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Title: Tensor network implementation of bulk entanglement spectrum

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 90; Journal Issue: 8; Journal ID: ISSN 1098-0121
American Physical Society
Country of Publication:
United States

Citation Formats

Hsieh, Timothy H., Fu, Liang, and Qi, Xiao-Liang. Tensor network implementation of bulk entanglement spectrum. United States: N. p., 2014. Web. doi:10.1103/PhysRevB.90.085137.
Hsieh, Timothy H., Fu, Liang, & Qi, Xiao-Liang. Tensor network implementation of bulk entanglement spectrum. United States. doi:10.1103/PhysRevB.90.085137.
Hsieh, Timothy H., Fu, Liang, and Qi, Xiao-Liang. Mon . "Tensor network implementation of bulk entanglement spectrum". United States. doi:10.1103/PhysRevB.90.085137.
title = {Tensor network implementation of bulk entanglement spectrum},
author = {Hsieh, Timothy H. and Fu, Liang and Qi, Xiao-Liang},
abstractNote = {},
doi = {10.1103/PhysRevB.90.085137},
journal = {Physical Review B},
number = 8,
volume = 90,
place = {United States},
year = {Mon Aug 25 00:00:00 EDT 2014},
month = {Mon Aug 25 00:00:00 EDT 2014}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevB.90.085137

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Cited by: 14works
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  • For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parametrization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parametrization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposesmore » between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few-qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight into the possible origin of entanglement for such densities.« less
  • 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 approach that removes local entanglement and produces a coarse-grained 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{sub inv} plus the symmetry group G{sub 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, asmore » illustrated by two-dimensional (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{sub sym},T{sub 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{sub sym},T{sub 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.« less