Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries.

We study quantum many-body systems in the presence of an exotic antiunitary translation or inversion symmetry involving time reversal. Based on a symmetry-twisting method and spectrum robustness, we propose that a half-integer spin chain that respects any of these two antiunitary crystalline symmetries in addition to the discrete Z_{2}×Z_{2} global spin-rotation symmetry must either be gapless or possess degenerate ground states. This explains the gaplessness of a class of chiral spin models not indicated by the Lieb-Schultz-Mattis theorem and its known extensions.

Quasi-Periodic Growth of One-Dimensional Copper Boride on Cu(110).

An unexplored material of copper boride has been realized recently in two-dimensional form at a (111) surface of the copper crystal. Here, one-dimensional (1-D) boron growth was observed on the Cu(110) surface, as probed by atomically resolved scanning probe microscopy. The 1-D copper boride was composed of quasi-periodic atomic chains periodically aligned parallel to each other, as confirmed by Fourier transform analysis.

Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions.

Dissipative quantum phase transition has been widely believed to occur in a Josephson junction coupled to a resistor despite a lack of concrete experimental evidence. Here, on the basis of both numerical and analytical nonperturbative renormalization group analyses, we reveal breakdown of previous perturbative arguments and defy the common wisdom that the transition always occurs at the quantum resistance R_{Q}=h/(4e^{2}). We find that renormalization group flows in nonperturbative regimes induce nonmonotonic renormalization of the charging energy and lead to a qualitatively different phase diagram, where the insulator phase is strongly suppressed to the deep charge regime (Cooper pair box), while the system is always superconducting in the transmon regime.

Gappability Index for Quantum Many-Body Systems.

We propose an index I_{G} which characterizes the degree of gappability, namely the difficulty to induce a unique ground state with a nonvanishing excitation gap, in the presence of a symmetry G. I_{G} represents the dimension of the subspace of ambient uniquely gapped theories in the entire G-invariant "theory space." The celebrated Lieb-Schultz-Mattis theorem corresponds, in our formulation, to the case I_{G}=0 (completely ingappable) for the symmetry G including the lattice translation symmetry.

Twisted Boundary Condition and Lieb-Schultz-Mattis Ingappability for Discrete Symmetries.

We discuss quantum many-body systems with lattice translation and discrete on-site symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell forms a projective representation of the on-site discrete symmetry. Based on the quantum transfer matrix formalism, we show that, if the system is gapped, the ground-state degeneracy under the twisted boundary condition also implies a ground-state (quasi)degeneracy under the periodic boundary conditions.

Non-Fermi Liquids in Conducting Two-Dimensional Networks.

We explore the physics of novel fermion liquids emerging from conducting networks, where 1D metallic wires form a periodic 2D superstructure. Such structure naturally appears in marginally twisted bilayer graphenes, moire transition metal dichalcogenides, and also in some charge-density wave materials. For these network systems, we theoretically show that a remarkably wide variety of new non-Fermi liquids emerge and that these non-Fermi liquids can be classified by the characteristics of the junctions in networks.

Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks.

We propose a new principle to realize flatbands which are robust in real materials, based on a network superstructure of one-dimensional segments. This mechanism is naturally realized in the nearly commensurate charge-density wave of 1T-TaS_{2} with the honeycomb network of conducting domain walls, and the resulting flatband can naturally explain the enhanced superconductivity. We also show that corner states, which are a hallmark of the higher-order topological insulators, appear in the network superstructure.

Anomaly Matching and Symmetry-Protected Critical Phases in SU(N) Spin Systems in 1+1 Dimensions.

We study (1+1)-dimensional SU(N) spin systems in the presence of global SU(N) rotation and lattice translation symmetries. Knowing the mixed anomaly of the two symmetries at low energy, we identify, by the anomaly matching argument, a topological index for the spin model-the total number of Young-tableau boxes of spins per unit cell modulo N-characterizing the "ingappability" of the system. A nontrivial index implies either a ground-state degeneracy in a gapped phase, which can be thought of as a field-theory version of the Lieb-Schultz-Mattis theorem, or a restriction of the possible universality classes in a critical phase, regarded as the symmetry-protected critical phases.

Emergent SU(4) Symmetry in α-ZrCl_{3} and Crystalline Spin-Orbital Liquids.

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets.

Designing Kitaev Spin Liquids in Metal-Organic Frameworks.

Kitaev's honeycomb lattice spin model is a remarkable exactly solvable model, which has a particular type of spin liquid (Kitaev spin liquid) as the ground state. Although its possible realization in iridates and α-RuCl_{3} has been vigorously discussed recently, these materials have substantial non-Kitaev direct exchange interactions and do not have a spin liquid ground state. We propose metal-organic frameworks (MOFs) with Ru^{3+} (or Os^{3+}), forming the honeycomb lattice as promising candidates for a more ideal realization of Kitaev-type spin models, where the direct exchange interaction is strongly suppressed.

Symmetry Protection of Critical Phases and a Global Anomaly in 1+1 Dimensions.

We derive a selection rule among the (1+1)-dimensional SU(2) Wess-Zumino-Witten theories, based on the global anomaly of the discrete Z_{2} symmetry found by Gepner and Witten. In the presence of both the SU(2) and Z_{2} symmetries, a renormalization-group flow is possible between level-k and level-k^{'} Wess-Zumino-Witten theories only if k≡k^{'} mod 2 . This classifies the Lorentz-invariant, SU(2)-symmetric critical behavior into two "symmetry-protected" categories corresponding to even and odd levels, restricting possible gapless critical behavior of translation-invariant quantum spin chains.

Absence of Quantum Time Crystals.

In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and vigorous debates whether it can be realized in a physical system. However, a precise definition of the time crystal is needed to resolve the issue.

Orbital angular momentum and spectral flow in two-dimensional chiral superfluids.

We study the orbital angular momentum (OAM) L_{z} in two-dimensional chiral (p_{x}+ip_{y})^{ν}-wave superfluids (SFs) of N fermions on a disk at zero temperature, in terms of spectral asymmetry and spectral flow. It is shown that L_{z}=νN/2 for any integer ν, in the Bose-Einstein condensation regime. In contrast, in the BCS limit, while the OAM is L_{z}=N/2 for the p+ip-wave SF, for chiral SFs with ν≥2, the OAM is remarkably suppressed as L_{z}=N×O(Δ_{0}/ϵ_{F})≪N, where Δ_{0} is the gap amplitude and ϵ_{F} is the Fermi energy.

Distinct trivial phases protected by a point-group symmetry in quantum spin chains.

The ground state of the S=1 antiferromagnetic Heisenberg chain belongs to the Haldane phase--a well-known example of the symmetry-protected topological phase. A staggered field applied to the S=1 antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state.

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.

Boundary resonances in S=1/2 antiferromagnetic chains under a staggered field.

We develop a boundary field theory approach to electron spin resonance in open S=1/2 Heisenberg antiferromagnetic chains with an effective staggered field. In terms of the sine Gordon effective field theory with boundaries, we point out the existence of boundary bound states of elementary excitations, and modification of the selection rules at the boundary. We argue that several "unknown modes" found in electron spin resonance experiments on KCuGaF(6) [I.

Instability in magnetic materials with a dynamical axion field.

It has been pointed out that axion electrodynamics exhibits instability in the presence of a background electric field. We show that the instability leads to a complete screening of an applied electric field above a certain critical value and the excess energy is converted into a magnetic field. We clarify the physical origin of the screening effect and discuss its possible experimental realization in magnetic materials where magnetic fluctuations play the role of the dynamical axion field.

Electron spin resonance shift in spin ladder compounds.

We analyze the effects of different coupling anisotropies in a spin-1/2 ladder on the electron spin resonance (ESR) shift. Combining a perturbative expression in the anisotropies with density matrix renormalization group computation of the short range correlations at finite temperature, we provide the full temperature and magnetic field evolution of the ESR paramagnetic shift. We show that for well chosen parameters the ESR shift can be in principle used to extract quantitatively the anisotropies and, as an example, discuss the material BPCB.

Dynamical theory of superfluidity in one dimension.

A theory accounting for the dynamical aspects of the superfluid response of one dimensional (1D) quantum fluids is reported. In long 1D systems, the onset of superfluidity is related to the dynamical suppression of quantum phase slips at low temperatures. The effect of this suppression as a function of frequency and temperature is discussed within the framework of the experimentally relevant momentum response function.

Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases.

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations.

Dynamics of one-dimensional Bose liquids: Andreev-like reflection at Y junctions and the absence of the Aharonov-Bohm effect.

We study one-dimensional Bose liquids of interacting ultracold atoms in the Y-shaped potential when each branch is filled with atoms. We find that the excitation packet incident on a single Y junction should experience a negative density reflection analogous to the Andreev reflection at normal-superconductor interfaces, although the present system does not contain fermions. In a ring-interferometer-type configuration, we find that the transport is completely insensitive to the (effective) flux contained in the ring, in contrast with the Aharonov-Bohm effect of a single particle in the same geometry.

Universal temperature dependence of the magnetization of gapped spin chains.

A Haldane chain under applied field is analyzed numerically, and a clear minimum of magnetization is observed as a function of temperature. We elucidate its origin using the effective theory near the critical field and propose a simple method to estimate the gap from the magnetization at finite temperatures. We also demonstrate that there exists a relation between the temperature dependence of the magnetization and the field dependence of the spin-wave velocity.

Stable Skyrmions in spinor condensates.

Globally symmetric spinor condensates in free space are argued not to support stable topological defects in either two or three dimensions. In the latter case, however, we show that a topological Skyrmion can be stabilized by forcing it to adopt certain density profiles. A sufficient condition for the existence of Skyrmion solutions in three dimensions is formulated and illustrated in simple examples.