arXiv subjects

Seiji Yunoki

Publications and source records attributed to Seiji Yunoki.

At least 73 records · Page 4Linked to original sources

arXiv2021

QMC study of the chiral Heisenberg Gross-Neveu universality class

We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a $d$-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the $d$-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number $N$ of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.

cond-mat.str-el↗

arXiv2021

Higher-Order Topological Mott Insulator on the Pyrochlore Lattice

We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a $\mathbb{Z}_{4}$ spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.

cond-mat.str-el↗

arXiv2021

Phase transitions in the frustrated Ising ladder with stoquastic and nonstoquastic catalysts

The role of nonstoquasticity in the field of quantum annealing and adiabatic quantum computing is an actively debated topic. We study a strongly-frustrated quasi-one-dimensional quantum Ising model on a two-leg ladder to elucidate how a first-order phase transition with a topological origin is affected by interactions of the $\pm XX$-type. Such interactions are sometimes known as stoquastic (negative sign) and nonstoquastic (positive sign) "catalysts". Carrying out a symmetry-preserving real-space renormalization group analysis and extensive density-matrix renormalization group computations, we show that the phase diagrams obtained by these two methods are in qualitative agreement with each other and reveal that the first-order quantum phase transition of a topological nature remains stable against the introduction of both $XX$-type catalysts. This is the first study of the effects of nonstoquasticity on a first-order phase transition between topologically distinct phases. Our results indicate that nonstoquastic catalysts are generally insufficient for removing topological obstacles in quantum annealing and adiabatic quantum computing.

quant-ph↗

arXiv2021

Quantum-inspired search method for low-energy states of classical Ising Hamiltonians

We develop a quantum-inspired numerical procedure for searching low-energy states of a classical Hamiltonian composed of two-body fully-connected random Ising interactions and a random local longitudinal magnetic field. In this method, we introduce infinitesimal quantum interactions that do not commute with the original Ising Hamiltonian, and repeatedly generate and truncate direct product states, inspired by the Krylov subspace method, to obtain the low-energy states of the original classical Ising Hamiltonian. The computational cost is controlled by the form of infinitesimal quantum interactions (e.g., one-body or two-body interactions) and the numbers of infinitesimal interaction terms introduced, different initial states considered, and low-energy states kept during the iteration. For a demonstrate of the method, here we introduce as the infinitesimal quantum interactions pair products of Pauli $X$ operators acting on different sites and on-site Pauli $X$ operators into the random Ising Hamiltonian, in which the numerical cost is $O(N^3)$ per iteration with the system size $N$. We consider 120 instances of the random coupling realizations for the random Ising Hamiltonian with $N$ up to 600 and search the 120 lowest-energy states for each instance. We find that the time-to-solution by the quantum-inspired method proposed here, with parallelization in terms of the different initial states, for searching the ground state of the random Ising Hamiltonian scales approximately as $N^5$ for $N$ up to 600. We also examine the basic physical properties such as the ensemble-averaged ground-state and first-excited energies and the ensemble-averaged number of states in the low-energy region of the random Ising Hamiltonian.

cond-mat.stat-mech↗

arXiv2021

Quantum spin solver near saturation: QS$^3_{~}$

We develop a program package named QS$^{3}$ [\textipa{kjú:-és-kjú:b}] based on the (thick-restart) Lanczos method for analyzing spin-1/2 XXZ-type quantum spin models on spatially uniform/non-uniform lattices near fully polarized states, which can be mapped to dilute hardcore Bose systems. All calculations in QS$^{3}$, including eigenvalue problems, expectation values for one/two-point spin operators, and static/dynamical spin structure factors, are performed in the symmetry-adapted bases specified by the number $N_{\downarrow}$ of down spins and the wave number $\boldsymbol{k}$ associated with the translational symmetry without using the bit representation for specifying spin configurations. Because of these treatments, QS$^{3}$ can support large-scale quantum systems containing more than 1000 sites with dilute $N_{\downarrow}$. We show the benchmark results of QS$^{3}$ for the low-energy excitation dispersion of the isotropic Heisenberg model on the $10\times10\times10$ cubic lattice, the static and dynamical spin structure factors of the isotropic Heisenberg model on the $10\times10$ square lattice, and the open-MP parallelization efficiency on the supercomputer (Ohtaka) based on AMD Epyc 7702 installed at the Institute for the Solid State Physics (ISSP). Theoretical backgrounds and the user interface of QS$^{3}$ are also described.

physics.comp-ph↗

arXiv2021

Spin-charge conversion and current vortex in spin-orbit coupled systems

Using response theory, we calculate the charge-current vortex generated by spin pumping at a point-like contact in a system with Rashba spin-orbit coupling. We discuss the spatial profile of the current density for finite temperature and for the zero-temperature limit. The main observation is that the Rashba spin precession leads to a charge current that oscillates as a function of the distance from the spin-pumping source, which is confirmed by numerical simulations. In our calculations, we consider a Rashba model on a square lattice, for which we first review the basic properties related to charge and spin transport. In particular, we define the charge- and spin-current operators for the tight-binding Hamiltonian as the currents coupled linearly with the U(1) and SU(2) gauge potentials, respectively. By analogy to the continuum model, the spin-orbit-coupling Hamiltonian on the lattice is then introduced as the generator of the spin current.

cond-mat.mes-hall↗

arXiv2021

Unified description of cuprate superconductors using four-band $d$-$p$ model

In the 35 years since the discovery of cuprate superconductors, we have not yet reached a unified understanding of their properties, including their material dependence of the superconducting transition temperature $T_{\text{c}}$. The preceding theoretical and experimental studies have provided an overall picture of the phase diagram, and some important parameters for the $T_{\text{c}}$, such as the contribution of the Cu $d_{z^2}$ orbital to the Fermi surface and the site-energy difference $Δ_{dp}$ between the Cu $d_{x^2-y^2}$ and O $p$ orbitals. However, they are somewhat empirical and limited in scope, always including exceptions, and do not provide a comprehensive view of the series of cuprates. Here we propose a four-band $d$-$p$ model as a minimal model to study material dependence in cuprates. Using the variational Monte Carlo method, we theoretically investigate the phase diagram for the La$_2$CuO$_4$ and HgBa$_2$CuO$_4$ systems and the correlation between the key parameters and the superconductivity. Our results comprehensively account for the empirical correlation between $T_{\text{c}}$ and model parameters, and thus can provide a guideline for new material design. We also show that the effect of the nearest-neighbor $d$-$d$ Coulomb interaction $V_{dd}$ is actually quite important for the stability of superconductivity and phase competition.

cond-mat.supr-con↗

arXiv2021

Generation of current vortex by spin current in Rashba systems

Employing unbiased large-scale time-dependent density-matrix renormalization-group simulations, we demonstrate the generation of a charge-current vortex via spin injection in the Rashba system. The spin current is polarized perpendicular to the system plane and injected from an attached antiferromagnetic spin chain. We discuss the conversion between spin and orbital angular momentum in the current vortex that occurs because of the conservation of the total angular momentum and the spin-orbit interaction. This is in contrast to the spin Hall effect, in which the angular-momentum conservation is violated. Finally, we predict the electromagnetic field that accompanies the vortex with regard to possible future experiments.

cond-mat.mes-hall↗

arXiv2021

Emergent long-range interaction and state-selective localization in a strongly driven $ XXZ $ model

The nonlinear effect of a driving force in periodically driven quantum many-body systems can be systematically investigated by analyzing the effective Floquet Hamiltonian. In particular, under an appropriate definition of the effective Hamiltonian, simple driving forces may result in non-local interactions. Here we consider a driven $ XXZ $ model to show that four-site interactions emerge owing to the driving force, which can produce state-selective localization, a phenomenon where some limited Ising-like product states become fixed points of dynamics. We first derive the effective Hamiltonian of a driven $ XXZ $ model on an arbitrary lattice for general spin $ S $. We then analyze in detail the case of a one-dimensional chain with $ S=1/2 $ as a special case and find a condition imposed on the cluster of four consecutive sites as a necessary and sufficient condition for the state of the whole system to be localized. We construct such a localized state based on this condition and demonstrate it by numerical simulation of the original time-periodic model.

quant-ph↗

arXiv2021

Quantum Power Method by a Superposition of Time-Evolved States

We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |ψ\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a time-independent Hamiltonian of interest, and $|ψ\rangle$ is a quantum state. We show that the number of gates required for approximating $\hat{\cal H}^n$ scales linearly in the power and the number of qubits, making it a promising application for near term quantum computers. Using numerical simulation, we show that the power method can control systematic errors in approximating the Hamiltonian power ${\hat{\cal H}^n}$ for $n$ as large as 100. As an application, we combine our method with a multireference Krylov-subspace-diagonalization scheme to show how one can improve the estimation of ground-state energies and the ground-state fidelities found using a variational-quantum-eigensolver scheme. Finally, we outline other applications of the quantum power method, including several moment-based methods. We numerically demonstrate the connected-moment expansion for the imaginary-time evolution and compare the results with the multireference Krylov-subspace diagonalization.

quant-ph↗

arXiv2021

Discretized quantum adiabatic process for free fermions and comparison with the imaginary-time evolution

Motivated by recent progress of quantum technologies, we study a discretized quantum adiabatic process for a one-dimensional free fermion system described by a variational wave function, i.e., a parametrized quantum circuit. The wave function is composed of $M$ layers of two elementary sets of time-evolution operators, each set being decomposed into commutable local operators. The evolution time of each time-evolution operator is treated as a variational parameter so as to minimize the expectation value of the energy. We show that the exact ground state is reached by applying the layers of time-evolution operators as many as a quarter of the system size. This is the minimum number $M_B$ of layers set by the limit of speed, i.e., the Lieb-Robinson bound, for propagating quantum entanglement via the local time-evolution operators. Quantities such as the energy $E$ and the entanglement entropy $S$ of the optimized variational wave function with $M < M_B$ are independent of the system size $L$ but fall into some universal functions of $M$. The development of the entanglement in these ansatz is further manifested in the progressive propagation of single-particle orbitals in the variational wave function. We also find that the optimized variational parameters show a systematic structure that provides the optimum scheduling function in the quantum adiabatic process. We also investigate the imaginary-time evolution of this variational wave function, where the causality relation is absent due to the non-unitarity of the imaginary-time evolution operators, thus the norm of the wave function being no longer conserved. We find that the convergence to the exact ground state is exponentially fast, despite that the system is at the critical point, suggesting that implementation of the non-unitary imaginary-time evolution in a quantum circuit is highly promising to further shallow the circuit depth.

quant-ph↗

arXiv2020

Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited

We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components $N$=8 in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a $d$-wave pairing field, inducing Dirac cones in the single particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, that is the canonical model for graphene, despite the unit cells being apparently different (e.g. they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting $N$ and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the $N$=8 chiral Heisenberg universality class are $ν$=1.05(5), $η_ϕ$=0.75(4), and $η_ψ$=0.23(4), which are compared with the previous numerical estimations.

cond-mat.str-el↗

arXiv2020

Spin Dynamics in the t-t'-J Model: Dynamical Density-Matrix Renormalization Group Study

The ground state of a hole-doped t-t'-J ladder with four legs favors a striped charge distribution. Spin excitation from the striped ground state is known to exhibit incommensurate spin excitation near q=(pi,pi) along the leg direction (qx direction). However, an outward dispersion from the incommensurate position toward q=(0,pi) is strong in intensity, inconsistent with inelastic neutron scattering (INS) experiment in hole-doped cuprates. Motivated by this inconsistency, we use the t-t'-J model with m x n=96 lattice sites by changing lattice geometry from four-leg (24x4) to rectangle (12x8) shape and investigate the dynamical spin structure factor by using the dynamical density matrix renormalization group. We find that the outward dispersion has weak spectral weights in the 12x8 lattice, accompanied with the decrease of excitation energy close to q=(pi,pi), being consistent with the INS data. In the 12x8 lattice, weakening of incommensurate spin correlation is realized even in the presence of the striped charge distribution. For further investigation of geometry related spin dynamics, we focus on direction dependent spin excitation reported by recent resonant inelastic x-ray scattering (RIXS) for cuprate superconductors and obtain a consistent result with RIXS by examining an 8x8 t-t'-J square lattice.

cond-mat.str-el↗

arXiv2020

Emergence of a thermal equilibrium in a subsystem of a pure ground state by quantum entanglement

By numerically exact calculations of spin-1/2 antiferromagnetic Heisenberg models on small clusters, we demonstrate that quantum entanglement between subsystems $A$ and $B$ in a pure ground state of a whole system $A+B$ can induce thermal equilibrium in subsystem $A$. Here, the whole system is bipartitoned with the entanglement cut that covers the entire volume of subsystem $A$. Temperature ${\cal T}_{A}$ of subsystem $A$ is not a parameter but can be determined from the entanglement von Neumann entropy ${\cal S}_{A}$ and the total energy ${\cal E}_{A}$ of subsystem $A$ calculated for the ground state of the whole system. We show that temperature ${\cal T}_{A}$ can be derived by minimizing the relative entropy for the reduced density matrix operator of subsystem $A$ and the Gibbs state (i.e., thermodynamic density matrix operator) of subsystem $A$ with respect to the coupling strength between subsystems $A$ and $B$. Temperature ${\cal T}_{A}$ is essentially identical to the thermodynamic temperature, for which the entropy and the internal energy evaluated using the canonical ensemble in statistical mechanics for the isolated subsystem $A$ agree numerically with the entanglement entropy ${\cal S}_{A}$ and the total energy ${\cal E}_{A}$ of subsystem $A$.Fidelity calculations ascertain that the reduced density matrix operator of subsystem $A$ for the pure but entangled ground state of the whole system $A+B$ matches, within a maximally $1.5\%$ error in the finite size clusters studied, the thermodynamic density matrix operator of subsystem $A$ at temperature ${\cal T}_{A}$. We argue that quantum fluctuation in an entangled pure state can mimic thermal fluctuation in a subsystem. We also provide two simple but nontrivial analytical examples of free bosons and free fermions for which these statements are exact. We furthermore discuss implications and possible applications of our finding.

quant-ph↗

arXiv2020

Proximate Kitaev system for an intermediate magnetic phase in in-plane magnetic fields

Motivated by the magnetic phase transition of a proximate Kitaev system $α$-RuCl$_3$ in the presence of a magnetic field, we study the simplest but essential quantum spin model with the ferromagnetic nearest neighboring (NN) Kitaev interaction and additional antiferromagnetic third NN Heisenberg interaction. Employing both exact diagonalization and density matrix renormalization group methods, we demonstrate that the model shows the magnetic phase transition from the zigzag order phase to the spin polarized phase through an intermediate phase in both cases when an in-plane magnetic field is applied perpendicular to the NN bond direction and when an out-of-plane field is applied, in good agreement with experimental observations. Furthermore, we verify that additional symmetric off-diagonal $Γ$ interaction and ferromagnetic Heisenberg interaction between NN spins can both suppress the intermediate phase with the in-plane field. Our result gives important clues on determining relevant interactions in the field-induced magnetic phase transition of proximate Kiteav systems.

cond-mat.str-el↗

arXiv2020

Effect of on-site Coulomb repulsion on ferromagnetic fluctuations in heavily over-doped cuprates

We theoretically study ferromagnetic (FM) fluctuations that are experimentally observed in the heavily overdoped region of cuprate superconductors. To explore the origin of FM fluctuations, we evaluate the spin susceptibilities of a single-band Hubbard model within the fluctuation exchange approximation. Model parameters are derived using the Wannierization technique and the constrained random phase approximation method based on the maximally localized Wannier functions. The constrained random phase approximation calculations reveal that the on-site Coulomb interaction decreases with an increase in hole doping. By taking this reduction of the on-site Coulomb interaction into account, the emergence of FM fluctuations in heavily overdoped cuprates can be explained.

cond-mat.supr-con↗

arXiv2020

Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model

We investigate the phase transition of the dodecahedron model on the square lattice. The model is a discrete analogue of the classical Heisenberg model, which has continuous $O(3)$ symmetry. In order to treat the large on-site degree of freedom $q = 20$, we develop a massively parallelized numerical algorithm for the corner transfer matrix renormalization group method, incorporating EigenExa, the high-performance parallelized eigensolver. The scaling analysis with respect to the cutoff dimension reveals that there is a second-order phase transition at $T^{~}_{\rm c}=0.4398(8)$ with the critical exponents $ν=2.88(8)$ and $β=0.21(1)$. The central charge of the system is estimated as $c=1.99(6)$.

cond-mat.stat-mech↗

arXiv2020

Charge stiffness and long-range correlation in the optically induced $η$-pairing state of the one-dimensional Hubbard model

We show that optical excitation of the Mott insulating phase of the one-dimensional Hubbard model can create a state possessing two of the hallmarks of superconductivity: a nonvanishing charge stiffness and long-ranged pairing correlation. By employing the exact diagonalization method, we find that the superposition of the $η$-pairing eigenstates induced by the optical pump exhibits a nonvanishing charge stiffness and a pairing correlation that decays very slowly with system size in sharp contrast to the behavior of an ensemble of thermally excited eigenstates, which has a vanishing charge stiffness and no long-ranged pairing correlations. We show that the charge stiffness is indeed directly associated with the $η$-pairing correlation in the Hubbard model. Our finding demonstrates that optical pumping can actually lead to superconducting-like properties on the basis of the $η$-pairing states.

cond-mat.str-el↗