arXiv subjects

Yutaka Akagi

Publications and source records attributed to Yutaka Akagi.

30 records · Page 2Linked to original sources

arXiv2018

Learning Disordered Topological Phases by Statistical Recovery of Symmetry

In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. Given the disorder that keeps the discrete symmetries of the ensemble as a whole, translational symmetry which is broken in the quasiparticle distribution individually is recovered statistically by taking an ensemble average. By using this, we classify the phases by the artificial neural network that learned the quasiparticle distribution in the clean limit, and show that the result is totally consistent with the calculation by the transfer matrix method or noncommutative geometry approach. If all three phases, namely the $\mathbb{Z}_2$, trivial, and the thermal metal phases appear in the clean limit, the machine can classify them with high confidence over the entire phase diagram. If only the former two phases are present, we find that the machine remains confused in the certain region, leading us to conclude the detection of the unknown phase which is eventually identified as the thermal metal phase. In our method, only the first moment of the quasiparticle distribution is used for input, but application to a wider variety of systems is expected by the inclusion of higher moments.

cond-mat.dis-nn↗

arXiv2017

A New Numerical Method for $\mathbb{Z}_2$ Topological Insulators with Strong Disorder

We propose a new method to numerically compute the $\mathbb{Z}_2$ indices for disordered topological insulators in Kitaev's periodic table. All of the $\mathbb{Z}_2$ indices are known to be derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties make it possible to numerically determine the indices of disordered topological insulators highly efficiently. The method is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a $\mathbb{Z}_2$ index in two and three dimensions, respectively.

cond-mat.mes-hall↗

arXiv2016

Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice

Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than $SU(2)$. Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with $SU(3)$ symmetry. Using a combination of homotopy analysis and analytic field-theory we identify a new family of solitonic wave functions characterised by integer charge ${\bf Q} = (Q_A, Q_B, Q_C)$, with $Q_A + Q_B + Q_C = 0$. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a finite lattice. We find that, while solitons with charge ${\bf Q} = (Q, -Q, 0)$ are stable, wave functions with more general charge spontaneously decay into pairs of solitons with emergent interactions. This result suggests that it could be possible to realise a new class of interacting soliton, with no classical analogue, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge--group U(1)$\times$U(1).

cond-mat.str-el↗

arXiv2015

Spontaneous formation of kagome network and Dirac half-semimetal on a triangular lattice

In spin-charge coupled systems, geometrical frustration of underlying lattice structures can give rise to nontrivial magnetic orders and electronic states. Here we explore such a possibility in the Kondo lattice model with classical localized spins on a triangular lattice by using a variational calculation and simulated annealing. We find that the system exhibits a four-sublattice collinear ferrimagnetic phase at 5/8 filling for a large Hund's-rule coupling. In this state, the system spontaneously differentiates into the up-spin kagome network and the isolated down-spin sites, which we call the kagome network formation. In the kagome network state, the system becomes Dirac half-semimetallic: The electronic structure shows a massless Dirac node at the Fermi level, and the Dirac electrons are almost fully spin polarized due to the large Hund's-rule coupling. We also study the effect of off-site Coulomb repulsion in the kagome network phase where the system is effectively regarded as a 1/3-filling spinless fermion system on the kagome lattice. We find that, at the level of the mean-field approximation, a $\sqrt{3} \times \sqrt{3}$-type charge order occurs in the kagome network state, implying the possibility of fractional charge excitations in this triangular lattice system. Moreover, we demonstrate that the kagome network formation with fully-polarized Dirac electrons are controllable by an external magnetic field.

cond-mat.str-el↗

arXiv2014

Surface and interface effects on a magnetic Chern insulator

Effects of an open surface on a magnetic Chern insulator are investigated in comparison with those of an interface to a capping magnetic layer. In magnets, an open surface often perturbs the magnetic order by a reconstruction of the magnetic moment directions near the surface. On the other hand, in topological insulators, it leads to the formation of topologically protected surface states. These two contrasting effects may coexist in magnetic Chern insulators, which give rise to nontrivial surface reconstruction. For instance, the chiral edge current is largely enhanced by the edge reconstruction in a two-dimensional magnetic Chern insulator realized in a quarter-filled Kondo lattice model on a triangular lattice. We here show that the edge reconstruction can be described semiquantitatively by a simple junction model between the bulk topological magnetic state and a ferromagnetic capping layer. We further clarify how the chiral edge current is affected by the magnetic structure in the capping layer. Our results indicate that the topological edge state can be controlled magnetically through the junctions.

cond-mat.str-el↗

arXiv2014

Reconstruction of chiral edge states in a magnetic Chern insulator

We study reconstruction of the chiral edge states in a magnetic Chern insulator in the Kondo lattice model on a triangular lattice at 1/4 filling. In this state, the spin scalar chirality associated with a four-sublattice noncoplanar magnetic order assures the topological nature characterized by a nonzero Chern number. Performing a Langevin-based numerical simulation for finite-size clusters with the open boundary condition in one direction, we clarify how the magnetic and electronic properties are modulated near the edges of the system. As a result, we find that the magnetic state near the edges is reconstructed to develop ferromagnetic spin correlations. At the same time, the electronic state is also modified and the chiral edge current is enhanced. We discuss this enhancement from the viewpoint of the electronic band structure for the gapless edge states.

cond-mat.str-el↗

arXiv2013

Effect of Quantum Spin Fluctuation on Scalar Chiral Ordering in the Kondo Lattice Model on a Triangular Lattice

Spin scalar chiral ordering gives rise to nontrivial topological characters and peculiar transport properties. We here examine how quantum spin fluctuations affect the spin scalar chiral ordering in itinerant electron systems. We take the Kondo lattice model on a triangular lattice, and perform the linear spin wave analysis in the Chern insulator phases with spin scalar chiral ordering obtained in the case that the localized spins are classical. We find that, although the quantum fluctuation destabilizes the spin scalar chiral phase at 3/4 filling that originates from the perfect nesting of Fermi surface, it retains the phase at 1/4 filling that is induced by an effective positive biquadratic interaction. The reduction of the ordered magnetic moment by the zero-point quantum fluctuation is considerably small, compared with those in spin-only systems. The results suggest that the Chern insulator at 1/4 filling remains robust under quantum fluctuations.

cond-mat.str-el↗

arXiv2013

Linear Spin Wave Analysis for General Magnetic Orders in the Kondo Lattice Model

We extend the formulation of the spin wave theory for the Kondo lattice model, which was mainly used for the ferromagnetic metallic state, to general magnetic orders including complex noncollinear and noncoplanar orders. The 1/S expansion is reformulated in the matrix form depending on the size of the magnetic unit cell. The noncollinearity and noncoplanarity of the localized moments are properly taken into account by the matrix elements of the para-unitary matrix used in the diagonalization of the Bogoliubov-de Gennes type Hamiltonian for magnons. We apply the formulation within the linear spin wave approximation to a typical noncollinear case, the $120^{\circ}$ N{é}el order on a triangular lattice at half filling. We calculate the magnon excitation spectrum and the quantum correction to the magnitude of ordered moments as functions of the strength of the Hund's-rule coupling, $J_{\rm H}/t$. We find that the magnon excitation shows softening at $J_{\rm H}/t \simeq 2.9$, which indicates that the $120^{\circ}$ order is destabilized for smaller $J_{\rm H}/t$. On the other hand, we show that the $120^{\circ}$ order is stable in the entire range of $J_{\rm H}/t \gtrsim 2.9$, and, in the limit of $J_{\rm H}/t \to \infty$, the form of the spin wave spectrum approaches that for the antiferromagnetic Heisenberg model, while the bandwidth is proportional to $t^2/J_{\rm H}$. The reduction of the ordered moment is smaller than that for the spin-only model, except in the vicinity of the softening.

cond-mat.str-el↗

arXiv2012

Ground-state phase diagram of the Kondo lattice model on triangular-to-kagome lattices

We investigate the ground-state phase diagram of the Kondo lattice model with classical localized spins on triangular-to-kagome lattices by using a variational calculation. We identify the parameter regions where a four-sublattice noncoplanar order is stable with a finite spin scalar chirality while changing the lattice structure from triangular to kagome continuously. Although the noncoplanar spin states appear in a wide range of parameters, the spin configurations on the kagome network become coplanar as approaching the kagome lattice; eventually, the scalar chirality vanishes for the kagome lattice model.

cond-mat.str-el↗

arXiv2012

Hidden Multiple-spin Interactions as an Origin of Spin Scalar Chiral Order in Frustrated Kondo Lattice Models

We reveal the significance of kinetic-driven multiple-spin interactions hidden in geometrically-frustrated Kondo lattice models. Carefully examining the perturbation in terms of the spin-charge coupling up to the fourth order, we find that a positive biquadratic interaction is critically enhanced and plays a crucial role on stabilizing a spin scalar chiral order near 1/4 filling in a triangular lattice case. This is a generalized Kohn anomaly, appearing only when the second-order perturbation is inefficient because of the degeneracy under frustration. The mechanism is potentially common to frustrated spin-charge coupled systems, leading to emergence of unusual magnetic orders.

cond-mat.str-el↗

arXiv2011

Noncoplanar spin canting in lightly-doped ferromagnetic Kondo lattice model on a triangular lattice

Effect of the coupling to mobile carriers on the 120$^\circ$ antiferromagnetic state is investigated in a ferromagnetic Kondo lattice model on a frustrated triangular lattice. Using a variational calculation for various spin orderings up to a four-site unit cell, we identify the ground-state phase diagram with focusing on the lightly-doped region. We find that an electron doping from the band bottom immediately destabilizes a 120$^\circ$ coplanar antiferromagnetic order and induces a noncoplanar three-sublattice ordering accompanied by an intervening phase separation. This noncoplanar phase has an umbrella-type spin configuration with a net magnetic moment and a finite spin scalar chirality. This spin-canting state emerges in competition between the antiferromagnetic superexchange interaction and the ferromagnetic double-exchange interaction under geometrical frustration. In contrast, a hole doping from the band top retains the 120$^\circ$-ordered state up to a finite doping concentration and does not lead to a noncolpanar ordering.

cond-mat.str-el↗

arXiv2010

Spin chirality ordering and anomalous Hall effect in the ferromagnetic Kondo lattice model on the triangular lattice

We investigate the ground-state phase diagram for the ferromagnetic Kondo lattice model on a triangular lattice by a variational calculation for various spin orderings up to a four-site unit cell. We find that a noncoplanar four-sublattice ordering with a finite scalar spin chirality emerges at and around 1/4 filling, in addition to the 3/4-filled case, which was predicted to be induced by the perfect nesting of the Fermi surface [I. Martin and C. D. Batista: Phys. Rev. Lett. {\bf 101} (2008) 156402]. The 1/4-filling phase is stable in a wider range of parameters than the 3/4-filling one, and includes a large region of gapped insulating state characterized by a Chern number. We also compute the Hall conductivity in the chiral-ordered phases.

cond-mat.str-el↗