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Boundary Tensor Renormalization Group

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arxiv 1905.02351 v2 pith:UWO42UEW submitted 2019-05-07 cond-mat.stat-mech cond-mat.str-elhep-th

Shumpei Iino , Satoshi Morita , Naoki Kawashima This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.str-elhep-th
keywords boundarytensorsalgorithmbulkconformalfixedgrouppoint
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We develop the tensor renormalization group (TRG) algorithm for statistical systems with open boundaries, which allows us to investigate not only the bulk but also the boundary property, such as the surface magnetization. We demonstrate that the tensors representing the boundary in our algorithm exhibit the fixed point structures just as bulk tensors in previous TRG algorithms. At criticality, the scale-invariant boundary fixed point tensors have the information of the conformal tower, which is described by the underlying boundary conformal field theory.

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Cited by 3 Pith papers

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  2. Applying the Triad network representation to four-dimensional ATRG method

    hep-lat 2024-12 conditional novelty 5.0 of 10

    Triad-ATRG applies the triad and MDTRG decomposition to four-dimensional ATRG, reducing the contraction cost to O(r^2 χ^7) while reproducing ATRG free energies and transition temperatures.

  3. Initial tensor construction for the tensor renormalization group

    hep-lat 2025-01 conditional novelty 4.0 of 10

    A delta-function index-shifting algorithm builds locally connected initial tensors for the tensor renormalization group from arbitrary Boltzmann factors, and boundary-style squeezers remove the initial-tensor dependen...

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