While spin parity effects, physics crucially depending on whether the spin quantum number
S is half-odd integral or integral, have for decades been a source of new developments for the quantum physics of antiferromagnetic spin chains, the investigation into their possible ferromagnetic counterparts has remained largely unchartered, especially in the fully quantum (as opposed to the semiclassical) regime. Here we present such studies for monoaxial chiral ferromagnetic spin chains. We start by examining magnetization curves for finite-sized systems, where a magnetic field is applied perpendicular to the helical axis. For half-odd integer
S, the curves feature discontinuous jumps identified as a series of level crossings, each accompanied by a shift of the crystal momentum
k by an amount of $\ensuremath{\pi}$. The corresponding curves for integer valued
S are continuous and exhibit crossover processes. For the latter case,
k=0 throughout. These characteristics are observed numerically when the strength of the Dzyaloshinskii-Moriya interaction (DMI)
D is comparable to or larger than that of the ferromagnetic exchange interaction
J. Solitons are known to be responsible for stepwise changes seen in magnetization curves in the classical limit. These findings therefore prompt us to revise the notion of a soliton, for arbitrary
S, into a quantum mechanical entity. To unravel this phenomenon at the fully quantum level as is appropriate to spin chains with small
S, we examine in detail special limiting Hamiltonians amenable to rigorous analysis, consisting of only the DMI and the Zeeman energy. Dubbed the
DH model (for
S=21) and the projected
DH (
pDH) model (for general
S), they have a set of
2S conserved quantities, each of which is the number of solitons of a specific integer-valued height (as measured in the
Sz basis), which ranges from 1 to
2S. We discuss how to determine the exact crystal momentum of the lowest-energy state belonging to a sector with a given set of the
2S soliton numbers. Combined with energetic considerations, this information enables us to reproduce the spin parity effect in the magnetization curves. Finally, we show that the ground states of the special models have substantial numerical overlap with those for generic systems with a finite exchange interaction, suggesting the same physics to be valid there as well.
Spin parity effects refer to those special situations where a dichotomy in the physical behavior of a system arises, solely depending on whether the relevant spin quantum number is integral or half-odd integral. As is the case with the Haldane conjecture in antiferromagnetic spin chains, their pursuit often derives deep insights and invokes new developments in quantum condensed matter physics. Here, we put forth a simple and general scheme for generating such effects in any spatial dimension through the use of anisotropic interactions, and a setup within reasonable reach of state-of-the-art cold-atom implementations. We demonstrate its utility through a detailed analysis of the magnetization behavior of a specific one-dimensional spin chain model, an anisotropic antiferromagnet in a transverse magnetic field, unraveling along the way the quantum origin of finite-size effects observed in the magnetization curve that had previously been noted but not clearly understood.
The one-dimensional quantum Heisenberg antiferromagnet with exchange alternation is related to the nonlinear 0(3) sigma model with a topological ‘‘θ term’’ in the Langrangian. The models with parity symmetry (θ=0 or π) are respectively related to the integer and half-integer spin models without exchange alternation. The nonlinear quantum physics of Heisenberg antiferromagnets is placed in a wider context of topologically nontrivial field theories and the spin-Peierls effect in half-integer spin systems (and its absence in integer spin systems) explained.
The zero-temperature phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N)$ antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general
N. A fully gapped
SU(N) valence bond solid made of
N sites is formed above a critical value of
J2/J1 for all
N. We find that the extension of this
N-merized phase for larger values of
J2 strongly depends on the parity of
N. For even
N, the phase smoothly interpolates to the large
J2 regime where the model can be viewed as a zigzag
SU(N) two-leg spin ladder. The phase exhibits both a
N-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the
N-merized phase with odd
N has only a finite extent with no incommensuration. A gapless phase in the
SU(N)1 universality class is stabilized for larger
J2 that stems from the existence of a massless renormalization group flow from
SU(N)2 to
SU(N)1 conformal field theories when
N is odd.