Work

The Yang–Baxter integrability of the critical Ising chain

Year: 2025

Type: article

Abstract: We demonstrate that the one-dimensional critical transverse field Ising model (TFIM) is Yang–Baxter integrable. This is achieved by constructing commuting transfer matrices derived from an R-matrix that satisfies the Yang–Baxter equation with additive spectral parameters. The R-matrix is nonlocal because it is expressed in terms of Majorana fermions. It is also non-regular. Nevertheless, we show that the quantum inverse scattering method can still be suitably adapted. Using the boost operator method, we recursively obtain the conserved quantities in the infinite volume. Among the conserved charges, we identify the Kramers–Wannier duality and other non-invertible symmetries for the periodic TFIM.

Source: Journal of Statistical Mechanics Theory and Experiment

DOI: 10.1088/1742-5468/ae0690

Authors: Akash Sinha, Tinu Justin, Pramod Padmanabhan, Vladimir Korepin

Institutions: Indian Institute of Technology Bhubaneswar, Stony Brook University

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, Office of Science

Awards: G241279073, G357145406, G5765906131, G7463374569