Quantum phase transitions and composite excitations of antiferromagnetic spin trimer chains in a magnetic field

Abstract

Motivated by recent advancements in theoretical and experimental studies of the high-energy excitations on an antiferromagnetic trimer chain, we numerically investigate the quantum phase transition and composite dynamics in this system by applying a magnetic field. The numerical methods we used include the exact diagonalization, density matrix renormalization group, time-dependent variational principle, and cluster perturbation theory. From calculating the entanglement entropy, we have revealed the phase diagram which includes the XY-I, $1/3$ magnetization plateau, XY-II, and ferromagnetic phases. Both the critical XY-I and XY-II phases are characterized by the conformal field theory with a central charge $c\simeq 1$. By analyzing the dynamic spin structure factor, we elucidate the distinct features of spin dynamics across different phases. In the regime with weak intertrimer interaction, we identify the intermediate-energy and high-energy modes in the XY-I and $1/3$ magnetization plateau phases as internal trimer excitations, corresponding to the propagating of doublons and quartons, respectively. Notably, applying a magnetic field splits the high-energy spectrum into two branches, labeled as the upper quarton and lower quarton. Furthermore, we explore the spin dynamics of a frustrated trimerized model closely related to the quantum magnet \ce{Na_2Cu_3Ge_4O_12}. In the end, we extend our discuss on the possibility of the quarton Bose-Einstein condensation in the trimer systems. Our results are expected to be further verified through the inelastic neutron scattering and resonant inelastic X-ray scattering, and also provide valuable insights for exploring high-energy exotic excitations.

15+6 pages, 16 figures, to be published in npj Quantum materials

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Cited by in corpus (9)

• Magnetization Plateaus in the Two-dimensional S = 1/2 Heisenberg Model with a 3$\times$3 Checkerboard Structure
• Resonant inelastic x-ray scattering spectra of spinon, doublon, and quarton excitations of a spin-$\frac{1}{2}$ antiferromagnetic Heisenberg trimer chain
• Magnetic Ground State and Spin Excitations in the 2D Trimerized Collinear-II Lattice Antiferromagnet Li2Ni3P4O14
• Quantum Entanglement Control in Two-Spin-1/2 NMR Systems Through Magnetic Fields and Temperature
• Thresholded Quantum Sensing with a Frustrated Kitaev Trimer
• Phonon anomalies and critical scaling in the spin-$1/2$ trimer chain Na${}_2$Cu${}_3$Ge${}_4$O${}_{12}$
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• Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism
• Fermionic Approach to Elementary Excitations and Magnetization Plateaus in an S=1/2 XX Hybrid Trimer-Dimer Chain