Hydrodynamics of interacting spinons in the magnetized spin-1/2 chain with a uniform Dzyaloshinskii-Moriya interaction

We use a hydrodynamic approach to investigate dynamic spin susceptibility of the antiferromagnetic spin-1/2 Heisenberg chain with a uniform Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We find that transverse (with respect to the magnetic field) spin susceptibility harbors two (respectively, three) spin excitation modes when the magnetic field is parallel (respectively, orthogonal) to the DM axis. In all cases, the marginally irrelevant backscattering interaction between the spinons creates a finite energy splitting between optical branches of excitations at k = 0. Additionally, for the orthogonal geometry, the two lower spin branches exhibit avoided crossing at finite momentum which is determined by the total magnetic field (the sum of the external and internal molecular fields) acting on spinons. Our approximate analytical calculations compare well with numerical results obtained using matrix-product-state (MPS) techniques. Physical consequences of our findings for the electron spin resonance experiments are discussed in detail.

Automated summary

We investigated the dynamic spin susceptibility of an antiferromagnetic spin-1/2 Heisenberg chain with a uniform Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field using a hydrodynamic approach. We found that the transverse spin susceptibility exhibits two or three spin excitation modes, depending on the orientation of the magnetic field with respect to the DM axis. The weak backscattering interaction between the spinons leads to a finite energy splitting between the optical branches of excitations at k = 0 in all cases. In the orthogonal geometry, the two lower spin branches show avoided crossing at finite momentum determined by the total magnetic field acting on spinons. Our approximate analytical calculations are in good agreement with numerical results obtained using matrix-product-state (MPS) techniques. The physical implications of our findings for electron spin resonance experiments are discussed.