order parameters for fermion chains via the partial transpose
  64, 011903 (2023) [Crossref]
• Weichselbaum, QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
  SciPost Phys. Codebases, 40 (2024) [Crossref]
• Naumann et al., An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
  SciPost Phys. Lect. Notes, 86 (2024) [Crossref]
• Sinha et al., Finite-temperature tensor network study of the Hubbard model on an infinite square lattice
  Phys. Rev. B 106, 195105 (2022) [Crossref]
• Chen et al., Emergent conformal symmetry at the multicritical point of (2+1)D SO(5) model with Wess-Zumino-Witten term on a sphere
  Phys. Rev. B 110, 125153 (2024) [Crossref]
• Lukin et al., Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
  Phys. Rev. Research 6, 023128 (2024) [Crossref]
• Schneider et al., Simulating both parity sectors of the Hubbard model with tensor networks
  Phys. Rev. B 104, 155118 (2021) [Crossref]
• Chen et al., Continuous ferromagnetic quantum phase transition on an anisotropic Kondo lattice
  Phys. Rev. B 106, 075114 (2022) [Crossref]
• Li et al., Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model
  Phys. Rev. Lett. 130, 226502 (2023) [Crossref]
• Chen et al., Phases of (2+1)D SO(5) Nonlinear Sigma Model with a Topological Term on a Sphere: Multicritical Point and Disorder Phase
  Phys. Rev. Lett. 132, 246503 (2024) [Crossref]
• ten Brink et al., Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods
  156, 234109 (2022) [Crossref]
• Consiglio et al., Variational quantum eigensolver for SU(N) fermions
  J. Phys. A: Math. Theor. 55, 265301 (2022) [Crossref]
• Lukin et al., Single-layer tensor network approach for three-dimensional quantum systems
  Phys. Rev. B 110, 064422 (2024) [Crossref]