Phase diagram of spin-$1$ chains with Dzyaloshinskii-Moriya interaction

Abstract: We investigate an antiferromagnetic spin-$1$ Heisenberg chain in the presence of Dyzaloshinskii-Moriya interactions (DMI) and an external magnetic field. We study the resulting spin chain using a combination of numerical and analytical techniques. Using DMRG simulations to determine the spectral gap and the entanglement spectrum, we map out the phase diagram as a function of magnetic field strength and DMI strength. We provide a qualitative interpretation for these numerical findings by mapping the spin-$1$ chain on a spin-$1/2$ ladder and using a bosonization approach.