arXiv subjects

Youhei Yamaji

Publications and source records attributed to Youhei Yamaji.

At least 37 records · Page 2Linked to original sources

arXiv2019

Ab Initio Study on Superconductivity and Inhomogeneity in Hg-based Cuprate Superconductor

Understanding physics of high-$T_c$ cuprate superconductors remains one of the important problems in materials science. Though a number of diverse theories argue about the superconductivity and competing orders, ab initio and quantitative understanding is lacking. Here, we reproduce the experimental phase diagram of HgBa$_2$CuO$_{4+y}$ by solving its ab initio low-energy effective Hamiltonian without adjustable parameters. It shows a superconducting phase in a wide range of hole density $δ$, and its competition with charge period-4 plus spin period-8 stripe order near $δ\sim 0.1$, in agreement with experimental results including recent X-ray scattering. Then a crucial role of off-site interactions in stabilizing the superconductivity is elucidated with emphasis on charge fluctuations. It also clarifies the condensation energy mainly contributed from the onsite Coulomb interaction. The present achievement will enable deeper, predictable understanding on open issues of the high-$T_c$ superconducting mechanism and promote ab initio studies on strongly correlated electrons beyond parametrized model studies.

cond-mat.str-el↗

arXiv2019

Effective Hamiltonian for cuprate superconductors derived from multi-scale ab initio scheme with level renormalization

Three-types (three-band, two-band and one-band) of effective Hamiltonians for the HgBa$_2$CuO$_4$ and three-band effective Hamiltonian for La$_2$CuO$_4$ are derived beyond the level of the constrained-GW approximation combined with the self-interaction correction (cGW-SIC) derived in Hirayama et al. Phys. Rev. B 98, 134501 (2018) by improving the treatment of the interband Hartree energy. The charge gap and antiferromagnetic ordered moment show good agreement with the experimental results when the present effective Hamiltonian is solved, indicating the importance of the present refinement. The obtained Hamiltonians will serve to clarify the electronic structures of these copper oxide superconductors and to elucidate the superconducting mechanism.

cond-mat.str-el↗

arXiv2018

Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method

The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the $d$-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration ($δ$) dependence of the Hubbard model in the ground states on a square lattice at strong coupling $U/t=10$, for the on-site interaction $U$ and the transfer $t$, using a variational Monte Carlo method. The method, which combines tensor network and Lanczos methods on top of Pfaffian wave functions, reveals a rich phase diagram, in which many orders compete severely and degenerate within the energy range of 0.01$t$. We have identified distinct phases including a uniform $d$-wave superconducting phase for $0.17\lesssim δ\lesssim0.22$ and a stripe charge/spin ordered phase for $δ\lesssim0.17$ with the stripe period depending on $δ$, together with presumable spatially coexisting antiferromagnetic and stripe order for $δ\lesssim0.07$ and coexisting stripe and $d$-wave superconductivity for $0.07\lesssimδ\lesssim0.17$. The present, improved method revealed a wider region of a charge uniform superconducting phase than the previous studies and shows a qualitative similarity to the phase diagram of the cuprate superconductors. The superconducting order parameter is largest at doping of around $δ=0.17$ in the ground state, which undergoes phase transitions from an inhomogeneous to a uniform state.

cond-mat.str-el↗

arXiv2018

Classical and quantum spin dynamics of the honeycomb $Γ$ model

Quantum to classical crossover is a fundamental question in dynamics of quantum many-body systems. In frustrated magnets, for example, it is highly non-trivial to describe the crossover from the classical spin liquid with a macroscopically-degenerate ground-state manifold, to the quantum spin liquid phase with fractionalized excitations. This is an important issue as we often encounter the demand for a sharp distinction between the classical and quantum spin liquid behaviors in real materials. Here we take the example of the classical spin liquid in a frustrated magnet with novel bond-dependent interactions to investigate the classical dynamics, and critically compare it with quantum dynamics in the same system. In particular, we focus on signatures in the dynamical spin structure factor. Combining Landau-Lifshitz dynamics simulations and the analytical Martin-Siggia-Rose (MSR) approach, we show that the low energy spectra are described by relaxational dynamics and highly constrained by the zero mode structure of the underlying degenerate classical manifold. Further, the higher energy spectra can be explained by precessional dynamics. Surprisingly, many of these features can also be seen in the dynamical structure factor in the quantum model studied by finite-temperature exact diagonalization. We discuss the implications of these results, and their connection to recent experiments on frustrated magnets with strong spin-orbit coupling.

cond-mat.stat-mech↗

arXiv2018

Path to stable quantum spin liquids in spin-orbit coupled correlated materials

The spin liquid phase is one of the prominent strongly interacting topological phases of matter whose unambiguous confirmation is yet to be reached despite intensive experimental efforts on numerous candidate materials. Recently, a new family of correlated honeycomb materials, in which strong spin-orbit coupling allows for various bond-dependent spin interactions, have been promising candidates to realize the Kitaev spin liquid. Here we study a model with bond-dependent spin interactions and show numerical evidence for the existence of an extended quantum spin liquid region, which is possibly connected to the Kitaev spin liquid state. These results are used to provide an explanation of the scattering continuum seen in neutron scattering on $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2018

Quantum spin liquid signatures in Kitaev-like frustrated magnets

Motivated by recent experiments on $α$-RuCl$_3$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K-Γ$ model, where $K$ and $Γ$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group (iDMRG), we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite size cluster computations and show that the results resemble the scattering continuum seen in neutron scattering experiments on $α$-RuCl$_3$. We discuss these results in light of recent and future experiments.

cond-mat.str-el↗

arXiv2018

Numerical Algorithm for Exact Finite Temperature Spectra and Its Application to Frustrated Quantum Spin Systems

A numerical algorithm to calculate exact finite-temperature spectra of many-body lattice Hamiltonians is formulated by combining the typicality approach and the shifted Krylov subspace method. The combined algorithm, which we name finite-temperature shifted Krylov subspace method for simulating spectra (FTK$ω$), efficiently reproduces the canonical-ensemble probability distribution at finite temperatures with the computational cost proportional to the Fock space dimension. The present FTK$ω$ enables us to exactly calculate finite-temperature spectra of many-body systems whose system sizes are twice larger than those handled by the canonical ensemble average and allows us to access the frequency domain without sequential real-time evolution often used in previous studies. By employing the reweighting method with the present algorithm, we obtain significant reduction of the numerical costs for temperature sweeps. Application to the Kiteav-Heisenberg model (KHM) on a honeycomb lattice demonstrates the capability of the FTK$ω$. The KHM shows quantum phase transitions from the quantum spin liquid (QSL) phase to magnetically ordered phases when the finite Heisenberg exchange coupling is introduced. We examine temperature dependence of dynamical spin structure factors of the KHM in proximity to the QSL. It is clarified that the crossover from a spin-excitation continuum, which is a characteristic of the QSL, to a damped high-energy magnon mode occurs at temperatures higher than the energy scale of the Heisenberg couplings or the spin gap that is a signature of the QSL at zero temperature. The crossover and the closeness to the Kitaev's QSL are quantitatively measured by the width of the excitation continuum or the magnon spectrum. The present results shed new light on analysis of neutron scattering and other spectroscopy measurements on QSL candidates.

cond-mat.str-el↗

arXiv2017

Finite-Temperature Signatures of Spin Liquids in Frustrated Hubbard Model

Finite-temperature properties of the frustrated Hubbard model are theoretically examined by using the recently proposed thermal pure quantum state, which is an unbiased numerical method for finite-temperature calculations. By performing systematic calculations for the frustrated Hubbard model, we show that the geometrical frustration controls the characteristic energy scale of the metal-insulator transitions. We also find that entropy remains large even at moderately high temperature around the region where the quantum spin liquid is expected to appear at zero temperature. We propose that this is a useful criterion whether the target systems have a chance to be the quantum spin liquid or the non-magnetic insulator at zero temperature.

cond-mat.str-el↗

arXiv2017

Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems

We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an artificial neural network is combined with a conventional variational Monte Carlo method with pair product (geminal) wave functions and quantum number projections. The combination allows an application of the machine learning scheme to interacting fermionic systems. The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.

cond-mat.str-el↗

arXiv2017

Ab initio effective Hamiltonians for cuprate superconductors

Ab initio low-energy effective Hamiltonians of two typical high-temperature copper-oxide superconductors, whose mother compounds are La$_2$CuO$_4$ and HgBa$_2$CuO$_4$, are derived by utilizing the multi-scale ab initio scheme for correlated electrons (MACE). The effective Hamiltonians obtained in the present study serve as platforms of future studies to accurately solve the low-energy effective Hamiltonians beyond the density functional theory. It allows further study on the superconducting mechanism from the first principles and quantitative basis without adjustable parameters not only for the available cuprates but also for future design of higher Tc in general. More concretely, we derive effective Hamiltonians for three variations, 1)one-band Hamiltonian for the antibonding orbital generated from strongly hybridized Cu $3d_{x^2-y^2}$ and O $2p_σ$ orbitals 2)two-band Hamiltonian constructed from the antibonding orbital and Cu $3d_{3z^2-r^2}$ orbital hybridized mainly with the apex oxygen $p_z$ orbital 3)three-band Hamiltonian consisting mainly of Cu $3d_{x^2-y^2}$ orbitals and two O $2p_σ$ orbitals. Differences between the Hamiltonians for La$_2$CuO$_4$ and HgBa$_2$CuO$_4$, which have relatively low and high critical temperatures, respectively, at optimally doped compounds, are elucidated. The main differences are summarized as i) the oxygen $2p_σ$ orbitals are farther(~3.7eV) below from the Cu $d_{x^2-y^2}$ orbital for the La compound than the Hg compound(~2.4eV) in the three-band Hamiltonian. This causes a substantial difference in the character of the $d_{x^2-y^2}-2p_σ$ antibonding band at the Fermi level and makes the effective onsite Coulomb interaction U larger for the La compound than the Hg compound for the two- and one-band Hamiltonians. ii)The ratio of the second-neighbor to the nearest transfer t'/t is also substantially different (~0.26) for the Hg and ~0.15 for the La compound in the one-band Hamiltonian.

cond-mat.supr-con↗

arXiv2017

Quantum Lattice Model Solver ${\mathcal H}Φ$

${\mathcal H}Φ$ [$aitch$-$phi$] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, ${\mathcal H}Φ$ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, ${\mathcal H}Φ$ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of ${\mathcal H}Φ$. We also show the benchmark results of ${\mathcal H}Φ$ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

cond-mat.str-el↗

arXiv2016

Ground state properties of $\mathrm{Na_2IrO_3}$ determined from $\textit{ab initio}$ Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

We investigate the ground state properties of $\mathrm{Na_2IrO_3}$ based on numerical calculations of the recently proposed {\it ab initio} Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study (Yamaji $\textit{et al.}$, Phys. Rev. Lett. $\textbf{113}$, 107201 (2014)), we apply two-dimensional density matrix renomalization group, and infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of $\mathrm{Na_2IrO_3}$ is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the $\textit{ab initio}$ value of $\mathrm{Na_2IrO_3}$ controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in $120$ degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a $16$-site unit-cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in $A_\mathrm{2}\mathrm{IrO_3}$ compounds for $A$ other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contribute to find a route to realize the Kitaev spin liquid.

cond-mat.str-el↗

arXiv2016

Finite-Temperature Variational Monte Carlo Method for Strongly Correlated Electron Systems

A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the variational Monte Carlo method originally developed for the ground state. The method is based on the path integral in the imaginary-time formulation, starting from the infinite-temperature state that is well approximated by a small number of certain random initial states. Lower temperatures are progressively reached by the imaginary-time evolution. The algorithm follows the framework of the quantum transfer matrix and finite-temperature Lanczos methods, but we extends them to treat much larger system sizes without the negative sign problem by optimizing the truncated Hilbert space on the basis of the time-dependent variational principle (TDVP). This optimization algorithm is equivalent to the stochastic reconfiguration (SR) method that has been frequently used for the ground state to optimally truncate the Hilbert space. The obtained finite-temperature states allow an interpretation based on the thermal pure quantum (TPQ) state instead of the conventional canonical-ensemble average. Our method is tested for the one- and two-dimensional Hubbard models and its accuracy and efficiency are demonstrated.

cond-mat.str-el↗

arXiv2016

Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na$_2$IrO$_3$

Contrary to the original expectation, Na$_2$IrO$_3$ is not a Kitaev's quantum spin liquid (QSL) but shows a zig-zag-type antiferromagnetic order in experiments. Here we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka $et$ $al$. in Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na$_2$IrO$_3$ proposed by Yamaji $et$ $al$. in Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and Neel temperatures: (1) Two peaks in the temperature dependence of specific heat at $T_{\ell}$ and $T_h$ caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, prominent plateau or shoulder pinned at $(R/2)\ln 2$ in the temperature dependence of entropy, where $R$ is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio $T_{\ell}/T_h$ close to or less than 0.03. According to the proposed criteria, Na$_2$IrO$_3$ is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na$_2$IrO$_3$ on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ and other related materials are also discussed.

cond-mat.str-el↗

arXiv2015

Dynamical properties of the honeycomb-lattice Iridates ${\rm Na_2IrO_3}$

We investigate the dynamical properties of ${\rm Na_2IrO_3}$. For five effective models proposed for ${\rm Na_2IrO_3}$, we numerically calculate dynamical structure factors (DSFs) with an exact diagonalization method. An effective model obtained from $ab$ $initio$ calculations explains inelastic neutron scattering experiments adequately. We further calculate excitation modes based on linearized spin-wave theory. The spin-wave excitation of the effective models obtained by $ab$ $initio$ calculations disagrees with the low-lying excitation of DSFs. We attribute this discrepancy to the location of ${\rm Na_2IrO_3}$ in a parameter space close to the phase boundary with the Kitaev spin-liquid phase.

cond-mat.str-el↗

arXiv2015

Variational Monte Carlo Method in the Presence of Spin-Orbit Interaction and Its Application to the Kitaev and Kitaev-Heisenberg Model

We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interaction. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and triplet Cooper pairs, Jastrow-Gutzwiller-type pro- jections, and quantum number projections. The generalized wave functions allow any symmetry breaking states, ranging from magnetic and/or charge ordered states to superconducting states and their fluctuations, on equal footing without any ad hoc ansatz for variational wave functions. We de- tail our optimization scheme for the generalized Pfaffian-Slater wave functions with complex-number variational parameters. Generalized quantum number projections are also introduced, which im- poses the conservation of not only spin and momentum quantum numbers but also Wilson loops. As a demonstration of the capability of the present variational Monte Carlo method, the accuracy and efficiency of the present method is tested for the Kitaev and Kitaev-Heisenberg models. The Kitaev model serves as a critical benchmark of the present method: The exact ground state of the model is a typical gapless quantum spin liquid far beyond the applicability range of simple mean-field wave functions. The newly introduced quantum number projections precisely reproduce the ground state degeneracy of the Kitaev spin liquids, in addition to their ground state energy. Our framework offers accurate solutions for the systems where strong electron correlation and spin-orbit interaction coexist.

cond-mat.str-el↗

arXiv2015

Stabilization of Topological Insulator Emerging from Electron Correlations on Honeycomb Lattice and Its Possible Relevance in Twisted Bilayer Graphene

Realization and design of topological insulators emerging from electron correlations, called topological Mott insulators (TMIs), is pursued by using mean-field approximations as well as multi-variable variational Monte Carlo (MVMC) methods for Dirac electrons on honeycomb lattices. The topological insulator phases predicted in the previous studies by the mean-field approximation for an extended Hubbard model on the honeycomb lattice turn out to disappear, when we consider the possibility of a long-period charge-density-wave (CDW) order taking over the TMI phase. Nevertheless, we further show that the TMI phase is still stabilized when we are able to tune the Fermi velocity of the Dirac point of the electron band. Beyond the limitation of the mean-field calculation, we apply the newly developed MVMC to make accurate predictions after including the many-body and quantum fluctuations. By taking the extrapolation to the thermodynamic and weak external field limit, we present realistic criteria for the emergence of the topological insulator caused by the electron correlations. By suppressing the Fermi velocity to a tenth of that of the original honeycomb lattice, the topological insulator emerges in an extended region as a spontaneous symmetry breaking surviving competitions with other orders. We discuss experimental ways to realize it in a bilayer graphenesystem.

cond-mat.str-el↗

arXiv2015

Nonequilibrium Pump-Probe Photoexcitation as a Tool for Analyzing Unoccupied Equilibrium States of Correlated Electrons

Relaxation of electrons in a Hubbard model coupled to a dissipative bosonic bath is studied to simulate the pump-probe photoemission measurement. From this insight, we propose an experimental method of eliciting unoccupied part of the single-particle spectra at the equilibrium of doped-Mott insulators. We reveal first that effective temperatures of distribution functions and electronic spectra are different during the relaxation, which makes the frequently employed thermalization picture inappropriate. Contrary to the conventional analysis, we show that the unoccupied spectra at equilibrium can be detected as the states that relax faster.

cond-mat.str-el↗