arXiv subjects

Haruki Watanabe

Publications and source records attributed to Haruki Watanabe.

At least 73 records · Page 4Linked to original sources

arXiv2018

Structure and Topology of Band Structures in the 1651 Magnetic Space Groups

The properties of electrons in magnetically ordered crystals are of interest both from the viewpoint of realizing novel topological phases, such as magnetic Weyl semimetals, and from the applications perspective of creating energy-efficient memories. A systematic study of symmetry and topology in magnetic materials has been challenging given that there are 1651 magnetic space groups (MSGs). Here, by using an efficient representation of allowed band structures, we obtain a systematic description of several basic properties of free electrons in all MSGs in three dimensions as well as in the 528 magnetic layer groups relevant to two dimensional magnetic materials. We compute constraints on electron fillings and band connectivity compatible with insulating behavior. Also, by contrasting with atomic insulators, we identify band topology entailed by the symmetry transformation of bands, as determined by the MSG alone. We give an application of our results to identifying topological semimetals arising in periodic arrangements of hedgehog-like magnetic textures.

cond-mat.str-el↗

arXiv2018

The Lieb-Schultz-Mattis-type filling constraints in the 1651 magnetic space groups

We present the first systematic study of the filling constraints to realize a `trivial' insulator symmetric under magnetic space group $\mathcal{M}$. The filling $ν$ must be an integer multiple of $m^{\mathcal{M}}$ to avoid spontaneous symmetry breaking or fractionalization in gapped phases. We improve the value of $m^{\mathcal{M}}$ in the literature and prove the tightness of the constraint for the majority of magnetic space groups. The result may shed light on the material search of exotic magnets with fractionalization.

cond-mat.str-el↗

arXiv2018

Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling

Understanding the interplay between the topological nature and the symmetry property of interacting systems has been a central matter of condensed matter physics in recent years. In this Letter, we establish nonperturbative constraints on the quantized Hall conductance of many-body systems with arbitrary interactions. Our results allow one to readily determine the many-body Chern number modulo a certain integer without performing any integrations, solely based on the rotation eigenvalues and the average particle density of the many-body ground state.

cond-mat.str-el↗

arXiv2017

Lattice Homotopy Constraints on Phases of Quantum Magnets

The Lieb-Schultz-Mattis (LSM) theorem and its extensions forbid trivial phases from arising in certain quantum magnets. Constraining infrared behavior with the ultraviolet data encoded in the microscopic lattice of spins, these theorems tie the absence of spontaneous symmetry breaking to the emergence of exotic phases like quantum spin liquids. In this work, we take a new topological perspective on these theorems, by arguing they originate from an obstruction to "trivializing" the lattice under smooth, symmetric deformations, which we call the "lattice homotopy problem." We conjecture that all LSM-like theorems for quantum magnets (many previously-unknown) can be understood from lattice homotopy, which automatically incorporates the full spatial symmetry group of the lattice, including all its point-group symmetries. One consequence is that any spin-symmetric magnet with a half-integer moment on a site with even-order rotational symmetry must be a spin liquid. To substantiate the claim, we prove the conjecture in two dimensions for some physically relevant settings.

cond-mat.str-el↗

arXiv2017

Symmetry-based Indicators of Band Topology in the 230 Space Groups

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.

cond-mat.str-el↗

arXiv2017

Energy gap of neutral excitations implies vanishing charge susceptibility

In quantum many-body systems with a U(1) symmetry, such as the particle number conservation and the axial spin conservation, there are two distinct types of excitations: charge-neutral excitations and charged excitations. The energy gaps of these excitations may be independent with each other in strongly correlated systems. The static susceptibility of the U(1) charge vanishes when the charged excitations are all gapped, but its relation to the neutral excitations is not obvious. Here we show that a finite excitation gap of the neutral excitations is, in fact, sufficient to prove that the charge susceptibility vanishes (i.e. the system is incompressible). This result gives a partial explanation on why the celebrated quantization condition $n(S-m_z)\in\mathbb{Z}$ at magnetization plateaus works even in spatial dimensions greater than one.

cond-mat.str-el↗

arXiv2017

Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions

We introduce a novel class of interaction-enabled topological crystalline insulators in two- and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal symmetry $\mathcal{T}$ and a mirror symmetry or a rotation symmetry $\mathcal{R}$. A topological crystalline magnet exhibits two intriguing features: (i) it cannot be adiabatically connected to any Slater insulator and (ii) the edge state is robust against coupling electrons to the edge. These features are protected by the anomalous symmetry transformation property $(\mathcal{R} \mathcal{T})^2=-1$ of the edge state. An anisotropic response to the external magnetic field can be an experimental signature.

cond-mat.str-el↗

arXiv2016

Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups

Nonsymmorphic symmetries like screws and glides produce electron band touchings, obstructing the formation of a band insulator and leading, instead, to metals or nodal semimetals even when the number of electrons in the unit cell is an even integer. Here, we calculate the electron fillings compatible with being a band insulator for all 230 space groups, for noninteracting electrons with time-reversal symmetry. Our bounds are tight - that is, we can rigorously eliminate band insulators at any forbidden filling and produce explicit models for all allowed fillings - and stronger than those recently established for interacting systems. These results provide simple criteria that should help guide the search for topological semimetals and, also, have implications for both the nature and stability of the resulting nodal Fermi surfaces.

cond-mat.str-el↗

arXiv2016

Filling-Enforced Quantum Band Insulators in Spin-Orbit Coupled Crystals

While band insulators are usually described in wavevector space in terms of fully filled bands, they are sometimes also described in terms of a complementary Wannier picture in which electrons occupy localized, atom-like orbitals. Under what conditions does the latter picture break down? The presence of irremovable quantum entanglement between different sites can obstruct a localized orbital description, which occurs in systems like Chern and topological insulators. We collectively refer to such states as Quantum Band Insulators (QBIs). Here we report the theoretical discovery of a filling-enforced QBI - that is, a free electron insulator in which the band filling is smaller than the minimum number dictated by the atomic picture. Consequently such insulators have no representation in terms of filling localized orbitals and must be QBIs. This is shown to occur in models of certain cubic crystals with non-symmorphic space groups. Like topological insulators, filling-enforced QBIs require spin-orbit coupling. However, in contrast, they do not typically exhibit protected surface states. Instead their nontrivial nature is revealed by studying the quantum entanglement of their ground state wavefunction.

cond-mat.str-el↗

arXiv2016

Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals

We determine conditions on the filling of electrons in a crystalline lattice to obtain the equivalent of a band insulator -- a gapped insulator with neither symmetry breaking nor fractionalized excitations. We allow for strong interactions, which precludes a free particle description. Previous approaches that extend the Lieb-Schultz-Mattis argument invoked spin conservation in an essential way, and cannot be applied to the physically interesting case of spin-orbit coupled systems. Here we introduce two approaches, the first an entanglement based scheme, while the second studies the system on an appropriate flat `Bieberbach' manifold to obtain the filling conditions for all 230 space groups. These approaches only assume time reversal rather than spin rotation invariance. The results depend crucially on whether the crystal symmetry is symmorphic. Our results clarify when one may infer the existence of an exotic ground state based on the absence of order, and we point out applications to experimentally realized materials. Extensions to new situations involving purely spin models are also mentioned.

cond-mat.str-el↗

arXiv2015

Electric Field-Induced Skyrmion Crystals via Charged Monopoles in Insulating Helimagets

Electrons propagating in a magnetically ordered medium experience an additional gauge field associated with the Berry phase of their spin following the local magnetic texture. In contrast to the usual electromagnetic field, this gauge field admits monopole excitations, corresponding to hedgehog defects of the magnetic order. In an insulator, these hedgehogs carry a well-defined electric charge allowing for them to be controlled by electric fields. One particularly robust mechanism that contributes to the charge is the orbital magnetoelectric effect, captured by a $θ$ angle, which leads to a charge of $eθ/2π$ on hedgehogs. This is a direct consequence of the Witten effect for magnetic monopoles in a $θ$ medium. A physical consequence is that external electric fields can induce skyrmion crystal phases in insulating helimagnets.

cond-mat.str-el↗

arXiv2015

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. Here we first present a definition of time crystals based on the time-dependent correlation functions of the order parameter. We then prove a no-go theorem that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.

cond-mat.stat-mech↗

arXiv2014

Effective Lagrangian for Nonrelativistic Systems

The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing $1$ dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in $1+1$ dimensions.

hep-th↗

arXiv2014

Anomalous Fermi liquid phase in metallic Skyrmion crystals

In non-centrosymmetric crystals such as MnSi, magnetic order can take the form of a skyrmion crystal (SkX) . In this phase, conduction electrons coupled to the local magnetic moments acquire a Berry's phase, leading to an emergent electromagnetism. Motivated by experimental reports of a non-Fermi liquid phase in MnSi, in which resistivity is observed to scale as $Δρ\sim T^{3/2}$, here we examine the effect of coupling phonons of an incommensurate SkX to electrons. Despite the formal similarity to a system consisting of a Fermi surface coupled to an electromagnetic field, the Berry phase fluctuations do not lead to non-Fermi liquid behavior. Instead, we propose a different mechanism in which electrons scatter off columnar fluctuation in a three-dimensional SkX. When the effects of lattice induced anisotropy are neglected, these fluctuations are ultra-soft and induce an `anomalous Fermi liquid' in which Landau quasiparticles survive but with an anomalous $Δρ(T)\sim T^{7/4}$ resistivity perpendicular to the columns, and a Fermi liquid resistivity along them.

cond-mat.str-el↗

arXiv2014

Englert-Brout-Higgs Mechanism in Nonrelativistic Systems

We study the general theory of Englert-Brout-Higgs mechanism without assuming Lorentz invariance. In the presence of a finite expectation value of non-Abelian matter charges, gauging those symmetries always results in spontaneous breaking of spatial rotation. If we impose the charge neutrality by assuming a background with the opposite charges, the dynamics of the background cannot be decoupled and has to be fully taken into account. In either case, the spectrum is continuous as the gauge coupling is switched off.

hep-th↗

arXiv2014

Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry

There are few general physical principles that protect the low energy excitations of a quantum phase. Of these, Goldstone's theorem and Landau Fermi liquid theory are the most relevant to solids. We investigate the stability of the resulting gapless excitations - Nambu Goldstone bosons (NGBs) and Landau quasiparticles - when coupled to one another, which is of direct relevance to metals with a broken continuous symmetry. Typically, the coupling between NGBs and Landau quasiparticles vanishes at low energies leaving the gapless modes unaffected. If however the low energy coupling is non-vanishing, non-Fermi liquid behavior and overdamped bosons are expected. Here we prove a general criterion which specifies when the coupling is non-vanishing. It is satisfied by the case of a nematic Fermi fluid, consistent with earlier microscopic calculations. In addition, the criterion identifies a new kind of symmetry breaking - of magnetic translations - where non-vanishing couplings should arise, opening a new route to realizing non-Fermi liquid phases.

cond-mat.str-el↗

arXiv2014

Noncommuting Momenta of Topological Solitons

We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology $H^2$ of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

hep-th↗

arXiv2014

Nambu-Goldstone bosons with fractional-power dispersion relations

We pin down the origin of a peculiar dispersion relation of domain wall fluctuation, the so-called ripplon, in a superfluid-superfluid interface. A ripplon has a dispersion relation $ω\propto k^{3/2}$ due to the nonlocality of the effective Lagrangian, which is mediated by gapless superfluid phonons in the bulk. We point out the analogy to the longitudinal phonon in the two-dimensional Wigner crystal.

hep-th↗