Work

Tensor Networks for Noninvertible Symmetries in 3 + 1 D and Beyond

Year: 2025

Type: article

Abstract: Tensor networks provide a natural language for noninvertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a noninvertible operator implementing the Wegner duality in 3 + 1 D lattice Z 2 gauge theory. The noninvertible algebra, which mixes with lattice translations, can be efficiently computed using ZX-calculus. We further deform the Z 2 gauge theory while preserving the duality and find a model with nine exactly degenerate ground states on a torus, consistent with the Lieb-Schultz-Mattis-type constraint imposed by the symmetry. Finally, we provide a ZX-diagram presentation of the noninvertible duality operators (including noninvertible parity and reflection symmetries) of generalized Ising models based on graphs, encompassing the 1 + 1 D Ising model, the three-spin Ising model, the Ashkin-Teller model, and the 2 + 1 D plaquette Ising model. The mixing (or lack thereof) with spatial symmetries is understood from a unifying perspective based on graph theory.

Source: Physical Review X

DOI: 10.1103/p32z-v884

Authors: Pranay Gorantla, Shu-Heng Shao, Nathanan Tantivasadakarn

Institutions: University of Chicago, Stony Brook University, Massachusetts Institute of Technology, California Institute of Technology

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $4,200

Funders: National Science Foundation, California Institute of Technology, Aspen Center for Physics, Walter Burke Institute for Theoretical Physics