Quasiparticle Interactions in the Spin-1/2 Heisenberg Spin Chain CuPzN

The spin-1/2 nearest-neighbor Heisenberg antiferromagnetic chain is a paradigmatic model of strongly correlated systems. In particular, its analytical solvability with the Bethe ansatz and the unequivocal existence of fractionalized quasiparticles – spinons – have attracted much theoretical and experimental attention. In general, when multiple quasiparticles are present, they interact. In this work, we explore how spinon-spinon interactions manifest in the dynamics at finite magnetization. We use magnetic inelastic neutron scattering to measure the dynamical structure factor S(Q,ω) in copper pyrazine dinitrate(CuPzN), a well-established quasi-one-dimensional spin-1/2 Heisenberg antiferromagnet. We compare the experimental results with density-matrix renormalization group(DMRG) and time-evolution block-decimation calculations and a recent analytical theory.

At zero field, we observe the hallmark two-spinon continuum in the magnetic scattering along the chain direction with no dispersion in the transverse direction, consistent with the one-dimensional spin-1/2 Heisenberg antiferromagnet description. With increasing field, finite magnetization produces a splitting of the spinon bands near Q→0 with a gap energy 2Δ that grows with magnetization. At μ_0 H=6.8T where M/M_sat=0.24, we extrapolate an energy gap of 2Δ(Q=0)=0.35(7)meV. At μ_0 H=11T (M/M_sat=0.42), the energy gap increased to 2Δ=0.73(5)meV. The measured spectra and extrapolated 2Δ are consistent with the spectral function calculated with DMRG and time-evolution block-decimation techniques. From the magnetization dependence of 2Δ, we extracted a spinon interaction strength of g=2.0(1), in agreement with an analytical theory for the nearest-neighbor one-dimensional spin-1/2 Heisenberg antiferromagnetic chain. Our results provide a experimental validation of the recent analytical description of interacting spinons in the nearest-neighbor spin-1/2 Heisenberg chain.