佐藤 正寛

Abstract The ability to drive a spin system to state far from the equilibrium is indispensable for investigating spin structures of antiferromagnets and their functional nonlinearities for spintronics. While optical methods have been considered for spin excitation, terahertz (THz) pulses appear to be a more convenient means of direct spin excitation without requiring coupling between spins and orbitals or phonons. However, room-temperature responses are usually limited to small deviations from the equilibrium state because of the relatively weak THz magnetic fields in common approaches. Here, we studied the magnetization dynamics in a HoFeO₃ crystal at room temperature. A custom-made spiral-shaped microstructure was used to locally generate a strong multicycle THz magnetic near field perpendicular to the crystal surface; the maximum magnetic field amplitude of about 2 T was achieved. The observed time-resolved change in the Faraday ellipticity clearly showed second- and third-order harmonics of the magnetization oscillation and an asymmetric oscillation behaviour. Not only the ferromagnetic vector M but also the antiferromagnetic vector L plays an important role in the nonlinear dynamics of spin systems far from equilibrium.

Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs. This theory is based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. Using this theory, we show that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We also show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.

<title>Abstract</title>A triplon refers to a fictitious particle that carries angular momentum <italic>S</italic>=1 corresponding to the elementary excitation in a broad class of quantum dimerized spin systems. Such systems without magnetic order have long been studied as a testing ground for quantum properties of spins. Although triplons have been found to play a central role in thermal and magnetic properties in dimerized magnets with singlet correlation, a spin angular momentum flow carried by triplons, a triplon current, has not been detected yet. Here we report spin Seebeck effects induced by a triplon current: triplon spin Seebeck effect, using a spin-Peierls system CuGeO₃. The result shows that the heating-driven triplon transport induces spin current whose sign is positive, opposite to the spin-wave cases in magnets. The triplon spin Seebeck effect persists far below the spin-Peierls transition temperature, being consistent with a theoretical calculation for triplon spin Seebeck effects.

We discuss DC electric-field controls of superexchange interactions. We first present generic results about antiferromagnetic and ferromagnetic superexchange interactions valid in a broad class of Mott insulators, where we also estimate typical field strength to observe DC electric-field effects: similar to 1 MV/cm for inorganic Mott insulators such as transition-metal oxides and similar to 0.1 MV/cm for organic ones. Next, we apply these results to geometrically frustrated quantum spin systems. Our theory widely applies to (quasi-)two-dimensional and thin-film systems and one-dimensional quantum spin systems on various lattices such as square, honeycomb, triangular, and kagome ones. In this paper, we give our attention to those on the square lattice and on the chain. For the square lattice, we show that DC electric fields can control a ratio of the nearest-neighbor and next-nearest-neighbor exchange interactions. In some realistic cases, DC electric fields make the two next-nearest-neighbor interactions nonequivalent and eventually turns the square-lattice quantum spin system into a deformed triangular-lattice one. For the chain, DC electric fields can induce singlet-dimer and Haldane-dimer orders. We show that the DC electric-field-induced spin gap proportional to vertical bar E vertical bar(2/3) in the Heisenberg antiferromagnetic chain will reach similar to 10% of the dominant superexchange interaction in the case of a spin-chain compound KCuMoO4(OH) when the DC electric field of similar to 1 MV/cm is applied.

Laser technology has developed and accelerated photo-induced nonequilibrium physics, from both the scientific and engineering viewpoints. Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is at the forefront of quantum physics of light-matter interaction. However, it is limited to ideal dissipationless systems. Extending Floquet engineering to various materials requires understanding of the quantum states emerging in a balance of the periodic drive and energy dissipation. Here, we derive a general description for nonequilibrium steady states (NESSs) in periodically driven dissipative systems by focusing on systems under high-frequency drive and time-independent Lindblad-type dissipation. Our formula correctly describes the time average, fluctuation, and symmetry properties of the NESS, and can be computed efficiently in numerical calculations. This approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems from atoms and molecules to mesoscopic systems, and condensed matter.

We theoretically propose a new route to control magnetic and topological<br /> orders in a broad class of insulating magnets with a DC electric field. We show<br /> from the strong-coupling expansion that magnetic exchange interactions along<br /> the electric-field direction are generally enhanced in Mott insulators. We<br /> demonstrate that several magnetic or topological ordered phases such as quantum<br /> spin liquids and Haldane-gap states can be derived if we apply a strong enough<br /> DC electric field to typical frustrated or low-dimensional magnets. Our<br /> proposal is effective especially for weak Mott insulators and magnets in the<br /> vicinity of quantum critical points, and would also be applicable for magnets<br /> under low-frequency AC electric fields such as terahertz laser pulses. A<br /> similar strategy of controlling exchange interactions can also be utilized in<br /> cold atomic systems.

We theoretically propose a method of rectifying spin current with a<br /> linearly-polarized electromagnetic wave in inversion-asymmetric magnetic<br /> insulators. To demonstrate the proposal, we consider quantum spin chains as a<br /> simple example; these models are mapped to fermion (spinon) models via<br /> Jordan-Wigner transformation. Using a nonlinear response theory, we find that a<br /> dc spin current is generated by the linearly-polarized waves. The spin current<br /> shows rich anisotropic behavior depending on the direction of the<br /> electromagnetic wave. This is a manifestation of the rich interplay between<br /> spins and the waves; inverse Dzyaloshinskii-Moriya, Zeeman, and<br /> magnetostriction couplings lead to different behaviors of the spin current. The<br /> resultant spin current is insensitive to the relaxation time of spinons, a<br /> property of which potentially benefits a long-distance propagation of the spin<br /> current. An estimate of the required electromagnetic wave is given.

We develop the Floquet-Magnus expansion for a classical equation of motion<br /> under a periodic drive that is applicable to both isolated and open systems.<br /> For classical systems, known approaches based on the Floquet theorem fail due<br /> to the nonlinearity and the stochasticity of their equations of motion (EOMs)<br /> in contrast to quantum ones. Here, employing their master equation, we<br /> successfully extend the Floquet methodology to classical EOMs to obtain their<br /> Floquet-Magnus expansions, thereby overcoming this difficulty. Our method has a<br /> wide range of application from classical to quantum as long as they are<br /> described by differential equations including the Langevin equation, the<br /> Gross-Pitaevskii equation, and the time-dependent Ginzburg-Landau equation. By<br /> analytically evaluating the higher-order terms of the Floquet-Magnus expansion,<br /> we find that it is, at least asymptotically, convergent and well approximates<br /> the relaxation to their prethermal or non-equilibrium steady states. To support<br /> these analytical findings, we numerically analyze two examples: (i) the Kapitza<br /> pendulum with friction and (ii) laser-driven magnets described by the<br /> stochastic Landau-Lifshitz-Gilbert equation. In both cases, the effective EOMs<br /> obtained from their Floquet-Magnus expansions correctly reproduce their exact<br /> time evolution for a long time up to their non-equilibrium steady states. In<br /> the example of driven magnets, we demonstrate the controlled generations of a<br /> macroscopic magnetization and a spin chirality by laser and discuss possible<br /> applications to spintronics.

Magnetic oscillation is a generic property of electronic conductors under<br /> magnetic fields and widely appreciated as a useful probe of their electronic<br /> band structure, i.e., the Fermi surface geometry. However, the usage of the<br /> strong static magnetic field makes the measurement insensitive to the magnetic<br /> order of the target material. That is, the magnetic order is anyhow turned into<br /> a forced ferromagnetic one. Here we theoretically propose an experimental<br /> method of measuring the magnetic oscillation in a magnetic-order-resolved way<br /> by using the azimuthal cylindrical vector (CV) beam, an example of topological<br /> lightwaves. The azimuthal CV beam is unique in that when focused tightly, it<br /> develops a pure longitudinal magnetic field. We argue that this characteristic<br /> focusing property and the discrepancy in the relaxation timescale between<br /> conduction electrons and localized magnetic moments allow us to develop the<br /> nonequilibrium analog of the magnetic oscillation measurement. Our optical<br /> method would be also applicable to metals the under ultra-high pressure of<br /> diamond anvil cells.

Edge/surface states often appear in a topologically nontrivial phase when the system has a boundary. The edge state of a one-dimensional topological insulator is one of the simplest examples. Electron spin resonance ( ESR) is an ideal probe to detect and analyze the edge state for its high sensitivity and precision. We consider ESR of the edge state of a generalized Su-Schrieffer-Heeger model with a next-nearest-neighbor (NNN) hopping and a staggered spin-orbit coupling. The spin-orbit coupling is generally expected to bring about nontrivial changes on the ESR spectrum. Nevertheless, in the absence of the NNN hoppings, we find that the ESR spectrum is unaffected by the spin-orbit coupling thanks to the chiral symmetry. In the presence of both the NNN hopping and the spin-orbit coupling, on the other hand, the edge ESR spectrum exhibits a nontrivial frequency shift. We derive an explicit analytical formula for the ESR shift in the second-order perturbation theory, which agrees very well with a nonperturbative numerical calculation.

Breaking the diffraction limit and focusing laser beams to subwavelength scale are becoming possible with the help of recent developments in plasmonics. Such subwavelength focusing bridges different length scales of laser beams and matter. Here we consider optical vortex, or laser beam carrying orbital angular momentum (OAM), and discuss potential subwavelength magnetic phenomena induced by such laser. On the basis of numerical calculations using Landau-Lifshitz-Gilbert equation, we propose two OAM-dependent phenomena induced by optical vortices, generation of radially anisotropic spin waves and generation of topological defects in chiral magnets. The former could lead to the transient topological Hall effect through the laser-induced scalar spin chirality, and the latter reduces the time scale of generating skyrmionic defects by several orders compared to other known means.

We have investigated the longitudinal thermal conductivity of<br /> $\alpha$-RuCl$_{3}$, the magnetic state of which is considered to be proximate<br /> to a Kitaev honeycomb model, along with the spin susceptibility and magnetic<br /> specific heat. We found that the temperature dependence of the thermal<br /> conductivity exhibits an additional peak around 100 K, which is well above the<br /> phonon peak temperature ($\sim$ 50 K). The higher-temperature peak position is<br /> comparable to the temperature scale of the Kitaev couplings rather than the<br /> N\&#039;eel temperatures below 15 K. The additional heat conduction was observed for<br /> all five samples used in this study, and was found to be rather immune to a<br /> structural phase transition of $\alpha$-RuCl$_{3}$, which suggests its<br /> different origin from phonons. Combined with experimental results of the<br /> magnetic specific heat, our transport measurement suggests strongly that the<br /> higher-temperature peak in the thermal conductivity is attributed to itinerant<br /> spin excitations associated with the Kitaev couplings of $\alpha$-RuCl$_{3}$. A<br /> kinetic approximation of the magnetic thermal conductivity yields a mean free<br /> path of $\sim$ 20 nm at 100 K, which is well longer than the nearest Ru-Ru<br /> distance ($\sim$ 3 \AA), suggesting the long-distance coherent propagation of<br /> magnetic excitations driven by the Kitaev couplings.

Controlling electric and magnetic properties of matter by laser beams is actively explored in the broad region of condensed matter physics, including spintronics and magneto-optics. Here we theoretically propose an application of optical and electron vortex beams carrying intrinsic orbital angular momentum to chiral ferro- and antiferromagnets. We analyze the time evolution of spins in chiral magnets under irradiation of vortex beams by using the stochastic Landau-Lifshitz-Gilbert equation. We show that beam-driven nonuniform temperature leads to a class of ring-shaped magnetic defects, what we call skyrmion multiplex, as well as conventional skyrmions. We discuss the proper beam parameters and the optimal way of applying the beams for the creation of these topological defects. Our findings provide an ultrafast scheme of generating topological magnetic defects in a way applicable to both metallic and insulating chiral (anti-) ferromagnets.

Spin liquid is a state of electron spins in which quantum fluctuation breaks<br /> magnetic ordering while maintaining spin correlation. It has been a central<br /> topic in magnetism because of its relevance to high-Tc superconductivity and<br /> topological states. However, utilizing spin liquid has been quite difficult.<br /> Typical spin liquid states are realized in one-dimensional spin systems, called<br /> quantum spin chains. Here, we show that a spin liquid in a spin-1/2 quantum<br /> chain generates and carries spin current via its long-range spin fluctuation.<br /> This is demonstrated by observing an anisotropic negative spin Seebeck effect<br /> along the spin chains in Sr2CuO3. The results show that spin current can flow<br /> even in an atomic channel owing the spin liquid state, which can be used for<br /> atomic spin-current wiring.

We propose an ultrafast way to generate spin chirality and spin current in a class of multiferroic magnets using a terahertz circularly polarized laser. Using the Floquet formalism for periodically driven systems, we show that it is possible to dynamically control the Dzyaloshinskii-Moriya interaction in materials with magnetoelectric coupling. This is supported by numerical calculations, by which additional resonant phenomena are found. Specifically, when a static magnetic field is applied in addition to the circularly polarized laser, a large resonant enhancement of spin chirality is observed resembling the electron spin resonance. Spin current is generated when the laser is spatially modulated by chiral plasmonic structures and could be detected using optospintronic devices.

We study the boundary nature of trapped bosonic Mott insulators in optical<br /> square lattices, by performing quantum Monte Carlo simulation. We show that a<br /> finite superfluid density generally emerges in the incommensurate-filling (IC)<br /> boundary region around the bulk Mott state, irrespectively of the width of the<br /> IC region. Both off-diagonal and density correlation functions in the IC<br /> boundary region exhibit a nearly power-law decay. The power-law behavior and<br /> superfluidity are well developed below a characteristic temperature. These<br /> results indicate that a gapless boundary mode always emerges in any atomic Mott<br /> insulators on optical lattices. This further implies that if we consider a<br /> topological insulating state in Bose or Fermi atomic systems, its boundary<br /> possesses at least two gapless modes (or coupled modes) of an above IC edge<br /> state and the intrinsic topologically-protected edge state.

We discuss universal features on the electron spin resonance (ESR) of a temperature-induced Tomonaga-Luttinger liquid phase in a wide class of weakly coupled S = 1/2 antiferromagnetic spin chains such as spin ladders, spin tubes and three-dimensionally coupled spin chains. We show that the ESR linewidth of various coupled chains increases with lowering temperature while the linewidth of a single spin chain is typically proportional to temperature. This broadening with lowering temperature is attributed to anisotropic interchain interactions and has been indeed observed in several kinds of three-dimensional (3D) magnets of weakly coupled spin chains above the 3D ordering temperature. We demonstrate that our theory can account for anomalous behaviors of the linewidths in an S = 1/2 four-leg spin tube compound Cu2Cl4 center dot H8C4SO2 (abbreviated to Sul-Cu2Cl4) and a three-dimensionally coupled S = 1/2 spin chain compound CuCl2 center dot 2NC(5)H(5).

We propose an all optical ultrafast method to highly magnetize general quantum magnets using a circularly polarized terahertz laser. The key idea is to utilize a circularly polarized laser and its chirping. Through this method, one can obtain magnetization curves of a broad class of quantum magnets as a function of time even without any static magnetic field. We numerically demonstrate the laser-induced magnetization process in realistic quantum spin models and find a condition for the realization. The onset of magnetization can be described by a many-body version of Landau-Zener mechanism. In a particular model, we show that a plateau state with topological properties can be realized dynamically.

We propose an all optical ultrafast method to highly magnetize general quantum magnets using a circularly polarized terahertz laser. The key idea is to utilize a circularly polarized laser and its chirping. Through this method, one can obtain magnetization curves of a broad class of quantum magnets as a function of time even without any static magnetic field. We numerically demonstrate the laser-induced magnetization process in realistic quantum spin models and find a condition for the realization. The onset of magnetization can be described by a many-body version of Landau-Zener mechanism. In a particular model, we show that a plateau state with topological properties can be realized dynamically.

We theoretically study laser driven nonequilibrium states in the Kitaev<br /> honeycomb model with a magnetoelectric cross coupling. We show that a<br /> topological spin liquid with a gapless chiral edge mode emerges when we apply<br /> an elliptically or circularly polarized laser. This is a strongly correlated<br /> quantum spin version of the Floquet topological insulator. In the topological<br /> phase, the edge mode is made from Majorana fermions and the bulk has gapped<br /> non-Abelian anyon excitations.

We study quantum phase transitions in the 1/3 plateau state of the three-leg spin-1/2 tube, where the low-energy effective chirality degree of freedom plays an essential role. Using the density matrix renormalization group and the effective chirality model, we find that, as the leg coupling increases, the chirality liquid, a novel spin imbalance phase and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. We also clarify the role of the S (3)-symmetry of the spin tube, behind these quantum phase transitions.

It is known that there is no phase transition down to zero temperature in the antiferromagnetic Ising model on spatially anisotropic triangular lattices, in which the exchange coupling of one direction is stronger than those of other two directions. In the model, the low-temperature physics is governed by domain-wall excitations (defects) residing on bonds of the strong-coupling direction. In this letter, we show that an additional small attractive interaction between defects (a ferromagnetic next-nearest-neighbor interaction in the weak-coupling direction) leads to a Berezinskii-Kosterlitz-Thouless (BKT) transition at a finite temperature, by performing the Monte Carlo simulation. The BKT phase can be viewed as the phase with a quasi long-range order of defects. We determine the phase diagram in a wide parameter regime and argue the phase structure from statistical-mechanics and field-theory viewpoints.

We develop a microscopic theory of finite-temperature spin-nematic orderings in three-dimensional spatially anisotropic magnets consisting of weakly coupled frustrated spin-1/2 chains with nearest-neighbor and next-nearest-neighbor couplings in a magnetic field. Combining a field theoretical technique with density-matrix renormalization group results, we complete finite-temperature phase diagrams in a wide magnetic-field range that possess spin-bond-nematic and incommensurate spin-density-wave ordered phases. The effects of a four-spin interaction are also studied. The relevance of our results to quasi-one-dimensional edge-shared cuprate magnets such as LiCuVO4 is discussed. DOI: 10.1103/PhysRevLett.110.077206

We study the nature of edge states in extrinsically and spontaneously dimerized states of two-dimensional spin-1/2 antiferromagnets, by performing quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the wide region of the dimerized phases, and the critical exponent of spin correlators along the edge deviates from the value of Tomonaga-Luttinger liquid (TLL) universality in large but finite systems at low temperatures. We also demonstrate that the gapless nature at edges is stable against several perturbations such as external magnetic field, easy-plane XXZ anisotropy, Dzyaloshinskii-Moriya interaction, and further-neighbor exchange interactions. The edge states exhibit non-TLL behavior, depending strongly on model parameters and kinds of perturbations. Possible ways of detecting these edge states are discussed. Properties of edge states we show in this paper could also be used as reference points to study other edge states of more exotic gapped magnetic phases such as spin liquids. DOI: 10.1103/PhysRevB.86.224411

We study theoretically the Raman-scattering spectra in the one-dimensional (1D) quantum spin-1/2 antiferromagnets. The analysis reveals that their low-energy dynamics is exquisitely sensitive to various perturbations to the Heisenberg chain with nearest-neighbor exchange interactions, such as magnetic anisotropy, longer-range exchange interactions, and bond dimerization. These weak interactions are mainly responsible for the Raman scattering and give rise to different types of spectra as functions of frequency, temperature, and external field. In contrast to the Raman spectra in higher dimensions in which the two-magnon process is dominant, those in 1D antiferromagnets provide much richer information on these perturbations.

We study the magnetization plateau state of the three-leg spin-1/2 tube in the strong rung coupling region, where S-3 symmetry breaking and the low-energy chirality degree of freedom play crucial roles. On the basis of the effective chirality model and density matrix renormalization group, we clarify that, as the leg coupling increases, the chirality liquid with gapless nonmagnetic excitations, the spin-imbalance phase, and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. The relevance of these results to experiments is also discussed.

Recently some quantum spin systems on tube lattices, so called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As the first step of theoretical study on the spin nanotube, we investigate the S=1/2 three-leg spin tube, which is the simplest one, using the numerical exact diagonalization and the finite-size scaling analysis. In our previous works the quantum phase transition between the spin-gap and gapless phases was revealed to occur due to the asymmetric lattice distortion. In addition the transition between the magnetization plateau and gapless phases at 1/3 of the saturation magnetization induced by the same distortion. Recently we found that the Tomonaga-Luttinger liquid is realized in the 1/3 magnetization plateau phase for the symmetric three-leg spin tube.

The ground-state phase diagram of a spin-1/2 XXZ chain with competing<br /> ferromagnetic nearest-neighbor (J_1&lt;0) and antiferromagnetic second-neighbor<br /> (J_2&gt;0) exchange couplings is studied by means of the infinite time evolving<br /> block decimation algorithm and effective field theories. For the<br /> SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the<br /> range -4&lt;J_1/J_2&lt;0 has a small but finite ferromagnetic dimer order. We argue<br /> that this spontaneous dimer order is associated with effective spin-1 degrees<br /> of freedom on dimerized bonds, which collectively form a valence bond solid<br /> state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin<br /> chain). We thus call this phase the Haldane dimer phase. With easy-plane<br /> anisotropy, the model exhibits a variety of phases including the vector chiral<br /> phase with gapless excitations and the even-parity dimer and Neel phases with<br /> gapped excitations, in addition to the Haldane dimer phase. Furthermore, we<br /> show the existence of gapped phases with coexisting orders in narrow regions<br /> that intervene between the gapless chiral phase and any one of Haldane dimer,<br /> even-parity dimer, and Neel phases. Possible implications for<br /> quasi-one-dimensional edge-sharing cuprates are discussed.

We summarize our theoretical findings on the ground-state phase diagram of<br /> the spin-1/2 XXZ chain having competing nearest-neighbor (J1) and<br /> antiferromagnetic next-nearest-neighbor (J2) couplings. Our study is mainly<br /> concerned with the case of ferromagnetic J1, and the case of antiferromagnetic<br /> J1 is briefly reviewed for comparison. The phase diagram contains a rich<br /> variety of phases in the plane of J1/J2 versus the XXZ anisotropy Delta:<br /> vector-chiral phases, N\&#039;eel phases, several dimer phases, and<br /> Tomonaga-Luttinger liquid phases. We discuss the vector-chiral order that<br /> appears for a remarkably wide parameter space, successive N\&#039;eel-dimer phase<br /> transitions, and an emergent nonlocal string order in a narrow region of<br /> ferromagnetic J1 side.

In the spin-1/2 frustrated chain with nearest-neighbor ferromagnetic exchange<br /> J1 and next-nearest-neighbor antiferromagnetic exchange J2 under magnetic<br /> field, magnetic multipolar-liquid (quadrupolar, octupolar, and hexadecapolar)<br /> phases are widely expanded from the saturation down to a low-field regime.<br /> Recently, we have clarified characteristic temperature and field dependence of<br /> the NMR relaxation rate 1/T_1 in the quadrupolar phase. In this paper, we<br /> examine those of 1/T_1 in the octupolar phase combining field theoretical<br /> method with numerical data. The relevance of the results to quasi<br /> one-dimensional J1-J2 magnets such as PbCuSO4(OH)2, Rb2Cu2Mo3O12 and Li2ZrCuO4<br /> is shortly discussed.

It is generally difficult to experimentally distinguish magnetic multipolar<br /> orders in spin systems. Recently, it was proposed that the temperature<br /> dependence of the nuclear magnetic resonance relaxation rate 1/T_1 can involve<br /> an indirect, but clear signature of the field-induced spin nematic or<br /> multipolar Tomonaga-Luttinger (TL) liquid phase [Phys. Rev. B79, 060406(R)<br /> (2009)]. In this paper, we evaluate accurately the field and temperature<br /> dependence of 1/T_1 in spin-1/2 frustrated J1-J2 chains combining<br /> field-theoretical techniques with numerical data. Our results demonstrate that<br /> isotherms of 1/T_1 as a function of magnetic field also exhibit distinctive<br /> non-monotonic behavior in spin nematic TL liquid, in contrast with the standard<br /> TL liquid in the spin-1/2 Heisenberg chain. The relevance of our results to<br /> quasi one-dimensional edge-sharing cuprate magnets, such as LiCuVO4, is<br /> discussed.

Comparing numerically evaluated excitation gaps of dimerized spin- 1 2 XXZ chains with the gap formula for the low-energy effective sine-Gordon theory, we determine coefficients dxy and dz of bosonized dimerization operators in spin- 1 2 XXZ chains, which are defined as ⊃( ⊃-1 ⊃) j (Sjx S j+1 x + Sjy S j+1 y) = dxy sin [√ 4π (x)] + and ⊃( ⊃-1 ⊃) j Sjz S j+1 z = dz sin [√ 4π (x)] +. We also calculate the coefficients of both spin and dimer operators for the spin- 1 2 Heisenberg antiferromagnetic chain with a nearest-neighbor coupling J and a next-nearest-neighbor coupling J2 =0.2411J. As applications of these coefficients, we present ground-state phase diagrams of dimerized spin chains in a magnetic field and antiferromagnetic spin ladders with a four-spin interaction. The optical conductivity and electric polarization of one-dimensional Mott insulators with Peierls instability are also evaluated quantitatively. © 2010 The American Physical Society.

Comparing numerically evaluated excitation gaps of dimerized spin-1/2 XXZ chains with the gap formula for the low-energy effective sine-Gordon theory, we determine coefficients d(xy) and d(z) of bosonized dimerization operators in spin-1/2 XXZ chains, which are defined as (-1)(j)((SjSj+1x)-S-x + (SjSj+1y)-S-y) = d(xy) sin[root 4 pi phi(x)]+ ... and (-1)(SjSj+1z)-S-j-S-z = d(z) sin[root 4 pi phi(x)]+ ... . We also calculate the coefficients of both spin and dimer operators for the spin-1/2 Heisenberg antiferromagnetic chain with a nearest-neighbor coupling J and a next-nearest-neighbor coupling J(2)=0.2411J. As applications of these coefficients, we present ground-state phase diagrams of dimerized spin chains in a magnetic field and antiferromagnetic spin ladders with a four-spin interaction. The optical conductivity and electric polarization of one-dimensional Mott insulators with Peierls instability are also evaluated quantitatively.

Recent developments of theoretical studies on spin nanotubes are reviewed, especially focusing on the S = 1/2 three-leg spin tube. In contrast to the three-leg spin ladder, the tube has a spin gap in the case of the regular-triangle unit cell when the rung interaction is sufficiently large. The effective theory based on the Hubbard Hamiltonian indicates a quantum phase transition to a gapless spin liquid due to the lattice distortion to an isosceles triangle. This is also supported by the numerical diagonalization and the density matrix renormalization group analyses. Furthermore, combining analytical and numerical approaches, we reveal several novel magnetic-field-induced phenomena: Néel, dimer, chiral and/or inhomogeneous orders, a new mechanism for the magnetization plateau formation, and others. The recently synthesized spin tube materials are also briefly introduced. © 2010 IOP Publishing Ltd.