Tensor Networks for Chiral Topological Order

• Applicant: Professor Dr. Roman Orus
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 262801491

• Final Report Year: 2018

Final Report Abstract

This DFG project allowed us to study in detail several aspects of chiral topological order. Our results on SPT and SPt phases for 1d systems revealed new phases of matter with topological and symmetry properties which could be assessed accurately using Matrix Product States. The work was later extended to 2d systems, where several chiral topological phases, either exact or conjectured, were assessed using Projected Entangled Pair States and entanglement spectrum. Finally, our results motivated a new research direction, namely, the effect of dissipation and finite temperature in 2d topological order, for which we already developed some of the relevant tensor network tools. Work along this promising new direction is currently in progress.

Publications

• “All spin-1 topological phases in a single spin-2 chain”, Phys. Rev. B 91, 205118 (2015)
  A. Kshetrimayum, H.-Hao Tu, R. Orus
  (See online at https://doi.org/10.1103/PhysRevB.91.205118)
• “Symmetry-protected intermediate trivial phases in quantum spin chains”, Phys. Rev. B 93, 245112 (2016)
  A. Kshetrimayum, H.-Hao Tu, R. Orus
  (See online at https://doi.org/10.1103/PhysRevB.93.245112)
• “Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry”, Phys. Rev. B 94, 205124 (2016)
  M. Mambrini, R. Orus, D. Poilblanc
  (See online at https://doi.org/10.1103/PhysRevB.94.205124)
• “The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders”, Phys. Rev. B 94, 235146 (2016)
  A. Kshetrimayum, T. Picot, R. Orus, D. Poilblanc
  (See online at https://doi.org/10.1103/PhysRevB.94.235146)
• “A simple tensor network algorithm for two-dimensional steady states”, Nature Communications 8, 1291 (2017)
  A. Kshetrimayum, H. Weimer, R. Orus
  (See online at https://doi.org/10.1038/s41467-017-01511-6)