Lattice-reflection symmetry in tensor-network renormalization group with entanglement filtering in two and three dimensions

• URL: http://arxiv.org/abs/2510.19428v1
• Date: Wed, 22 Oct 2025 09:54:41 GMT
• Title: Lattice-reflection symmetry in tensor-network renormalization group with entanglement filtering in two and three dimensions
• Abstract summary: We introduce a transposition trick for exploiting and imposing the lattice-reflection symmetry in two basic TNRG operators.<n>Our work paves the way for understanding the lattice-rotation symmetry in TNRG.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Tensor-network renormalization group (TNRG) is an efficient real-space renormalization group method for studying the criticality in both classical and quantum lattice systems. Exploiting symmetries of a system in a TNRG algorithm can simplify the implementation of the algorithm and can help produce correct tensor RG flows. Although a general framework for considering a global on-site symmetry has been established, it is still unclear how to incorporate a lattice symmetry like rotation or reflection in TNRG. As a first step for lattice symmetries, we propose a method to incorporate the lattice-reflection symmetry in the context of a TNRG with entanglement filtering in both two and three dimensions (2D and 3D). To achieve this, we write down a general definition of lattice-reflection symmetry in tensor-network language. Then, we introduce a transposition trick for exploiting and imposing the lattice-reflection symmetry in two basic TNRG operators: projective truncations and entanglement filtering. Using the transposition trick, the detailed algorithms of the TNRG map in both 2D and 3D are laid out, where the lattice-reflection symmetry is preserved and imposed. Finally, we demonstrate how to construct the linearization of the TNRG maps in a given lattice-reflection sector, with the help of which it becomes possible to extract scaling dimensions in each sector separately. Our work paves the way for understanding the lattice-rotation symmetry in TNRG.

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