Mesons in a quantum Ising ladder

Abstract

When two transverse-field Ising chains (TFICs) with magnetic order are coupled, the original free excitations become confined, giving rise to meson-like bound states. In this work, we study such bound states systematically. The mesons are characterized by their fermion number parity and chain-exchanging properties, which lead to distinct sets of mesonic states. The meson masses are determined by solving the Bethe-Salpter equation. An interesting observation is the additional degeneracy in the chain-exchanging odd sectors. Beyond the two particle approximation, we exploit the truncated free fermionic space approach to calculate the spectrum numerically. Corrections to the meson masses are obtained, and the degeneracy is further confirmed. The characterization and degeneracy can be connected to the situation when each chain is tuned to be quantum critical, where the system is described by the Ising${}_h^2$ integrable model, a sine-Gordon theory with ${\mathbb{Z}}_2$ orbifold. Here we establish a clear correspondence between the particles in the bosonized form and their fermionic counterparts. Near this point, the stability of these particles is analyzed using the form factor perturbation scheme, where four particles are always present. Additionally, we calculate the evolution of the dominant dynamical structure factor for local spin operators, providing further insight into the low-energy excitations and their role in the system's behavior. The two-particle confinement framework as well as the parity classifications may inspire the study for other coupled bi-partite systems.

38 pages, 7 figures

References in corpus (26)

• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• Real time confinement following a quantum quench to a non-integrable model
• Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Multi-Chain Mean-Field Theory of Quasi One-Dimensional Quantum Spin Systems
• Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
• Confinement and Entanglement Dynamics on a Digital Quantum Computer
• Decay of particles above threshold in the Ising field theory with magnetic field
• Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in Transverse Magnetic Field
• Nonperturbative study of the two-frequency sine-Gordon model
• $E_8$ Spectra of Quasi-one-dimensional Antiferromagnet BaCo${}_2$V${}_2$O${}_8$ under Transverse Field
• Observation of E8 Particles in an Ising Chain Antiferromagnet
• Finite temperature spin dynamics in a perturbed quantum critical Ising chain with an $E_8$ symmetry
• Confinement in the q-state Potts field theory
• 2D Ising Field Theory in a Magnetic Field: The Yang-Lee Singularity
• On the weak confinement of kinks in the one-dimensional quantum ferromagnet CoNb2O6
• Confinement in the q-state Potts model: an RG-TCSA study
• Confinement and bound states of bound states in a transverse-field two-leg Ising ladder
• Perturbative post-quench overlaps in Quantum Field Theory
• Soliton Confinement in a Quantum Circuit
• Spin dynamics of the $E_8$ particles
• Magnetization oscillations in a periodically driven transverse field Ising chain
• 2d QCD and Integrability, Part I: 't Hooft model
• One-point functions in integrable coupled minimal models
• Soliton confinement in the double sine-Gordon model
• Confinement and false vacuum decay on the Potts quantum spin chain

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• Emergent $D_8^{(1)}$ spectrum and topological soliton excitation in CoNb${}_2$O${}_6$