arXiv subjects

Masahiko G. Yamada

Publications and source records attributed to Masahiko G. Yamada.

At least 19 recordsLinked to original sources

arXiv2026

Gapped topological spin-orbital liquid on the honeycomb lattice

We perform large-scale density matrix renormalization group simulations of the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice to address the long-standing question of its ground state in an unbiased and quantitatively controlled manner. We find reliable numerical evidence that the ground state is a gapped spin-orbital liquid, presumably with a $Z_4$ topological order, characterized by a finite topological entanglement entropy close to $\ln(4)$, the absence of both $\mathrm{SU}(4)$ and lattice symmetry breaking, and a variationally optimized ground-state energy well below the previously proposed $π$-flux variational state. By exploiting full $\mathrm{SU}(4)$ symmetry and keeping up to 12,800 $\mathrm{SU}(4)$ multiplets, corresponding to more than one million $\mathrm{U}(1)$ states, we achieve unprecedented accuracy for two-dimensional $\mathrm{SU}(4)$ quantum magnets. Finite-size scaling of energies and entanglement entropies supports a robust gapped phase in the two-dimensional limit, while a gapless critical state on narrow cylinders is identified as a proximate remnant of a Dirac spin-orbital liquid. Our results find the $\mathrm{SU}(4)$ honeycomb Heisenberg model a realization of a gapped topological spin-orbital liquid and provide convincing numerical evidence for topological order in a highly symmetric two-dimensional quantum magnet.

cond-mat.str-el↗

arXiv2026

Motivic GUT Part I: Grand Unified Theory of Topological Order

In the series of papers Motivic GUT Part I: Grand Unified Theory of Topological Order, Motivic GUT Part II: Grand Unified Theory of Symmetry-Protected Topological Order, and Motivic GUT Part III: Grand Unified Theory of Symmetry-Enriched Topological Order, we propose a unified framework for gapped topological phases based on the Grothendieck-Kitaev-Lurie motivic yoga. In the spirit of Grothendieck's rising sea, we argue that the classification problem can only be properly addressed after identifying the correct higher-categorical ambient space in which its full richness appears. In this first part, we propose a unified definition of gapped topological order in spatial dimension $d$ in terms of unitary fusion $(\infty,d)$-categorical data, considered up to Morita equivalence. For $d=2$, this framework recovers unitary modular tensor categories. For $d>2$, it naturally leads to genuinely higher-categorical structures. This suggests a Copernican turn in the theory of topological phases: many existing classification schemes should be reinterpreted as lower-categorical shadow realizations of intrinsically $\infty$-categorical objects.

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arXiv2024

Nonreciprocal heat transport in the Kitaev chiral spin liquid

Nonreciprocal transport, characterized by its direction-selective nature, holds significant potential for applications in various devices. In this study, we investigate nonreciprocal heat transport in Majorana systems, specifically focusing on the Kitaev chiral spin liquid under external magnetic fields. Our theoretical examination focuses on effects of open boundaries in which the Majorana edge modes exist, and the inversion symmetry is broken, which leads to the Dzyaloshinskii-Moriya interaction (DMI). Through perturbation theory, we demonstrate that DMI induces asymmetric hopping, resulting in the asymmetry of the Majorana band. The results of nonreciprocal heat currents are presented for various directions of external magnetic fields, and we discuss the relation between the current and the field-directions. The potential exists to manipulate both of the directions and magnitude of the nonreciprocal current by varying external magnetic fields and apply to heat transfer devices.

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arXiv2023

Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid

In the Kitaev chiral spin liquid, Ising anyons are realized as $Z_2$ fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a $Z_2$ flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this non-local spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the non-local correlation can be detected electrically via the measurement of non-local conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.

cond-mat.str-el↗

arXiv2022

Matrix Product Renormalization Group: Potential Universal Quantum Many-Body Solver

The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous tensor network algorithms, which we name a matrix product renormalization group (MPRG). MPRG is a universal quantum many-body solver, which potentially works at both zero and finite temperatures, in two and higher dimensions, and is even applicable to open quantum systems. Furthermore, MPRG does not rely on any variational principles and thus supports any kind of non-Hermitian systems in any dimension. As a demonstration, we present critical properties of the Yang-Lee edge singularity in one dimension as a representative non-Hermitian system.

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arXiv2022

Engineering Yang-Lee anyons via Majorana bound states

We propose the platform of a Yang-Lee anyon system which is constructed from Majorana bound states in topological superconductors. Yang-Lee anyons, described by the non-unitary conformal field theory with the central charge $c=-22/5$, are non-unitary counterparts of Fibonacci anyons, obeying the same fusion rule, but exhibiting non-unitary non-Abelian braiding statistics. We consider a topological superconductor junction system coupled with dissipative electron baths, which realizes a non-Hermitian interacting Majorana system. Numerically estimating the central charge, we examine the condition that the non-Hermitian Majorana system can simulate the Ising spin model of the Yang-Lee edge singularity, and confirm that, by controlling model parameters in a feasible way, the Yang-Lee edge criticality is realized. On the basis of this scenario, we present the scheme for the fusion, measurement and braiding of Yang-Lee anyons in our proposed setup.

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arXiv2022

Intrinsic Anomalous Thermal Hall Effect in the Unconventional Superconductor UTe2

We investigate the intrinsic anomalous thermal Hall effect as an effective probe of the order parameters of non-unitary pairing states of the putative spin-triplet superconductor UTe$_2$. We consider all symmetry-allowed non-unitary states under magnetic fields comprehensively, and calculate the anomalous Hall conductivity arising from time-reversal symmetry-breaking Weyl point nodes of the gap functions, assuming three types of Fermi surfaces; ellipsoid-shaped, cylinder-shaped, and ring-shaped ones, which are predicted by previous band calculations. We find the nonzero anomalous thermal Hall conductivity in the certain ratio of the two irreducible representations. The results may be utilized for future exploration of pairing states of UTe$_2$.

cond-mat.supr-con↗

arXiv2022

Thermodynamic signature of the $\mathrm{SU}(4)$ spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem

The $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice is expected to host a quantum spin-orbital liquid at low temperature with an astonishing candidate material, $α$-ZrCl$_3$. We employed the canonical thermal pure quantum state method to investigate the finite-temperature phase of this model. Exploiting the full symmetry of $\mathrm{SU}(4)$, the calculation up to a 24-site cluster, which is equivalent to 48 sites in the spin-1/2 language, is possible. This state-of-the-art computation with large-scale parallelization enables us to capture the thermodynamic properties of the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice. In particular, the specific heat shows a characteristic peak-and-shoulder structure, which should be related to the nature of the low-temperature quantum spin-orbital liquid phase. We also discuss what can be concluded from the assumption that the ground state is gapped and symmetric in view of the generalized Lieb-Schultz-Mattis theorem.

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arXiv2021

Quantum liquid crystals in the finite-field K$Γ$ model for $α$-RuCl$_3$

We study the extended Kitaev model called the K$Γ$ model, using a perturbative expansion combined with a well-controlled mean-field approximation and a cutting-edge exact diagonalization. In the phase diagram, we discover a nematic Kitaev spin liquid and a Kekulé Kitaev spin liquid. The former potentially explains the high-field nematic state with zero Chern number experimentally observed in $α$-RuCl$_3$, even for sufficiently small values of $Γ/|K|$. The latter has a Majorana zero mode in its $Z_3$ vortex core, which can be potentially controlled by the domain wall motion. This opens a possible application of the quantum liquid crystal phases in the K$Γ$ model to the topological quantum computation.

cond-mat.str-el↗

arXiv2021

Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid

$α$-RuCl$_3$ is a promising candidate material for the Kitaev spin liquid state where the half quantization of the thermal Hall effect, suggesting a topological character, has been observed. However, its relation to the existence of chiral Majorana fermions, which is predicted from the theory of the Kitaev model, is still under debate. Here we propose a more direct signature of a chiral Majorana edge mode which emerges in a universal scaling of the Drude weight of the edge spin Seebeck effect in the Kitaev model. Moreover, the absence of backscatterings in the chiral edge mode results in the generation of a dissipationless spin current in spite of an extremely short spin correlation length close to a lattice constant in the bulk. This result is not only experimentally observable, but also opens a way towards spintronics application of Kitaev materials. In contrast to magnetically ordered systems, a Kitaev spin liquid state is stable even in the atomic scale and makes it possible to fabricate a highly integrated device with substantial efficiency to generate a spin current. This proposal for using $α$-RuCl$_3$ as a nano-scale device will pioneer Kitaev spintronics.

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arXiv2021

$\mathrm{SU}(4)$-Symmetric Quantum Spin-Orbital Liquids on Various Lattices

An emergent $\mathrm{SU}(4)$ symmetry discovered in the microscopic model for $d^1$ honeycomb materials [M.~G.~Yamada, M.~Oshikawa, and G.~Jackeli, Phys. Rev. Lett. \textbf{121}, 097201 (2018).] has enabled us to tailor exotic $\mathrm{SU}(4)$ models in real materials. In the honeycomb structure, the emergent $\mathrm{SU}(4)$ Heisenberg model would potentially have a quantum spin-orbital liquid ground state due to the \textit{multicomponent frustration}, and we can expect similar spin-orbital liquids also in three-dimensinal versions of the honeycomb lattice. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and entangled together due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic \textit{orbitalon} excitations at low temperature.

cond-mat.str-el↗

arXiv2021

Electric probe for the toric code phase in Kitaev materials through the hyperfine interaction

The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and $α$-RuCl$_3$. In the recent experiment of $α$-RuCl$_3$, the signature of a nematic transition to the gapped toric code phase, which breaks the $C_3$ symmetry of the system, has been observed through the angle dependence of the heat capacity. We here propose a mechanism by which the nematic transition can be detected electrically. This is seemingly impossible because $J_\textrm{eff}=1/2$ spins do not have an electric quadrupole moment (EQM). However, in the second-order perturbation the virtual state with a nonzero EQM appears, which makes the nematic order parameter detectable by nuclear magnetic resonance and Mössbauer spectroscopy. The purely magnetic origin of EQM is different from conventional electronic nematic phases, allowing the direct detection of the realization of Kitaev's toric error-correction code.

cond-mat.str-el↗

arXiv2021

Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields

We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets. It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from $\pm 1$ to zero. This gapful spin liquid state with zero Chern number is nothing but the toric code phase. Our result potentially explains the topological nematic transition recently observed in $α$-RuCl$_3$ via heat capacity measurements [O. Tanaka et al., arXiv:2007.06757].

cond-mat.str-el↗

arXiv2020

Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group

A projective symmetry group (PSG) has been regarded as a classification theory of spin liquids. However, it does not include a symmetry-protected topological order of fermionic spinon excitations, and thus the classification of gapped spin liquids is incomplete. We demonstrate the classification beyond PSG by utilizing the Kitaev model on the squareoctagon lattice, where two gapped spin liquids are distinguished by a topological $Z_2$ invariant. This $Z_2$ invariant can be defined solely by the time-reversal and translation symmetries on condition that the time-reversal symmetry is implemented projectively. Thus, it is a hidden class of topological Kitaev spin liquids with helical edge states, which has been ignored for a long time. This suggests that there exists an unknown classification scheme of gapped spin liquids beyond PSG.

cond-mat.str-el↗

arXiv2020

Anderson-Kitaev spin liquid

The bond-disordered Kitaev model attracts much attention due to the experimental relevance in $α$-RuCl$_3$ and $A_3$LiIr$_2$O$_6$ ($A=$ H, D, Ag, $\textit{etc.}$). Applying a magnetic field to break the time-reversal symmetry leads to a strong modulation in mass terms for Dirac cones. Because of the smallness of the flux gap of the Kitaev model, a small bond disorder can have large influence on itinerant Majorana fermions, and Majorana fermions will be in the Anderson localization state immediately. We call this immobile liquid state Anderson-Kitaev liquid state with two localized Majorana fermions, one frozen by gauge fluctuations and the other localized by disordered mass terms. The quantization of the thermal Hall conductivity $κ/T$ disappears by a quantum Hall transition induced by a small disorder, and $κ/T$ shows a rapid crossover into the Anderson-Kitaev liquid with a negligible Hall current. Especially, the critical disorder strength $δJ_{c1} \sim 0.05$ in the unit of the Kitaev interaction would have many implications for the stability of Kitaev spin liquids.

cond-mat.str-el↗

arXiv2020

Quantum valence bond ice theory for proton-driven quantum spin-dipole liquids

We present a theory of a hybrid quantum liquid state, $\textit{quantum spin-dipole liquid}$ (QSDL), in a hydrogen-bonded electron system, by combining a quantum proton ice and Anderson's resonating valence bond spin liquid theory, motivated by the recent experimental discovery of a quantum spin liquid with proton fluctuations in $κ$-H$_3$(Cat-EDT-TTF)$_2$ (a.k.a. H-Cat). In our theory, an electron spin liquid and a proton dipole liquid are realized simultaneously in the ground state called $\textit{quantum valence bond ice}$. In this state, neither of them can be established independently of the other. Analytical and numerical calculations reveal that this state has a large entanglement entropy between spins and dipoles, which is far beyond the (crude) Born-Oppenheimer approximation. We also examine the stability of QSDL with respect to perturbations and discuss implications for experiments in H-Cat and its deuterated analog D-Cat.

cond-mat.str-el↗

arXiv2020

Magnetic and Electronic Properties of Spin-Orbit Coupled Dirac Electrons on a $(001)$ Thin Film of Double Perovskite Sr$_2$FeMoO$_6$

We present an interacting model for the electronic and magnetic behavior of a strained $(001)$ atomic layer of Sr$_2$FeMoO$_6,$ which shows room-temperature ferrimagnetism and magnetoresistance with potential spintronics application in the bulk. We find that the strong spin-orbit coupling in the molybdenum 4$d$ shell gives rise to a robust ferrimagnetic state with an emergent spin-polarized electronic structure consisting of flat bands and four massive or massless Dirac dispersions. Based on the spin-wave theory, we demonstrate that the magnetic order remains intact for a wide range of doping, leading to the possibility of exploring flat band physics, such as Wigner crystallization in electron-doped Sr$_{2-x}$La$_{x}$FeMoO$_6.$

cond-mat.str-el↗

arXiv2020

PhD Thesis: Searching for an emergent SU(4) symmetry in real materials

The enhancement of the spin-space symmetry from the usual $\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ with $N>2$ is promising for finding nontrivial quantum spin liquids, but the realization of $\mathrm{SU}(N)$ spin systems in real materials is still challenging. Although there is a proposal in cold atomic systems, in magnetic materials with a spin-orbital degree of freedom it is difficult to achieve the $\mathrm{SU}(N)$ symmetry by fine tuning. Here we propose a new mechanism by which the $\mathrm{SU}(4)$ 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 $\mathrm{SU}(4)$-breaking hopping between the $J_\textrm{eff}=3/2$ quartets. However, in the honeycomb structure, a gauge transformation maps the system to an $\mathrm{SU}(4)$-symmetric Hubbard model, which means that the system has a hidden symmetry in spite of its large spin-orbit coupling. In the strong repulsion limit at quarter filling, as expected in $α$-ZrCl$_3,$ the low-energy effective model is the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and correlated together at low temperature due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic "orbitalon" excitations at low temperature, which we have named here in distinction from orbitons in the symmetry-broken Jahn-Teller phases.

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