Critical Spontaneous Breaking of U(1) Symmetry at Zero Temperature in One Dimension.

The Hohenberg-Mermin-Wagner theorem states that there is no spontaneous breaking of continuous internal symmetries in spatial dimensions d≤2 at finite temperature. At zero temperature, the quantum-to-classical mapping further implies the absence of such symmetry breaking in one dimension, which is also known as Coleman's theorem in the context of relativistic quantum field theories. One route to violate this "folklore" is requiring an order parameter to commute with a Hamiltonian, as in the classic example of the Heisenberg ferromagnet and its variations.

Rigorous Results on the Ground State of the Attractive SU(N) Hubbard Model.

We study the attractive SU(N) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites N_{A} (N_{B}) in the A (B) sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU(N) quantum number.

Onsager's Scars in Disordered Spin Chains.

We propose a class of nonintegrable quantum spin chains that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct scarred models for arbitrary spin quantum number S. There are two types of scar states, namely, coherent states associated with an Onsager-algebra element and one-magnon scar states.

Transforming generalized Ising models into Boltzmann machines.

We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local external fields.

Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model.

We present rigorous and universal results for the ground states of the f=2 spinor Bose-Hubbard model. The model includes three two-body on-site interaction terms, two of which are spin dependent while the other one is spin independent. We prove that, depending only on the coefficients of the two spin-dependent terms, the ground state exhibits maximum or minimum total spin or SU(5) ferromagnetism.

Ground-state energies of spinless free fermions and hard-core bosons.

We compare the ground-state energies of bosons and fermions with the same form of the Hamiltonian. If both are noninteracting, the ground-state energy of bosons is always lower, owing to Bose-Einstein condensation. However, the comparison is nontrivial when bosons do interact.

Ground states of the spin-1 Bose-Hubbard model.

We prove basic theorems about the ground states of the S=1 Bose-Hubbard model. The results are quite universal and depend only on the coefficient U2 of the spin-dependent interaction. We show that the ground state exhibits saturated ferromagnetism if U2<0, is spin-singlet if U2>0, and exhibits "SU(3)-ferromagnetism" if U2=0, and completely determine the degeneracy in each region.

Theory of Raman scattering in one-dimensional quantum spin-1/2 antiferromagnets.

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.

General relationship between the entanglement spectrum and the edge state spectrum of topological quantum states.

We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional conformal field theory, such as, e.g., a general quantum Hall state.

Nearly flatbands with nontrivial topology.

We report the theoretical discovery of a class of 2D tight-binding models containing nearly flatbands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Because of the similarity with 2D continuum Landau levels, these topologically nontrivial nearly flatbands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials.

Localization and fractality in inhomogeneous quantum walks with self-duality.

We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The models are shown to be self-dual with respect to the Fourier transform, which is analogous to the Aubry-André model describing the one-dimensional tight-binding model with a quasiperiodic potential.

Theory of the thermal Hall effect in quantum magnets.

We present a theory of the thermal Hall effect in insulating quantum magnets, where the heat current is totally carried by charge-neutral objects such as magnons and spinons. Two distinct types of thermal Hall responses are identified. For ordered magnets, the intrinsic thermal Hall effect for magnons arises when certain conditions are satisfied for the lattice geometry and the underlying magnetic order.

Theory of the optical conductivity of spin liquid states in one-dimensional Mott insulators.

The low-energy dynamical optical response of dimerized and undimerized spin liquid states in a one-dimensional charge transfer Mott insulator is theoretically studied. An exact analysis is given for the low-energy asymptotic behavior using conformal field theory for the undimerized state. In the dimerized state, the infrared absorption due to the bound state of two solitons, i.

Quantum spin Hall effect in a transition metal oxide Na2IrO3.

We study theoretically the electronic states in a 5d transition metal oxide Na2IrO3, in which both the spin-orbit interaction and the electron correlation play crucial roles. A tight-binding model analysis together with the first-principles band structure calculation predicts that this material is a layered quantum spin Hall system. Because of the electron correlation, an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures.

Quantum theory of multiferroic helimagnets: collinear and helical phases.

We study the quantum fluctuation in the cycloidal helical magnet in terms of the Schwinger boson approach. In sharp contrast to the classical fluctuation, the quantum fluctuation is collinear in nature which gives rise to the collinear spin density wave state slightly above the helical cycloidal state as the temperature is lowered. Physical properties such as the reduced elliptic ratio of the spiral, the neutron scattering and infrared absorption spectra are discussed from this viewpoint with the possible relevance to the quasi-one dimensional LiCu2O2 and LiCuVO4.

Dynamical magnetoelectric coupling in helical magnets.

We develop a theory of collective mode dynamics in the helical magnets coupled to electric polarization via spin-orbit interaction. The low-lying modes associated with the ferroelectricity are not the transverse optical phonons, but are the spin waves hybridized with the electric polarization. This hybridization leads to the Drude-like dielectric function epsilon(omega) in the limit of zero magnetic anisotropy.

Electron localization or delocalization in incommensurate helical magnets.

The electronic states in incommensurate helical magnets are studied theoretically from the viewpoint of the localization or delocalization. It is found that in the multiband system with a relativistic spin-orbit interaction, the electronic wave functions show both an extended and localized nature along the helical axis depending on the orbital, helical wave number, and the direction of the plane on which spins rotate. The possible realization of this localization is discussed.

Spin current and magnetoelectric effect in noncollinear magnets.

A new mechanism of the magnetoelectric effect based on the spin supercurrent is theoretically presented in terms of a microscopic electronic model for noncollinear magnets. The electric polarization P(ij) produced between the two magnetic moments S(i) and S(j) is given by P proportional e(ij) X (S(i) X S(j)) with e(ij) being the unit vector connecting the sites i and j. Applications to the spiral spin structure and the gauge theoretical interpretation are discussed.