Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order

Physics – Condensed Matter – Strongly Correlated Electrons

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

25 pages, 32 figures

Scientific paper

10.1103/PhysRevB.80.155131

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization (TEFR) approach that removes local entanglement and coarse grain the lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors $T_{inv}$ plus the symmetry group $G_{sym}$ of the tensors (i.e. the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, as illustrated by 2D statistical Ising model, 2D statistical loop gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a $(G_{sym}, T_{inv}) $ characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry protected topological phase. The $(G_{sym}, T_{inv})$ characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-134384

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.