Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="script">D</mi><mrow><mn>8</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math> spectrum

Yunjing Gao; Xiao Wang; Ning Xi; Yunfeng Jiang; Rong Yu; Jianda Wu

doi:10.1103/PhysRevB.111.L201117

Letter

Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with $D_{8}^{(1)}$ spectrum

Yunjing Gao ¹, Xiao Wang ¹, Ning Xi ^2,3, Yunfeng Jiang⁴, Rong Yu ^2,1,5,*, and Jianda Wu ^1,6,7,†

¹Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China
²Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, China
³CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁴School of Phyiscs and Shing-Tung Yau Center, Southeast University, Nanjing 210096, China
⁵Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, China
⁶School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁷Shanghai Branch, Hefei National Laboratory, Shanghai 201315, China

^*Contact author: rong.yu@ruc.edu.cn
^†Contact author: wujd@sjtu.edu.cn

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Phys. Rev. B 111, L201117 – Published 27 May, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L201117

Abstract

Emergent ${Ising}_{h}^{2}$ integrability is anticipated in a quantum Ising ladder composed of two weakly coupled critical transverse field Ising chains. The system is remarkable for including eight types of massive relativistic particles, whose scattering matrix and mass spectrum are characterized by the $D_{8}^{(1)}$ Lie algebra. In this article, by computing the spin dynamical structure factors using analytical form-factor approach, we clearly identify dispersive single-particle excitations of (anti) soliton and breathers as well as their multiparticle continua in the spectra, which is further confirmed by numerical simulations. We show that the selection rule inherent in the parity and topological charge of the theory causes a significant result: charge-parity-odd particles, termed dark particles, cannot be directly excited from the ground state through any local or quasilocal operations. This, in turn, suggests the long lifetime of the lightest dark particle.

Physical Review B

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Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with $D_{8}^{(1)}$ spectrum

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Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with D8(1) spectrum

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Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with $D_{8}^{(1)}$ spectrum