Long-range spin chirality dimer order in the Heisenberg chain with modulated Dzyaloshinskii-Moriya interactions

JAPARIDZE, G.I.; ROSSINI, G.L.; AVALISHVILI N.

PHYSICAL REVIEW B

AMER PHYSICAL SOC

Lugar: New York; Año: 2019 vol. 99 p. 205159 - 205171

1098-0121

The ground state phase diagram of a spin $S=1/2$ $XXZ$ Heisenbergchain with spatially modulated Dzyaloshinskii-Moriya (DM)interaction$${cal H}= sum_{n}left[Jleft(S^{x}_{n}S^{x}_{n+1}+S^{y}_{n}S^{y}_{n+1}ight)+J_z S^{z}_{n}S^{z}_{n+1}+(D_{0}+(-1)^{n}D_{1})left(S^{x}_{n}S^{y}_{n+1}-S^{y}_{n}S^{x}_{n+1} ight) ight]$$is studied using the continuum-limit bosonization approach andextensive density matrix renormalization group computations. It isshown that the effective continuum-limit bosonized theory of themodel is given by the double frequency sine-Gordon model (DSG) wherethe frequences i.e. the scaling dimensions of the two competingcosine perturbation terms depend on the effective anisotropyparameter $gamma^{ast}=J_z /sqrt{J^2+D_{0}^{2}+D_{1}^{2}}$.Exploring the ground state properties of the DSG model we have showthat the zero-temperature phase diagram contains the following fourphases: (i) the ferromagnetic phase at $gamma^{ast}leq -1$; (ii)the gapless Luttinger-liquid (LL) phase at $-1