arXiv subjects

Haruki Watanabe

Publications and source records attributed to Haruki Watanabe.

At least 55 records · Page 3Linked to original sources

arXiv2020

Corner charge and bulk multipole moment in periodic systems

A formula for the corner charge in terms of the bulk quadrupole moment is derived for two-dimensional periodic systems. This is an analog of the formula for the surface charge density in terms of the bulk polarization. In the presence of an $n$-fold rotation symmetry with $n=3$, $4$, and $6$, the quadrupole moment is quantized and is independent of the spread or shape of Wannier orbitals, depending only on the location of Wannier centers of filled bands. In this case, our formula predicts the fractional part of the quadrupole moment purely from the bulk property. The system can contain many-body interactions as long as the ground state is gapped and topologically trivial in the sense it is smoothly connected to a product state limit. An extension of these results to three-dimensional systems is also discussed. In three dimensions, in general, even the fractional part of the corner charge is not fully predictable from the bulk perspective even in the presence of point group symmetry.

cond-mat.str-el↗

arXiv2020

Proof of the absence of long-range temporal orders in Gibbs states

We address the question whether time translation symmetry can be spontaneously broken in a quantum many-body system. One way of detecting such a symmetry breaking is to examine the time-dependence of a correlation function. If the large-distance behavior of the correlation function exhibits a nontrivial time-dependence in the thermodynamic limit, the system would develop a temporal long-range order, realizing a time crystal. In an earlier publication, we sketched a proof for the absence of such time dependence in the thermal equilibrium described by the Gibbs state [H. Watanabe and M. Oshikawa, Phys. Rev. Lett. 114, 251603 (2015)]. Here we present a complete proof and extend the argument to a more general class of stationary states than the Gibbs states.

cond-mat.stat-mech↗

arXiv2019

Difficulties in operator-based formulation of the bulk quadrupole moment

Electric multipole moments are the most fundamental properties of insulating materials. However, the general formulation of bulk multipoles has been a long standing problem. The solution for the electric dipole moment was provided decades ago by King-Smith, Vanderbilt, and Resta. Recently, there have been attempts at generalizing Resta's formula to higher-order multipoles. We point out several issues in the recent proposals.

cond-mat.str-el↗

arXiv2019

Counting Rules of Nambu-Goldstone Modes

When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu-Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy, particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be fewer than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this article, we review recently established formulas for NGMs associated with broken internal symmetries that work equally for relativistic and nonrelativistic systems. We also discuss complexities of NGMs originating from space-time symmetry breaking. In the process we cover many illuminating examples from various context. We also present a complementary point of view from the Lieb-Schultz-Mattis theorem.

cond-mat.other↗

arXiv2019

Refined symmetry indicators for topological superconductors in all space groups

Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to cover all space groups. Our main result is the exhaustive computation of the indicator groups for superconductors under a variety of symmetry settings. We further illustrate the power of this approach by analyzing four-fold symmetric superconductors with or without inversion symmetry, and show that the indicators can diagnose topological superconductors with surface states of different dimensionalities or dictate gaplessness in the bulk excitation spectrum.

cond-mat.supr-con↗

arXiv2019

A proof of the Bloch theorem for lattice models

The Bloch theorem is a powerful theorem stating that the expectation value of the U(1) current operator averaged over the entire space vanishes in large quantum systems. The theorem applies to the ground state and to the thermal equilibrium at a finite temperature, irrespective of the details of the Hamiltonian as far as all terms in the Hamiltonian are finite ranged. In this work we present a simple yet rigorous proof for general lattice models. For large but finite systems, we find that both the discussion and the conclusion are sensitive to the boundary condition one assumes: under the periodic boundary condition, one can only prove that the current expectation value is inversely proportional to the linear dimension of the system, while the current expectation value completely vanishes before taking the thermodynamic limit when the open boundary condition is imposed. We also provide simple tight-binding models that clarify the limitation of the theorem in dimensions higher than one.

cond-mat.stat-mech↗

arXiv2019

Quantum Quench and $f$-Sum Rules on Linear and Non-linear Conductivities

Considering a quench process in which an electric field pulse is applied to the system, "$f$-sum rule" for the conductivity for general quantum many-particle systems is derived. It is furthermore extended to an infinite series of sum rules, applicable to the nonlinear conductivity at every order.

cond-mat.str-el↗

arXiv2019

Symmetry indicators for topological superconductors

The systematic diagnosis of band topology enabled by the method of "symmetry indicators" underlies the recent advances in the search for new materials realizing topological crystalline insulators. Such an efficient method has been missing for superconductors because the band structure in the superconducting phase is not usually available. In this work, we establish symmetry indicators for weak-coupling superconductors that detect nontrivial topology based on the representations of the metallic band structure in the normal phase, assuming a symmetry property of the gap function. We demonstrate the applications of our formulas using examples of tight-binding models and density-functional-theory band structures of realistic materials.

cond-mat.supr-con↗

arXiv2019

Geometric orbital magnetization in adiabatic processes

We consider periodic adiabatic processes of gapped many-body spinless electrons. We find an additional contribution to the orbital magnetization due to the adiabatic time evolution, dubbed \textit{geometric} orbital magnetization, which can be expressed as derivative of the many-body Berry phase with respect to an external magnetic field. For two-dimensional band insulators, we show that the geometric orbital magnetization generally consists of two pieces, the topological piece that is expressed as third Chern-Simons form in $(t,k_x,k_y)$ space, and the non-topological piece that depends on Bloch states and energies of both occupied and unoccupied bands.

cond-mat.mes-hall↗

arXiv2019

Many-body Chern number without integration

The celebrated work of Niu, Thouless, and Wu demonstrated the quantization of Hall conductance in the presence of many-body interactions by revealing the many-body counterpart of the Chern number. The generalized Chern number is formulated in terms of the twisted angles of the boundary condition, instead of the single particle momentum, and involves an integration over all possible twisted angles. However, this formulation is physically unnatural, since topological invariants directly related to observables should be defined for each Hamiltonian under a fixed boundary condition. In this work, we show via numerical calculations that the integration is indeed unnecessary - the integrand itself is effectively quantized and the error decays exponentially with the system size. This implies that the numerical cost in computing the many-body Chern number could, in principle, be significantly reduced as it suffices to compute the Berry connection for a single value of the twisted boundary condition if the system size is sufficiently large.

cond-mat.str-el↗

arXiv2019

Fragile topological phases in interacting systems

Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on noninteracting electrons in crystals have unveiled a peculiar variety of topological phases, which harbors nontrivial entanglement that can be dissolved simply by the the addition of entanglement-free, but charged, degrees of freedom. Such topological phases have a weaker sense of robustness than their conventional counterparts, and are therefore dubbed "fragile topological phases." In this work, we show that fragile topology is a general concept prevailing beyond systems of noninteracting electrons. Fragile topological phases can generally occur when a system has a $\mathrm{U}(1)$ charge conservation symmetry, such that only particles with one sign of the charge are physically allowed (e.g. electrons but not positrons). We demonstrate that fragile topological phases exist in interacting systems of both fermions and of bosons.

cond-mat.str-el↗

arXiv2019

Insensitivity of bulk properties to the twisted boundary condition

The symmetry and the locality are the two major sources of various nontrivial statements in quantum many-body systems. We demonstrate that, in gapped phases of a U(1) symmetric Hamiltonian with finite-range interactions, the bulk properties such as the expectation value of local operators, the ground state energy and the excitation gap, and the static and low-frequency dynamical responses in general, do not depend on the U(1) phase of the twisted boundary condition in the limit of the large system size. Specifically, their dependence on the twisted angle is exponentially suppressed with the linear dimension of the system. The argument is based on the exponential decay of various types of equal-time correlation functions.

cond-mat.stat-mech↗

arXiv2019

Inequivalent Berry phases for the bulk polarization

We discuss characterization of the polarization for insulators under the periodic boundary condition in terms of the Berry phase, clarifying confusing subtleties. For band insulators, the Berry phase can be formulated in terms of the Bloch function in the momentum space. More generally, in the presence of interactions or disorders, one can instead use the many-body ground state as a function of the flux piercing the ring. However, the definition of the Bloch function and the way describing the flux are not unique. As a result, the value of the Berry phase and its behavior depend on how precisely it is defined. In particular, identifying the Berry phase as a polarization, its change represents a polarization current which also depends on the definition. We demonstrate this by elucidating mutual relations among different definitions of the Berry phase, and that they correspond to the current measured differently in the real space. Despite the non-uniqueness of the polarization current, the total charge transported during a Thouless pumping process is independent of the definition, reflecting its topological nature.

cond-mat.str-el↗

arXiv2018

Connecting higher-order topological insulators to lower-dimensional topological insulators

In recent years, the role of crystal symmetries in enriching the variety of TIs have been actively investigated. Higher-order TIs are a new type of topological crystalline insulators that exhibit gapless boundary states whose dimensionality is lower than those on the surface of conventional TIs. In this paper, relying on a concrete tight-binding model, we show that higher-order TIs can be smoothly connected to conventional TIs in a lower dimension without the bulk-gap closing or symmetry breaking. Our result supports the understanding of higher- order TIs as a stacking of lower-dimensional TIs in a way respecting all the crystalline symmetry.

cond-mat.str-el↗

arXiv2018

Space-group theory of photonic bands

The wide-range application of photonic crystals and metamaterials benefits from the enormous design space of three-dimensional sub-wavelength structures. In this work, we study the space group constraints on photonic dispersions for all 230 space groups with time-reversal symmetry. Our theory carefully treats the unique singular point of photonic bands at zero frequency and momentum, which distinguishes photonic bands from their electronic counterpart. The results are given in terms of minimal band connectivities at zero~($M$) and non-zero frequencies~($M'$). Topological band degeneracies are guaranteed to be found in space groups that do not allow band gaps between the second and third photonic bands~($M>2$). Our work provides theoretical guidelines for the choice of spatial symmetries in photonics design.

physics.optics↗

arXiv2018

Unified understanding of symmetry indicators for all internal symmetry classes

The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band topology can be extracted by focusing the symmetry representations of valence bands without computing Wilson loops. In this work, we extend the previous studies on this subject to all 10 Altland-Zirnbauer symmetry classes in each of 230 space groups. We derive various general statements that should be useful in the search for topological superconductors and topological semimetals.

cond-mat.mtrl-sci↗

arXiv2018

Fragile Topology and Wannier Obstructions

Topological phases, such as Chern insulators, are defined in terms of additive indices that are stable against the addition of trivial degrees of freedom. Such topology presents an obstruction to any Wannier representation, namely, the representation of the electronic states in terms of symmetric, exponentially localized Wannier functions. Here, we address the converse question: Do obstructions to Wannier representation imply stable band topology? We answer this in the negative, pointing out that some bands can also display a distinct type of "fragile topology." Bands with fragile topology do not admit any Wannier representation by themselves, but such a representation becomes possible once certain additional trivial degrees of freedom are supplied. We construct a physical model of fragile topology on the honeycomb lattice that also helps resolve a recent puzzle in band theory. This model provides a counterexample to the assumption that splitting of an "elementary band representation" introduced in [Nature 547, 298--305 (2017)] leads to bands that are individually topological. Instead, half of the split bands of our model realizes a trivial band with exponentially localized symmetric Wannier functions, whereas the second half possess fragile topology. Our work highlights an important and previously overlooked connection between band structure and Wannier functions, and is expected to have far reaching consequences given the central role played by Wannier functions in the modeling of real materials.

cond-mat.mes-hall↗

arXiv2018

Symmetry indicators and anomalous surface states of topological crystalline insulators

The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to the symmetries at hand. While isolated examples of TCI have been identified and studied, the same variety demands a unified theoretical framework. In this work, we show how the surfaces of TCIs can be analyzed within a general surface theory with multiple flavors of Dirac fermions, whose mass terms transform in specific ways under crystalline symmetries. We identify global obstructions to achieving a fully gapped surface, which typically lead to gapless domain walls on suitably chosen surface geometries. We perform this analysis for all 32 point groups, and subsequently for all 230 space groups, for spin-orbit-coupled electrons. We recover all previously discussed TCIs in this symmetry class, including those with "hinge" surface states. Finally, we make connections to the bulk band topology as diagnosed through symmetry-based indicators. We show that spin-orbit-coupled band insulators with nontrivial symmetry indicators are always accompanied by surface states that must be gapless somewhere on suitably chosen surfaces. We provide an explicit mapping between symmetry indicators, which can be readily calculated, and the characteristic surface states of the resulting TCIs.

cond-mat.str-el↗