The Heisenberg spin-1/2 XXZ chain in the presence of electric and magnetic fields

Abstract

We study the interplay of electric and magnetic order in the one dimensional Heisenberg spin-1/2 XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (D-M) interaction and with longitudinal and transverse magnetic fields, interpreting the D-M interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped Néel phase with antiferromagnetic (AF) order, gapped saturated phase and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the Néel phase (even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.

14 pages, 12 figures, to be published in Physical Review B (2018)

References in corpus (14)

• Spin current and magneto-electric effect in non-collinear magnets
• Experimental Observation of Bethe Strings
• Laser-Driven Multiferroics and Ultrafast Spin Current Generation
• Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
• Novel ordering of an S = 1/2 quasi one-dimensional Ising-like anitiferromagnet in magnetic field
• Spin-orbital effects in magnetized quantum wires and spin chains
• Magnetic correlations of the quasi-one-dimensional half-integer spin-chain antiferromagnets Sr$M_2$V${}_2$O${}_8$ ($M$ = Co, Mn)
• Dynamic probes of quantum spin chains with the Dzyaloshinskii-Moriya interaction
• From confined spinons to emergent fermions: Observation of elementary magnetic excitations in a transverse-field Ising chain
• Exact description of the magnetoelectric effect in the spin-1/2 XXZ-chain with Dzyaloshinskii-Moriya interaction
• Low-temperature ordered phases of the spin-$\frac{1}{2}$ XXZ chain system Cs${}_2$CoCl${}_4$
• Polarized Neutron Inelastic Scattering Study of the Anisotropic Magnetic Fluctuations in the Quasi-1D Ising-like Antiferromagnet TlCoCl${}_3$
• Spin-orbit interaction driven dimerization in one dimensional frustrated magnets
• Anisotropic magnetic interactions and spin dynamics in the spin-chain compound Cu(py)${}_2$Br${}_2$: An experimental and theoretical study

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• Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interaction
• Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets
• Factorization, coherence and asymmetry in the Heisenberg spin-1/2 XXZ chain a transverse magnetic field and with Dzyaloshinskii-Moriya interaction
• Spin-1/2 XY chain magnetoelectric: effect of zigzag geometry
• Influence of $XY$ anisotropy on a magnetoelectric effect in spin-1/2 $XY$ chain in a transverse magnetic field
• Orbital antiferroelectricity and higher dimensional magnetoelectric order in the spin-$1/2$ XX chain extended with three-spin interactions
• On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain
• Electric-field driven flat bands in the distorted sawtooth chain via the Katsura-Nagaosa-Balatsky mechanism