Published papers

We investigated the magnetoelastic properties of the quasi-one-dimensional spin-12 frustrated magnet LiCuVO4. Longitudinal-magnetostriction experiments were performed at 1.5 K in high magnetic fields of up to 60 T applied along the b axis, i.e., the spin-chain direction. The magnetostriction data qualitatively resemble the magnetization results, and saturate at Hsat≈54 T, with a relative change in sample length of ΔL/L≈1.8×10-4. Remarkably, both the magnetostriction and the magnetization evolve gradually between Hc3≈48 T and Hsat, indicating that the two quantities consistently detect the spin-nematic phase just below the saturation. Numerical analyses for a weakly coupled spin-chain model reveal that the observed magnetostriction can overall be understood within an exchange-striction mechanism. Small deviations found may indicate nontrivial changes in local correlations associated with the field-induced phase transitions.

A spin-12 Heisenberg model with a chirality–chirality interaction (CCI) on a two-leg ladder provides a minimal setup to explore an interplay between spin and chirality degrees of freedom. This model is potentially relevant for understanding the effects of a four-spin ring exchange and a phonon-mediated interaction on a ladder. By applying the Abelian bosonization and two types of spin-chirality duality, we derive a comprehensive ground-state phase diagram that includes previously unexplored cases of a ferromagnetic rung exchange Jτ < 0 or a negative CCI Kch < 0. The phase diagram consists of the rung singlet (RS) phase, the Haldane phase, and three non-magnetic ordered phases. Moreover, the RS and Haldane phases consist of several regions with different dominant correlations in terms of spin, dimer, or chirality. We perform numerical simulations to confirm the predicted phase structure and critical properties.

We consider a system of two coupled Tomonaga-Luttinger liquids (TLL's) on parallel chains and study the Rényi entanglement entropy Sn between the two chains. Here the entanglement cut is introduced between the chains, not along the perpendicular direction, as has been done in previous studies of one-dimensional systems. The limit n→1 corresponds to the von Neumann entanglement entropy. The system is effectively described by two-component bosonic field theory with different TLL parameters in the symmetric and antisymmetric channels as far as the coupled system remains in a gapless phase. We argue that in this system, Sn is a linear function of the length of the chains (boundary law) followed by a universal subleading constant γn determined by the ratio of the two TLL parameters. The formulas of γn for integer n≥2 are derived using (a) ground-state wave functionals of TLL's and (b) boundary conformal field theory, which lead to the same result. These predictions are checked in a numerical diagonalization analysis of a hard-core bosonic model on a ladder. Although the analytic continuation of γn to n→1 turns out to be a difficult problem, our numerical result suggests that the subleading constant in the von Neumann entropy is also universal. Our results may provide useful characterization of inherently anisotropic quantum phases such as the sliding Luttinger liquid phase via qualitatively different behaviors of the entanglement entropy with the entanglement partitions along different directions. © 2011 American Physical Society.

A recent study has proposed a remarkable spin model for (CuCl)LaNb 2O7, in which dimers are ferromagnetically coupled to each other on the distorted Shastry-Sutherland lattice. In this model, the intradimer exchange coupling J>0 is antiferromagnetic, while the interdimer exchange couplings are ferromagnetic and take different values, J x,Jy<0, in the two bond directions. Anticipating that the highly frustrated character of this model may lead to a wide range of behaviors in (CuCl)LaNb2O7 and related compounds, we theoretically investigate the ground-state phase diagram of this model in detail using the following three approaches: a strong-coupling expansion for small Jx and Jy, exact diagonalization for finite clusters, and a Schwinger boson mean-field theory. When |Jx|,|Jy| J, the system stays in a dimer singlet phase with a finite spin gap. This state is adiabatically connected to the decoupled-dimer limit Jx=J y=0. We show that the magnetization process of this phase depends crucially on the spatial anisotropy of the interdimer couplings. The magnetization shows a jump or a smooth increase for weak and strong anisotropy, respectively, after the spin gap closes at a certain magnetic field. When |Jx| or |Jy| J, quantum phase transitions to various magnetically ordered phases (ferromagnetic, collinear stripe, and spiral) occur. The Schwinger boson analysis demonstrates that quantum fluctuations split the classical degeneracy of different spiral ground states. Implications for (CuCl)LaNb2O7 and related compounds are discussed in light of our theoretical results and existing experimental data. © 2011 American Physical Society.

The ground-state phase diagram of a spin-12 XXZ chain with competing ferromagnetic nearest-neighbor (J 1<0) and antiferromagnetic second-neighbor (J 20) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range -4

Using the inelastic neutron scattering technique, we measured the spin wave dispersion over the entire Brillouin zone of room temperature multiferroic BiFeO 3 single crystals with magnetic excitations extending to as high as 72.5meV. The full spin waves can be explained by a simple Heisenberg Hamiltonian with a nearest-neighbor exchange interaction (J=4.38meV), a next-nearest-neighbor exchange interaction (J'=0.15meV), and a Dzyaloshinskii-Moriya-like term (D=0.107meV). This simple Hamiltonian determined, for the first time, for BiFeO 3 provides a fundamental ingredient for understanding the novel magnetic properties of BiFeO 3. © 2012 American Physical Society.

A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the degenerate ground states without the aid of empirical knowledge, and thus opens a way to explore unknown exotic orders. The applicability of this method is demonstrated numerically or rigorously in models that are considered to exhibit dimer, scalar chiral, and topological orders. © 2006 The American Physical Society.

© 2014 American Physical Society. Low-energy magnon excitations in multiferroic BiFeO3 were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly associated with the interplay of the Dzyaloshinskii-Moriya interaction and a small single-ion anisotropy. The temperature dependence of these and the exchange interactions were determined by fitting the measured magnon dispersion with spin-wave calculations. The spectra best fit an easy-axis type magnetic anisotropy and the deduced exchange and anisotropy parameters enable us to determine the anharmonicity of the magnetic cycloid. We then draw a direct connection between the changes in the parameters of spin Hamiltonian with temperature and the physical properties and structural deformations of BiFeO3.

We study the ground-state phase diagram of a one-dimensional spin- 1/2 easy-plane XXZ model with a ferromagnetic nearest-neighbor (NN) coupling J 1 and a competing next-nearest-neighbor (NNN) antiferromagnetic coupling J2 in the parameter range 0< J2/ | J 1| <0.4. When J2 / | J1 | <1/4, the model is in a Tomonaga-Luttinger liquid phase which is adiabatically connected to the critical phase of the XXZ model of J2=0. On the basis of the effective (sine-Gordon) theory and numerical analyses of low-lying energy levels of finite-size systems, we show that the NNN coupling induces phase transitions from the Tomonaga-Luttinger liquid to gapped phases with either Néel or dimer order. Interestingly, these two types of ordered phases appear alternately as the easy-plane anisotropy is changed toward the isotropic limit. The appearance of the antiferromagnetic (Néel) order in this model is remarkable, as it is strongly unfavored by both the easy-plane ferromagnetic NN coupling and the antiferromagnetic NNN coupling in the classical-spin picture. We argue that emergent trimer degrees of freedom play a crucial role in the formation of the Néel order. © 2010 The American Physical Society.

We report the magnetic properties of powder samples of the two-leg-ladder antiferromagnet Cu(DEP)Cl2 (DEP: 2,3-diethylpyradine) measured in magnetic fields of up to 40 T under pressures (P) of up to 1.7 GPa. Measured magnetic properties (magnetic susceptibility and high-field magnetization with two transition fields) at ambient P are compared with those calculated by a quantum Monte Carlo method and are well explained by the two-leg-ladder antiferromagnetic model with large rung exchange interaction (Jrung). A peak of magnetic susceptibility shifts largely to a higher temperature with a significant decrease in height, and both transition fields shift largely to higher fields at a critical pressure Pc of approximately 0.2 GPa. The results of an evaluation of these exchange constants below and above Pc indicate that antiferromagnetic two-leg ladders (Jrung > Jleg) with a very weak Jint changed into strongly coupled (Jrung) antiferromagnetic dimers with weak Jleg and Jint

We show by unbiased numerical calculations that the ferromagnetic nearest-neighbor exchange interaction stabilizes a vector spin chiral order against the quantum fluctuation in a frustrated spin-12 chain relevant to multiferroic cuprates, LiCu2O2 and LiCuVO4. Our realistic semiclassical analyses for LiCu2O2 resolve controversies on the helical magnetic structure and unveil the pseudo-Nambu-Goldstone modes as the origin of experimentally observed electromagnons. © 2010 The American Physical Society.

We summarize our theoretical findings on the ground-state phase diagram of the spin-1/2 XXZ chain having competing nearest-neighbor (J1) and antiferromagnetic next-nearest-neighbor (J2) couplings. Our study is mainly concerned with the case of ferromagnetic J1, and the case of antiferromagnetic J1 is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J1/J 2 versus the XXZ anisotropy Δ: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga-Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J1 side. © 2011 World Scientific Publishing Company.

© 2020 The Author(s) Volborthite offers an interesting example of a highly frustrated quantum magnet in which ferromagnetic and antiferromagnetic interactions compete on anisotropic kagome lattices. A recent density functional theory calculation has provided a magnetic model based on coupled trimers, which is consistent with a broad 13-magnetization plateau observed experimentally. Here we study the effects of Dzyaloshinskii-Moriya (DM) interactions in volborthite. We derive an effective model in which pseudospin-12 moments emerging on trimers form a network of an anisotropic triangular lattice. Using the effective model, we show that for a magnetic field perpendicular to the kagome layer, magnon excitations from the 13-plateau feel a Berry curvature due to the DM interactions, giving rise to a thermal Hall effect. Our magnon Bose gas theory can explain qualitative features of the magnetization and the thermal Hall conductivity measured experimentally. A further quantitative comparison with experiment poses constraints on the coupling constants in the effective model, promoting a quasi-one-dimensional picture. Based on this picture, we analyze low-temperature magnetic phase diagrams using effective field theory, and point out their crucial dependence on the field direction.

We study the ground-state phase diagram of a spin-12 XXZ model with a chirality-chirality interaction (CCI) on a two-leg ladder. This model offers a minimal setup to study an interplay between spin and chirality degrees of freedom. The spin-chirality duality transformation allows us to relate the regimes of weak and strong CCIs. By applying the Abelian bosonization and the duality, we obtain a rich phase diagram that contains distinct gapped featureless and ordered phases. In particular, Néel and vector chiral orders appear for easy-axis anisotropy, while two distinct symmetry-protected topological (SPT) phases appear for easy-plane anisotropy. The two SPT phases can be viewed as twisted variants of the Haldane phase. We also present an effective description in terms of (spinor) hard-core bosons, which reveals critical behavior on the self-dual line in the easy-axis and easy-plane regimes. We perform numerical simulations to confirm the predicted phase structure and critical properties. We further demonstrate that the two SPT phases and a trivial phase are distinguished by topological indices in the presence of certain symmetries. A similar phase structure is expected in a spin-12 XXZ ladder with four-spin ring exchange.

Entanglement in quantum many-body systems can exhibit universal phenomena governed by long-distance properties. We study universality and phase transitions of the entanglement inherent to open many-body systems, namely, the entanglement between a system of interest and its environment. Specifically, we consider the Tomonaga-Luttinger liquid (TLL) under a local measurement and analyze its unconditioned nonunitary evolution, where the measurement outcomes are averaged over. We quantify the system-environment entanglement by the Rényi entropy of the post-measurement density matrix, whose size-independent term encodes the universal low-energy physics. We develop a field-theoretical description to relate the universal term to the effective ground-state degeneracy known as the g function in a boundary conformal field theory, and use the renormalization group method to determine its value. We show that the universal contribution is determined by the TLL parameter K and can exhibit singularity signifying an entanglement phase transition. Surprisingly, in certain cases the size-independent contribution can increase as a function of the measurement strength in contrast to what is naïvely expected from the g-theorem. We argue that this unconventional behavior could be attributed to the dangerously irrelevant term which has been found in studies of the resistively shunted Josephson junction. We also check these results by numerical calculations in the spin-12 XXZ chain subject to a site-resolved measurement. Possible experimental realization in ultracold gases, which requires no postselections, is discussed.

©2017 American Physical Society. Coarsening dynamics theory describes equilibration of a broad class of systems. By studying the relaxation of a periodic array of microcondensates immersed in a Fermi gas, which mediates long-range spin interactions to simulate frustrated classical magnets, we show that coarsening dynamics can be suppressed by geometrical frustration. The system is found to eventually approach a metastable state which is robust against random field noise and characterized by finite correlation lengths together with the emergence of topologically stable Z2 vortices. We find universal scaling laws with no thermal-equilibrium analog that relate the correlation lengths and the number of vortices to the degree of frustration in the system.

We study the entanglement entropy and spectrum between components in binary Bose-Einstein condensates in d spatial dimensions. We employ effective field theory to show that the entanglement spectrum exhibits an anomalous square-root dispersion relation in the presence of intercomponent tunneling (Rabi coupling) and a gapped dispersion relation in its absence. These spectral features are associated with the emergence of long-range interactions in terms of the superfluid velocity and the particle density in the entanglement Hamiltonian. Our results demonstrate that unusual long-range interactions can be emulated in a subsystem of multicomponent BECs that have only short-range interactions. We also find that for a finite Rabi coupling the entanglement entropy exhibits a volume-law scaling with subleading logarithmic corrections originating from the Nambu-Goldstone mode and the symmetry restoration for a finite volume.

We propose a new method based on reduced density matrices for determining order parameters of quantum spin systems. Our method can extract the order parameter directly from ground-state wave functions without prior knowledge, and thus has a potential for detecting unknown exotic orders. We numerically apply our method to the multiple-spin exchange model on the ladder and detect the staggered dimer and the scalar chiral orders which have been found in previous studies. We also consider the resonating valence bond liquid in a solvable quantum dimer model and demonstrate through reduced density matrices that its ground states cannot be characterized by any local order parameter.

Resonating valence bond (RVB) liquids in two dimensions are believed to exhibit topological order and to admit no local order parameter of any kind. This is a defining property of 'liquids', but it has been confirmed explicitly only in a few exactly solvable models. In this paper, we investigate the quantum dimer model on the triangular lattice. This possesses an RVB-type liquid phase, however, for which the absence of a local order parameter has not been proved. We examine the question numerically with a measure based on reduced density matrices. We find a scaling of the measure which strongly supports the absence of any local order parameter. © IOP Publishing Ltd.

We theoretically study one-dimensional spin-1/2 multiferroic systems. We focus on the chiral ordered phase with gapless excitations that appears under easy-plane anisotropy. The in-plane chirality dynamics contains gapless solitons associated with local flips of the chirality. These excitations contribute to the low-frequency dielectric response through the magnetoelectric coupling.