Kavli Affiliate: Natalia Chepiga
| First 5 Authors: Aman Sharma, Aman Sharma, , ,
| Summary:
We investigate the nature of low-energy excitations in a spin chain with
antiferrmomagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and
three-site $J_3$ interactions using the time-dependent density matrix
renormalization group and the single mode approximation techniques. In the
absence of the $J_2$ interaction, we identify clear distinctions in the
spectral functions in the fully dimerized phase across the exactly dimerized
line for different magnitudes of the spins. In contrast to the spin-$1/2$
chain, where the spinon continuum dominates the spectral functions, the magnon
modes are prominent in the spectral functions of the spin-$1$ and spin-$3/2$
chains. Through single mode approximation and valence bond solid approaches, we
disentangle magnon and spinon contributions to the spectral functions. After
including the $J_2$ interactions, for the spin-$1$ chain we trace the evolution
of the dynamical structure factor along the phase transition line between the
Haldane phase and the fully dimerized phase. We find that the excitation
spectrum is a continuum along this line and the spectral gap closes as the
order of the transition changes from first order to second order. Along the
line of first-order transitions, the spinon-like domain walls are deconfined,
and the model exhibits their confinement into discrete bound states away from
the transition line. A similar phenomenon occurs in the spin-$3/2$ chain across
the phase transition between partially dimerized to fully dimerized phases,
revealing a universal spinon confinement phenomenon across first-order phase
transitions. This study presents the dynamical structure factor corresponding
to the ground state phase diagram and establishes a unified quasiparticle
framework for understanding the fundamental nature of excitations across
distinct quantum phases in frustrated $J_1$-$J_2$-$J_3$ Heisenberg spin chains.
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