arXiv subjects

Akihisa Koga

Publications and source records attributed to Akihisa Koga.

At least 37 records · Page 2Linked to original sources

arXiv2023

Ferromagnetically ordered states in the Hubbard model on the $H_{00}$ hexagonal golden-mean tiling

We study magnetic properties of the half-filled Hubbard model on the two-dimensional $H_{00}$ hexagonal golden-mean quasiperiodic tiling. The tiling is composed of large and small hexagons, and parallelograms, and its vertex model is bipartite with a sublattice imbalance. The tight-binding model on the tiling has macroscopically degenerate states at $E = 0$. We find the existence of two extended states in one of the sublattices, in addition to confined states in the other. This property is distinct from that of the well-known two-dimensional quasiperiodic tilings such as the Penrose and Ammann-Beenker tilings. Applying the Lieb theorem to the Hubbard model on the tiling, we obtain the exact fraction of the confined states as $1/2τ^2$, where $τ$ is the golden mean. This leads to a ferromagnetically ordered state in the weak coupling limit. Increasing the Coulomb interaction, the staggered magnetic moments are induced and gradually increase. Crossover behaviour in the magnetically ordered states is also addressed in terms of perpendicular space analysis.

cond-mat.str-el↗

arXiv2023

Hexagonal and trigonal quasiperiodic tilings

Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat. Motivated by the prevalence of experimental systems exhibiting aperiodic long-range order with hexagonal and trigonal symmetry, we introduce a generic two-parameter family of 2-dimensional quasiperiodic tilings with such symmetries. We focus on the special case of trigonal and hexagonal Fibonacci, or golden-mean, tilings, analogous to the well studied square Fibonacci tiling. We first generate the tilings using a generalized version of de Bruijn's dual grid method. We then discuss their interpretation in terms of projections of a hypercubic lattice from six dimensional superspace. We conclude by concentrating on two of the hexagonal members of the family, and examining a few of their properties more closely, while providing a set of substitution rules for their generation.

cond-mat.soft↗

arXiv2023

Majorana Gap Formation in the Anisotropic Kitaev Model with Ordered Flux Configuration

We study the Kitaev model with direction dependent interactions to investigate how the flux configuration and/or the anisotropy in the exchanges affect the Majorana excitations. Systematic numerical calculations demonstrate how the anisotropy of the exchange couplings and flux configuration make the Majorana excitation gapped. The induced gapped quantum spin liquid states are distinct from the gapped one realized in the large anisotropic limit. The nature of gapped states can be explained by the superlattice potential due to flux configuration.

cond-mat.str-el↗

arXiv2022

A three tile 6-fold golden-mean tiling

We present a multi-edge-length aperiodic tiling which exhibits 6--fold rotational symmetry. The edge lengths of the tiling are proportional to 1:$τ$, where $τ$ is the golden mean $\frac{1+\sqrt{5}}{2}$. We show how the tiling can be generated using simple substitution rules for its three constituent tiles, which we then use to demonstrate the bipartite nature of the tiling vertices. As such, we show that there is a relatively large sublattice imbalance of $1/[2τ^2]$. Similarly, we define allowed vertex configurations before analysing the tiling structure in 4-dimensional hyperspace.

cond-mat.other↗

arXiv2022

Confined states in the tight-binding model on the hexagonal golden-mean tiling

We study the tight-binding model with two distinct hoppings $(t_L, t_S)$ on the two-dimensional hexagonal golden-mean tiling and examine the confined states with $E=0$, where $E$ is the eigenenergy. Some confined states found in the case $t_L=t_S$ are exact eigenstates even for the system with $t_L \neq t_S$, where their amplitudes are smoothly changed. By contrast, the other states are no longer eigenstates of the system with $t_L \neq t_S$. This may imply the existence of macroscopically degenerate states which are characteristic of the system with $t_L=t_S$, and that a discontinuity appears in the number of the confined states in the thermodynamic limit.

cond-mat.str-el↗

arXiv2022

Anomalous temperature dependence of high-harmonic generation in Mott insulators

We reveal the crucial effect of strong spin-charge coupling on high-harmonic generation (HHG) in Mott insulators. In a system with antiferromagnetic correlations, the HHG signal is drastically enhanced with decreasing temperature, even though the gap increases and the production of charge carriers is suppressed. This anomalous behavior, which has also been observed in recent HHG experiments on Ca$_2$RuO$_4$, originates from a cooperative effect between the spin-charge coupling and the thermal ensemble, and the strongly temperature-dependent coherence between charge carriers. We argue that the peculiar temperature dependence of HHG is a generic feature of Mott insulators, which can be controlled via the Coulomb interaction and dimensionality of the system. Our results demonstrate that correlations between different degrees of freedom, which are a characteristic feature of strongly correlated solids, have significant and nontrivial effects on nonlinear optical responses.

cond-mat.str-el↗

arXiv2022

Optical response of the tightbinding model on the Fibonacci chain

We theoretically study the optical conductivity of the tightbinding model which has two types of the hopping integrals arranged in the Fibonacci sequence. Due to the lack of the translational symmetry, many peak structures appear in the optical conductivity as well as the density of states. When the ratio of two hopping integrals is large, the self-similar structure appears in the optical conductivity. This implies that the optical response between the high-energy bands is related to that within the low-energy bands, which should originate from critical behavior in the wave functions. The effects of disorders on the optical conductivity are also analyzed in order to show the absence of the self-similarity in the tightbinding model with the random sequence.

cond-mat.mes-hall↗

arXiv2022

Quantum algorithm for the microcanonical Thermal Pure Quantum method

We present a quantum algorithm for the microcanonical thermal pure quantum (TPQ) method, which has an advantage in evaluating thermodynamic quantities at finite temperatures, by combining with some recently developed techniques derived from quantum singular value transformation. When the ground energy of quantum systems has already been obtained precisely, the multiple products of the Hamiltonian are efficiently realized and the TPQ states at low temperatures are systematically constructed in quantum computations.

quant-ph↗

arXiv2022

High-harmonic generation in the Rice-Mele model: Role of intraband current originating from interband transition

We consider high-harmonic generation (HHG) in the Rice-Mele model to study the role of the intraband current originating from the change of the intraband dipole via interband transition. This contribution, which has been often neglected in previous works, is necessary for the consistent theoretical formulation of the light-matter coupling. We demonstrate that the contribution becomes crucial when the gap is smaller than or comparable to the excitation frequency and the system is close to the half filling.

cond-mat.mes-hall↗

arXiv2022

Scattering phenomena for spin transport in Kitaev spin liquid

The Kitaev model exhibits a canonical quantum spin liquid as a ground state and hosts two fractional quasiparticles, itinerant Majorana fermion and localized flux excitation. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. Here, we focus on spin transport in the presence of excited fluxes and report that they yield strong interference in the propagation of the Majorana fermions, which feel gauge-like potential emergent around the fluxes. We examine the transient spin dynamics triggered by a pulsed magnetic field at an edge. In the absence of excited fluxes, the magnetic-field pulse creates the plane wave of the Majorana fermions, which flows in the quantum spin liquid. Although this wave does not accompany the change of local spin moments in bulk, it induces local moments at the side opposite to the edge under the magnetic-field pulse. We observe the spatial modulation of induced spin moments when fluxes are excited in the bulk region. This behavior is more striking than the case of lattice defects. Moreover, we find that, although the amplitude of the spatial change is almost independent of the distance between lattice defects, it is strongly enhanced by increasing the distance for the case of excited fluxes. The difference is understood from the influence on the itinerant Majorana fermions; the lattice defects change the system locally, but flux excitations alter all the transfer integrals on the string connecting them. The present results will provide another route to observing intrinsic flux excitations distinguished from extrinsic effects such as lattice defects.

cond-mat.str-el↗

arXiv2022

Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling

We study magnetic properties of the half-filled Hubbard model on the two-dimensional hexagonal golden-mean tiling. We find that the vertex model of the tiling is bipartite, with a sublattice imbalance of $\sqrt{5}/(6τ^3)$ (where $τ$ is the golden mean), and that the non-interacting tight-binding model gives macroscopically degenerate states at $E=0$. We clarify that each sublattice has specific types of confined states, which in turn leads to an interesting spatial pattern in the local magnetizations in the weak coupling regime. Furthermore, this allows us to analytically obtain the lower bound on the fraction of the confined states as $(τ+9)/(6τ^6)\sim 0.0986$, which is conjectured to be the exact fraction. These results imply that a ferrimagnetically ordered state is realized even in the weak coupling limit. The introduction of the Coulomb interaction lifts the macroscopic degeneracy at the Fermi level, and induces finite staggered magnetization as well as uniform magnetization. Likewise, the spatial distribution of the magnetizations continuously changes with increasing interaction strength. The crossover behavior in the magnetically ordered states is also addressed in terms of the perpendicular space analysis.

cond-mat.str-el↗

arXiv2022

Thermally enhanced Majorana-mediated spin transport in the Kitaev model

We study how stable the Majorana-mediated spin transport in a quantum spin Kitaev model is against thermal fluctuations. Using the time-dependent thermal pure quantum state method, we examine finite-temperature spin dynamics in the Kitaev model. The model exhibits two characteristic temperatures $T_L$ and $T_H$, which correspond to energy scales of the local flux and the itinerant Majorana fermion, respectively. At low temperatures $(T\ll T_L)$, an almost flux-free state is realized and the spin excitation propagates in a similar way to that for the ground state. Namely, after the magnetic pulse is introduced at one of the edges, the itinerant Majorana fermions propagate the spin excitations even through the quantum spin liquid state region, and oscillations in the spin moment appear in the other edge with a tiny magnetic field. When $T\sim T_L$, larger oscillations in the spin moments are induced in the other edge, compared to the results at the ground state. At higher temperatures, excited $Z_2$ fluxes disturb the coherent motion of the itinerant Majorana fermions, which suppresses the spin propagation. Our results demonstrate a crucial role of thermal fluctuations in the Majorana-mediated spin transport.

cond-mat.str-el↗

arXiv2021

Photoinduced Phase Transition in Two-Band model on Penrose Tiling

We study the effects of the photo irradiation on the band insulating state in the two-band Hubbard model on the Penrose tiling. Examining the time- and site-dependent physical quantities, we find that the excitionic state is dynamically induced with site-dependent order parameters. It is also clarified that, in the excitonic state induced by the photo irradiation, local oscillatory behavior appears in the electron number as well as in the order parameter, which should be characteristic of the quasiperiodic lattice.

cond-mat.str-el↗

arXiv2021

Photo-induced Dynamics of Quasicrystalline Excitonic Insulator

We study the photo-induced dynamics of the excitonic insulator in the two-band Hubbard model on the Penrose tiling by means of the time-dependent real-space mean-field approximation. We show that, with a single-cycle electric-field pulse, the bulk (spatially averaged) excitonic order parameter decreases in the BCS regime, while it increases in the BEC regime. To clarify the dynamics peculiar to the Penrose tiling, we examine the coordination number dependence of observables and analyze the perpendicular space. In the BEC regime, characteristic oscillations of the electron number at each site are induced by the pulse, which are not observed in normal crystals. On the other hand, the dynamics in the BCS regime is characterized by drastic change in the spatial pattern of the excitonic order parameter.

cond-mat.str-el↗

arXiv2021

Role of Majorana fermions in spin transport of anisotropic Kitaev model

We study a quantum spin Kitaev model with zigzag edges to clarify the effects of anisotropy in the exchange couplings on the spin propagation. We simulate the spin and Majorana dynamics triggered by a magnetic pulse, using the real-space time-dependent Majorana mean-field theory. When the anisotropy is small, the dispersion of the itinerant Majorana fermions remains gapless, where the velocity of the spin propagation matches the group velocity of the itinerant Majorana fermions at the nodal points. On the other hand, in the gapped system with a large anisotropy, the spin propagation is strongly suppressed although its nature depends on the shape of the pulse. The spin transport in the junction system described by the Kitaev models with distinct anisotropies is also dressed.

cond-mat.str-el↗

arXiv2021

Majorana correlations in the Kitaev model with ordered-flux structures

We study the effects of the flux configurations on the emergent Majorana fermions in the $S=1/2$ Kitaev model on a honeycomb lattice, where quantum spins are fractionalized into itinerant Majorana fermions and localized fluxes. A quantum spin liquid appears as the ground state of the Kitaev model in the flux-free sector, which has intensively been investigated so far. In this flux sector, the Majorana fermion system has linear dispersions and shows power law behavior in the Majorana correlations. On the other hand, periodically-arranged flux configurations yield low-energy excitations in the Majorana fermion system, which are distinctly different from those in the flux-free state. We find that one of the periodically arranged flux states results in the gapped Majorana dispersion and the exponential decay in the Majorana correlations. The Kitaev system with another flux configuration exhibits a semi-Dirac like dispersion, leading to the power law decay with a smaller power than that in the flux-free sector along symmetry axes. We also examine the effect of the randomness in the flux configurations and clarify that the Majorana density of states is filled by increasing the flux density, and power-law decay in the Majorana correlations remains. The present results could be important to control the motion of Majorana fermions, which carries the spin excitations, in the Kitaev candidate materials.

cond-mat.str-el↗

arXiv2021

Unconventional Pairing from Local Orbital Fluctuations in Strongly Correlated A$_3$C$_{60}$

The pairing mechanism in A$_3$C$_{60}$ is investigated by studying the properties of a three-orbital Hubbard model with antiferromagnetic Hund coupling in the normal and superconducting phase. Local orbital fluctuations are shown to be substantially enhanced in the superconducting state, with a fluctuation energy scale that matches the low-energy peak in the spectral weight of the order parameter. Our results demonstrate that local orbital fluctuations provide the pairing glue in strongly correlated fulleride superconductors and support the spin/orbital freezing theory of unconventional superconductivity. They are also consistent with the experimentally observed universal relation between the gap energy and local susceptibility in a broad range of unconventional superconductors.

cond-mat.str-el↗

arXiv2020

High-harmonic generation in one-dimensional Mott insulator

We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three step model for a doublon-holon pair. We argue that the HHG in the one-dimensional Mott insulator is closely related to the dispersion of the doublon-holon pair with respect to its relative momentum, which is not necessarily captured by the single-particle spectrum due to the many-body nature of the elementary excitations. For the comparison to semiconductors, we introduce effective models obtained from the Schrieffer-Wolff transformation, i.e. a strong-coupling expansion, which allows us to disentangle the different processes involved in the Hubbard model: intraband dynamics of doublons and holons, interband dipole excitations, and spin exchanges. These demonstrate the formal similarity of the Mott system to the semiconductor models in the dipole gauge, and reveal that the spin dynamics, which does not directly affect the charge dynamics, can reduce the HHG intensity. We also show that the long-range component of the intraband dipole moment has a substantial effect on the HHG intensity, while the correlated hopping terms for the doublons and holons essentially determine the shape of the HHG spectrum. A new numerical method to evaluate single-particle spectra within the iTEBD method is also introduced.

cond-mat.str-el↗