Keisuke Totsuka

Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at halffilling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p-band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2I?+?1) symmetry which depend only on the nuclear-spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I(=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2I?+?1) symmetry.

Anomalous Magnetization of Two-Dimensional S ¼ 1=2 Frustrated Square-Lattice Antiferromagnet (CuCl)LaNb2O7

High-field magnetization measurements have been performed up to 56 T for a two-dimensional S = 1/2 frustrated square-lattice antiferromagnet (CuCl)LaNb 2 O 7 , a recently discovered spin gap system (Δ/ k B = 26.7 K). It is found that the spin gap closes at a surprisingly low field H c1 = 10.3 T compared with that expected from the zero-field spin gap (Δ/ g µ B = 18.4 T). For H > H c1 , the magnetization exhibits a linear increase without any trace of anomalies such as fractional plateaus until it saturates at H c2 = 30.1 T. This means that the gapless phase, where the field-induced magnetic ordering is expected to occur at low temperatures, is stable over a wide field region. These results suggest strong correlations of triplet excitations in the layer and the proximity of the spin-liquid phase to the magnetically ordered phase.

Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases

Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N)-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry- protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of this multicomponent Fermi gas turns out to be much richer and more exotic than in the standard SU(2) case. For N > 2, the phase diagram is quite rich already in the case of the single-band model, including a molecular Luttinger liquid (with dominant superfluid instability in the N-particle channel) for incommensurate fillings, as well as various Mott-insulating phases occurring at commensurate fillings. Particular attention will be paid to the cases with additional orbital degree of freedom (which is accessible experimentally either by taking into account two atomic states or by putting atoms in the p-band levels). We introduce two microscopic models which are relevant for these cases and discuss their symmetries and strong coupling limits. More intriguing phase diagrams are then presented including, for instance, symmetry protected topological phases characterized by non-trivial edge states.

Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermion systems

We investigate possible realizations of exotic SU(N) symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard SU(N) Fermi-Hubbard model, directly relevant to recent experiments, is performed. Using state-of-the-art analytical and numerical techniques, we map out the zero-temperature phase diagrams at half-filling and identify several Mott-insulating phases. While some of them are rather conventional (nondegenerate, charge-density wave, or spin-Peierls-like), we also identify, for even N, two distinct types of SPT phases: an orbital Haldane phase, analogous to a spin-N/2 Haldane phase, and a topological SU(N) phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the SU(N) topological phases found here.

Magnon Bose-Einstein condensation and various phases of three-dimensonal quantum helimagnets under high magnetic field

We study high-field phase diagram and low-energy excitation s f three-dimensional quantum helimagnets. Slightly below the saturation field, the emergence of magnet ic order may be viewed as Bose-Einstein condensation (BEC) of magnons. The method of dilute Bose gas enable s a quantitative analysis of quantum effects in these helimagnets and thereby three phases are found: con e, c planar fan and a phase-separated one. As an application, we map out the phase diagram of a 3D helimagnet w hich consists of frustrated J1-J2 chains as a function of frustration and an interchain coupling. Moreov r, we also calculate the stability of the 2-magnon bound state to investigate the possibility of the bound-mag non BEC.

Effect of Dzyaloshinskii-Moriya interactions on the phase diagram and magnetic excitations of SrCu2(BO3)2

The orthogonal dimer structure in the SrCu2(BO3)2 spin-1/2 magnet provides a realization of the Shastry-Sutherland model. Using a dimer-product variational wave function, we map out the phase diagram of the Shastry-Sutherland model including anisotropies. Based on the variational solution, we construct a bond-wave approach to obtain the excitation spectra as a function of magnetic field. The characteristic features of the experimentally measured neutron and ESR spectra are reproduced, like the anisotropy induced zero field splittings and the persistent gap at higher fields.

Quantum entanglement and topological order in hole-doped valence bond solid states

We present a detailed analysis of topological properties of the valence bond solid (VBS) states doped with fermionic holes. As concrete examples, we consider the supersymmetric extension of the SU(2)- and the SO(5) VBS states, dubbed UOSp(1|2) and UOSp(1|4) supersymmetric VBS states, respectively. Specifically, we investigate the string-order parameters and the entanglement spectra of these states to find that, even when the parent states (bosonic VBS states) do not support the string order, they recover it when holes are doped and the fermionic sector appears in the entanglement spectrum. These peculiar properties are discussed in light of the symmetry-protected topological order. To this end, we characterize a few typical classes of symmetry-protected topological orders in terms of supermatrix-product states (SMPS). From this, we see that the topological order in the bulk manifests itself in the transformation properties of the SMPS in question and thereby affects the structure of the entanglement spectrum. Then, we explicitly relate the existence of the string order and the structure of the entanglement spectrum to explain the recovery and the stabilization of the string order in the supersymmetric systems.

Phases of the generalized two-leg spin ladder : A view from the SU(4) symmetry

The zero-temperature phases of a generalized two-leg spin ladder with four-spin exchanges are discussed by means of a low-energy field theory approach starting from an SU(4) quantum critical point. The latter fixed point is shown to be a rich multicritical point that unifies different competing dimerized orders and a scalar chirality phase that breaks spontaneously the time-reversal symmetry. The quantum phase transition between these phases is dominated by spin-singlet fluctuations and belongs to the Luttinger universality class due to the existence of a

Magnetization plateaus of an easy-axis kagome antiferromagnet with extended interactions

\mathrm{U}(1)

Symmetry-protected topological order in magnetization plateau states of quantum spin chains

self-duality symmetry.