Antiferromagnetic Heisenberg spin chains in a sufficiently strong magnetic field are Luttinger liquids, whose parameters depend on the actual magnetization of the chain. Here we present precise numerical estimates of the Luttinger liquid dressed charge Z, which determines the critical exponents, by calculating the magnetization and quadrupole operator profiles for $S=1/2$ and $S=1$ chains using the density matrix renormalization group method. Critical amplitudes and the scattering length at the chain ends are also determined. Although both systems are Luttinger liquids the characteristic parameters differ considerably.Antiferromagnetic Heisenberg spin chains in a sufficiently strong magnetic field are Luttinger liquids, whose parameters depend on the actual magnetization of the chain. Here we present precise numerical estimates of the Luttinger liquid dressed charge Z, which determines the critical exponents, by calculating the magnetization and quadrupole operator profiles for $S=1/2$ and $S=1$ chains using the density matrix renormalization group method. Critical amplitudes and the scattering length at the chain ends are also determined. Although both systems are Luttinger liquids the characteristic parameters differ considerably.

arXiv:cond-mat/0208580Physical review. B, Condensed matterOct 24, 200333 citations

Role of a spin-flip scatterer in a magnetized Luttinger liquid

M. A. N. Araújo, Jamal Berakdar, Vitalii K Dugaev +1 more

We study the spin-dependent scattering of charge carriers in a magnetized one dimensional Luttinger liquid from a localized nonhomogeneous magnetic field, which might be brought about by the stray field of magnetic tip near a uniform liquid, or by a transverse domain wall (DW) between two oppositely magnetized liquids. From a renormalization group treatment of the electron interactions we deduce scaling equations for the transmission and reflection amplitudes as the bandwidth is progressively reduced to an energy scale set by the temperature. The repulsive interactions dictate two possible zero temperature insulator fixed points: one in which electrons are reflected in the same spin channel and another where the electron spin is reversed upon reflection. In the latter case, a finite spin current emerges in the absence of a charge current at zero temperature and the Friedel oscillations form a transverse spiraling spin density. Adding a purely potential scattering term has no effect on the fixed points of a uniformly magnetized liquid. For a DW we find that the introduction of potential scattering stabilizes the spin-flip insulator phase even if the single-particle spin-flip scattering produced by the DW is arbitrarily weak. The potential can be induced externally, e.g., by a local gate voltage or a constriction, providing a means for controlling the transport properties of the wire.We study the spin-dependent scattering of charge carriers in a magnetized one dimensional Luttinger liquid from a localized nonhomogeneous magnetic field, which might be brought about by the stray field of magnetic tip near a uniform liquid, or by a transverse domain wall (DW) between two oppositely magnetized liquids. From a renormalization group treatment of the electron interactions we deduce scaling equations for the transmission and reflection amplitudes as the bandwidth is progressively reduced to an energy scale set by the temperature. The repulsive interactions dictate two possible zero temperature insulator fixed points: one in which electrons are reflected in the same spin channel and another where the electron spin is reversed upon reflection. In the latter case, a finite spin current emerges in the absence of a charge current at zero temperature and the Friedel oscillations form a transverse spiraling spin density. Adding a purely potential scattering term has no effect on the fixed points of a uniformly magnetized liquid. For a DW we find that the introduction of potential scattering stabilizes the spin-flip insulator phase even if the single-particle spin-flip scattering produced by the DW is arbitrarily weak. The potential can be induced externally, e.g., by a local gate voltage or a constriction, providing a means for controlling the transport properties of the wire.

arXiv:0707.0784Physical Review BNov 14, 20076 citations

The separated spin-charge Luttinger liquid in a magnetic field

Kai-Hua Yang, Bin Chen, Yunfeng Sun +1 more

Physica C SuperconductivityNov 1, 20000 citations

Charge-Spin Separation and the Spectral Properties of Luttinger Liquids

Johannes Voit

NATO ASI series. Series B : PhysicsJan 1, 19952 citations

Scaling of temporal correlations in an attractive Tomonaga-Luttinger spin liquid

Kirill Yu. Povarov, D. Schmidiger, N. Reynolds +2 more

We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ in a magnetic field $H=9$ T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\ensuremath{\approx}1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ in a magnetic field $H=9$ T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\ensuremath{\approx}1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.

arXiv:1406.6876Physical Review BJan 23, 201534 citations

S=1/2

and

S=1

chains using the density matrix renormalization group method. Critical amplitudes and the scattering length at the chain ends are also determined. Although both systems are Luttinger liquids the characteristic parameters differ considerably.

We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder

{({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}

in a magnetic field

H=9

T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\ensuremath{\approx}1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.