Fermionic Approach to Elementary Excitations and Magnetization Plateaus in an S=1/2 XX Hybrid Trimer-Dimer Chain

TL;DR

This paper investigates the elementary excitations and magnetization plateaus in a one-dimensional spin-1/2 XX chain with trimer-dimer units, revealing how quantum states and phase diagrams depend on excitation gaps and periodicity, using fermionic mapping techniques.

Contribution

It introduces a fermionic approach to analyze elementary excitations and magnetization plateaus in a trimer-dimer chain, extending the OYA condition to generalized cluster chains based on global periodicity.

Findings

Distinct 1/5 and 3/5 magnetization plateaus at zero temperature.

Magnetization plateau widths are governed by excitation gaps.

Phase diagram includes Luttinger liquid, AFM, plateau, and polarized states.

Abstract

We study the elementary excitations and magnetization of a one-dimensional spin-1/2 XX chain comprising trimer-dimer units (the J1-J1-J2-J3-J2 topology) under a transverse magnetic field h. Using Green's function theory and the Jordan-Wigner transformation, we map the system onto spinless fermions and focus on antiferromagnetic (AFM) interactions. At zero temperature, distinct 1/5 and 3/5 magnetization plateaus emerge, determined by the global periodicity Q=5, with the number of plateaus matching the number of excitation gaps above the Fermi level of the spinless fermions. The magnetic phase diagram in the (h-Js) plane features a Luttinger liquid (LL) state, a gapless AFM state, two magnetization plateau states, and a fully polarized gapped magnetic state. The widths of the LL and gapless AFM phases are found to be proportional to the bandwidths gamma = |E(k=0)-E(k=pi)| of the corresponding elementary excitations, whereas the widths of the magnetization plateau states are governed by the excitation gaps. Our study opens new directions for exploring interacting trimer-dimer spin chains in quantum magnetism using experimental techniques such as neutron scattering, as well as theoretical and numerical approaches including quantum Monte Carlo (QMC) and density-matrix renormalization group (DMRG) methods. Furthermore, we extend the Oshikawa-Yamanaka-Affleck (OYA) condition to generalized cluster chains, demonstrating that the allowed magnetization plateaus are governed by the global periodicity of the chain (e.g., Q=5 for a trimer-dimer chain), rather than by the local periodicity of individual units (Q=3 for a trimer or Q=2 for a dimer).