Electron Spin Resonance of the Interacting Spinon Liquid.

We report experimental verification of the recently predicted collective modes of spinons, stabilized by backscattering interaction, in a model quantum spin chain material. We exploit the unique geometry of uniform Dzyaloshinskii-Moriya interactions in K_{2}CuSO_{4}Br_{2} to measure the interaction-induced splitting between the two components of the electron spin resonance (ESR) response doublet. From that we directly determine the magnitude of the "marginally irrelevant" backscattering interaction between spinons for the first time.

Amplitude Mode in Quantum Magnets via Dimensional Crossover.

We investigate the amplitude (Higgs) mode associated with longitudinal fluctuations of the order parameter at the continuous spontaneous symmetry breaking phase transition. In quantum magnets, due to the fast decay of the amplitude mode into low-energy Goldstone excitations, direct observation of this mode represents a challenging task. By focusing on a quasi-one-dimensional geometry, we circumvent the difficulty and investigate the amplitude mode in a system of weakly coupled spin chains with the help of quantum Monte Carlo simulations, stochastic analytic continuation, and a chain-mean field approach combined with a mapping to the field-theoretic sine-Gordon model.

Dynamical Signatures of Quasiparticle Interactions in Quantum Spin Chains.

We study the transverse dynamical susceptibility of an antiferromagnetic spin-1/2 chain in the presence of a longitudinal Zeeman field. In the low magnetization regime in the gapless phase, we show that the marginally irrelevant backscattering interaction between the spinons creates a nonzero gap between two branches of excitations at small momentum. We further demonstrate how this gap varies upon introducing a second neighbor antiferromagnetic interaction, vanishing in the limit of a noninteracting "spinon gas.

Spinon Magnetic Resonance of Quantum Spin Liquids.

We describe electron spin resonance in a quantum spin liquid with significant spin-orbit coupling. We find that the resonance directly probes spinon continuum, which makes it an efficient and informative probe of exotic excitations of the spin liquid. Specifically, we consider spinon resonance of three different spinon mean-field Hamiltonians, obtained with the help of projective symmetry group analysis, which model a putative quantum spin liquid state of the triangular rare-earth antiferromagnet YbMgGaO_{4}.

Quantum Lifshitz Field Theory of a Frustrated Ferromagnet.

We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase.

Unusual ordered phases of highly frustrated magnets: a review.

We review ground states and excitations of a quantum antiferromagnet on triangular and other frustrated lattices. We pay special attention to the combined effects of magnetic field h, spatial anisotropy R and spin magnitude S. The focus of the review is on the novel collinear spin density wave and spin nematic states, which are characterized by fully gapped transverse spin excitations with S(z) = ± 1.

Phases of a triangular-lattice antiferromagnet near saturation.

We consider 2D Heisenberg antiferromagnets on a triangular lattice with spatially anisotropic interactions in a high magnetic field close to the saturation. We show that this system possesses a rich phase diagram in a field or anisotropy plane due to competition between classical and quantum orders: an incommensurate noncoplanar spiral state, which is favored classically, and a commensurate coplanar state, which is stabilized by quantum fluctuations. We show that the transformation between these two states is highly nontrivial and involves two intermediate phases--the phase with coplanar incommensurate spin order and the one with noncoplanar double-Q spiral order.

Spin-current order in anisotropic triangular antiferromagnets.

We analyze instabilities of the collinear up-up-down state of a two-dimensional quantum spin-S spatially anisotropic triangular lattice antiferromagnet in a magnetic field. We find, within the large-S approximation, that near the end point of the plateau, the collinear state becomes unstable due to the condensation of two-magnon bound pairs rather than single magnons. The two-magnon instability leads to a novel two-dimensional vector chiral phase with alternating spin currents but no magnetic order in the direction transverse to the field.

Quantum stabilization of the 1/3-magnetization plateau in Cs2CuBr4.

We consider the phase diagram of a spatially anisotropic 2D triangular antiferromagnet in a magnetic field. Classically, the ground state is umbrellalike for all fields, but we show that the quantum phase diagram is much richer and contains a 1/3-magnetization plateau, two commensurate planar states, two incommensurate chiral umbrella phases, and, possibly, a spin density wave state separating the two chiral phases. Our analysis sheds light on several recent experimental findings for Cs2CuBr4.

Spin-orbit-mediated anisotropic spin interaction in interacting electron systems.

We investigate interactions between spins of strongly correlated electrons subject to the spin-orbit interaction. Our main finding is that of a novel, spin-orbit mediated anisotropic spin-spin coupling of the van der Waals type. Unlike the standard exchange, this interaction does not require the wave functions to overlap.

Spin-orbit-induced spin-density wave in a quantum wire.

We present analysis of the interacting quantum wire problem in the presence of magnetic field and spin-orbit interaction. We show that an interesting interplay of Zeeman and spin-orbit terms, facilitated by the electron-electron interaction, results in the spin-density wave state when the magnetic field and spin-orbit axes are orthogonal. This strongly affects charge transport through the wire: With the spin-density wave stabilized, single-particle backscattering off a nonmagnetic impurity becomes irrelevant.

Ordering in spatially anisotropic triangular antiferromagnets.

We investigate the phase diagram of the anisotropic spin-1/2 triangular lattice antiferromagnet, with interchain diagonal exchange J' much weaker than the intrachain exchange J. We find that fluctuations lead to a competition between (commensurate) collinear antiferromagnetic and (zigzag) dimer orders. Both states differ in symmetry from the spiral order known to occur for larger J', and are therefore separated by quantum phase transitions from it.

Dimerized phase and transitions in a spatially anisotropic square lattice antiferromagnet.

We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J( perpendicular )) and diagonal (J(x)), with respect to the chain, directions. Classically, the model admits two ordered ground states-with antiferromagnetic and ferromagnetic interchain spin correlations-separated by a first-order phase transition at J( perpendicular )=2J(x).

Spinons in a crossed-chains model of a 2D spin liquid.

Using the random phase approximation, we show that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a "sliding Luttinger liquid." In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.