arXiv subjects

Seiji Yunoki

Publications and source records attributed to Seiji Yunoki.

At least 55 records · Page 3Linked to original sources

arXiv2024

Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method

Nonequilibrium dynamics of highly-controlled quantum systems is a challenging issue in statistical physics and quantum many-body physics, relevant to recent experimental developments of analog and digital quantum simulations. In this work, we develop a discrete phase-space approach for general SU($N$) spin systems that utilizes cluster mean field equations, which capture non-trivial quantum correlations inside each cluster, beyond the capability of the standard discrete truncated Wigner approximation for individual classical spins. Our formalism, based on a cluster phase-point operator, enables efficient numerical samplings of cluster phase-space variables, where the total number of noise variables for a direct product state is independent of the specific way in which the entire system is divided into multiple equally sized finite clusters. We numerically demonstrate that the cluster discrete truncated Wigner approximation (C-dTWA) method can reproduce key results in a recent experiment on correlation propagation dynamics in a two dimensional Bose-Hubbard system. We further compare the results of C-dTWA for clusters of $2\times 2$ sites with those from a two-dimensional tensor network method and discuss that both approaches agree very well in the short-time region, where the energy conservation is well maintained in the tensor network simulations. Since we formulate the C-dTWA method in a general form, it has the potential for application to various dynamical problems in isolated and open quantum systems, even in higher dimensions.

cond-mat.quant-gas↗

arXiv2024

Density-Matrix Renormalization Group Study of Kitaev--Heisenberg Model on a Triangular Lattice

We study the Kitaev--Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev--Heisenberg model. As suggested by previous studies, we find a 120$^\circ$ antiferromagnetic (AFM) phase, a $\mathbb{Z}_2$-vortex crystal phase, a nematic phase, a dual $\mathbb{Z}_2$-vortex crystal phase (the dual counterpart of the $\mathbb{Z}_2$-vortex crystal phase), a $\mathbb{Z}_6$ ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the $\mathbb{Z}_6 $ ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev--Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.

cond-mat.str-el↗

arXiv2024

Spin and charge dynamics of doped one-dimensional Mott insulators

Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator Ba$_{2-x}$Sr$_x$CuO$_{3+δ}$ proposed the presence of attractive charge interactions between neighboring sites if an 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: the attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.

cond-mat.str-el↗

arXiv2024

Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation

Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all virtual bonds in constant time, irrespective of the system size, with controlled accuracy, while it maintains the stability of the wavefunction norm without necessitating sequential renormalization procedures. In addition, we introduce a parallel regauging technique to partially restore the deviated canonical form, thereby improving the accuracy of the simulation in subsequent steps. We further apply this method to simulate unitary quantum dynamics and introduce an improved parallel time-evolving block-decimation (pTEBD) algorithm. We employ the improved pTEBD algorithm for extensive simulations of typical one- and two-dimensional quantum circuits, involving over 1000 qubits. The obtained numerical results unequivocally demonstrate that the improved pTEBD algorithm achieves the same level of simulation precision as the current state-of-the-art MPS algorithm but in polynomially shorter time, exhibiting nearly perfect weak scaling performance on a modern supercomputer.

quant-ph↗

arXiv2024

Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene

We investigate if and how the valence-bond-solid (VBS) state emerges in the Hubbard model on the honeycomb lattice when the Peierls-type electron-lattice coupling is introduced. We consider all possible lattice-distortion patterns allowed for this lattice model for graphene which preserve the reflection symmetry and determine the most stable configuration in the adiabatic limit by using an unbiased quantum Monte Carlo method. The VBS phase with Kekulé dimerization is found to appear as an intermediate phase between a semimetal and an antiferromagnetic Mott insulator for a moderately rigid lattice. This implies that the undistorted semimetallic graphene can be driven into the VBS phase by applying strain, accompanied by the single-particle excitation gap opening.

cond-mat.str-el↗

arXiv2023

Quantum Simulation of Finite Temperature Schwinger Model via Quantum Imaginary Time Evolution

We study the Schwinger model at finite-temperature regime using a quantum-classical hybrid algorithm. The preparation of thermal state on quantum circuit presents significant challenges. To address this, we adopt the Thermal Pure Quantum (TPQ) state approach and apply the Quantum Imaginary Time Evolution (QITE) algorithm to implement the necessary imaginary time evolution. We first compute the chiral condensate in the massless Schwinger model, verifying its consistency with the analytical solution. We then simulate the massive Schwinger model with non-zero topological $θ$-term to investigate the temperature and $θ$-dependence of the chiral condensate. Our method works well even at non-zero $θ$ regime, while the conventional lattice Monte Carlo method suffers from the sign problem in this system.

hep-lat↗

arXiv2023

Spin loop-current textures in Hubbard models

The recent experimental observations of loop current in Sr$_{2}$IrO$_{4}$, YBa$_{2}$Cu$_{3}$O$_{7}$, and Sr$_{14}$Cu$_{24}$O$_{41}$ have inspired a theoretical study that broadly redefines loop current as a manifestation of quantum liquid crystals. Using the density-matrix renormalization group method, we investigate the emergence of spin loop-current (sLC) textures in carrier-doped (i) excitonic insulators, (ii) orbital-selective Mott insulators, and (iii) two-dimensional Mott insulators, modeled by a two-orbital Hubbard model on a ladder lattice in (i) and (ii) and a single-orbital Hubbard model on a square lattice in (iii). Calculating the spatial distribution of spin current around a bond to which a pinning field is applied, we find conditions for longer-ranged sLC correlations. In system (i), when using the model parameters employed to describe the excitonic condensation, we find that a sLC texture appears near half filling, associated with an excitonic condensation in a spin channel. In system (ii), using typical sets of model parameters for BaFe$_{2}$Se$_{3}$, we find that a sLC texture appears at electron fillings where a block-type antiferromagnetism develops. In system (iii), introducing a next-nearest-neighbor hopping $t'\sim -0.25$ (in units of the nearest-neighbor hopping) suggested for high-$T_\text{c}$ cuprates, we find that an axial-sLC texture emerges at hole-carrier density $δ=0.125$, where the charge stripe simultaneously appears.

cond-mat.str-el↗

arXiv2023

Efficient variational quantum circuit structure for correlated topological phases

We propose an efficient circuit structure of variational quantum circuit \textit{Ansätze} used for the variational quantum eigensolver (VQE) algorithm in calculating gapped topological phases on the currently feasible noisy intermediate-scale quantum computers. An efficient circuit \textit{Ansatz} should include two layers: the initialization layer and the variational layer. In the initialization layer, a fixed depth circuit state with a compatible entanglement structure to the target topological phase is constructed. The circuit state is further adjusted subsequently to capture the details of the local correlations, which is dictated with the Hamiltonian, in the parametrized variational layer. Based on this strategy, we design a circuit \textit{Ansatz} to investigate the symmetry-protected topological Haldane phase in a \textit{non-exactly} solvable alternating spin-$1/2$ Heisenberg chain by VQE calculations. Main characterizations of the Haldane phase, including the long-ranged string order, the four-fold nearly degenerate ground states associated with four different localized edge mode patterns for the system with open boundaries, and the two-fold degeneracy of the entanglement spectrum, are all observed for the optimized shallow circuit state with only one depth variational layer both in numerical simulations and on real quantum computers. We further demonstrate that the computational capacity (i.e., expressibility) of this quantum circuit \textit{Ansatz} is determined not by the system size but only by the intrinsic correlation length of the system, thus implying that the scalable VQE calculation is possible.

quant-ph↗

arXiv2023

Anomalous suppression of photo-induced in-gap weight in the optical conductivity of a two-leg Hubbard ladder

Photoinduced nonequilibrium states in the Mott insulators reflect the fundamental nature of competition between itinerancy and localization of the charge degrees of freedom. The spin degrees of freedom will also contribute to the competition in a different manner depending on lattice geometry. We investigate pulse-excited optical responses of a half-filled two-leg Hubbard ladder and compare them with those of a one-dimensional extended Hubbard chain. Calculating the time-dependent optical conductivity, we find that strong mono-cycle pulse inducing quantum tunneling gives rise to anomalous suppression of photo-induced in-gap weight, leading to negative weight. This is in contrast to finite positive weight in the Hubbard chain. The origin of this anomalous behavior in the two-leg ladder is attributed to photoinduced localized exciton that reflects strong spin-singlet dimer correlation in the ground state.

cond-mat.str-el↗

arXiv2023

Controlling inversion and time-reversal symmetries by subcycle pulses in the one-dimensional extended Hubbard model

Owning to their high controllability, laser pulses have contributed greatly to our understanding of strongly correlated electron systems. However, typical multicycle pulses do not control the symmetry of systems that plays an important role in the emergence of novel quantum phases. Here, we demonstrate that subcycle pulses whose oscillation is less than one period within a pulse envelope can control inversion and time-reversal symmetries in the electronic states of the one-dimensional extended Hubbard model. Using an ultrashort subcycle pulse, one can generate a steady electric current (SEC) in a photoexcited state due to an Aharonov-Bohm flux instantaneously introduced through the phase of an electric field. Consequently, time-reversal symmetry is broken. In contrast, a broad subcycle pulse does not induce SEC but instead generates electric polarization, thus breaking inversion symmetry. Both symmetry breakings in a photoexcited state can be monitored by second harmonic generation. These findings provide a new methodology for designing the symmetries of electronic states and open up a new field of subcycle-pulse engineering.

cond-mat.str-el↗

arXiv2023

Monte Carlo study of cuprate superconductors in a four-band $d$-$p$ model: Role of orbital degrees of freedom

Understanding the complex phase diagram of cuprate superconductors is a long-standing challenging problem. Recent studies have shown that orbital degrees of freedom, both Cu $e_g$ orbitals and O $p$ orbitals, are a key ingredient for a unified understanding of cuprate superconductors, including the material dependence. Here we investigate a four-band $d$-$p$ model derived from the first-principles calculations with the variational Monte Carlo method, which allows us to elucidate competing orders on an equal footing. The obtained results can consistently explain the doping dependence of superconductivity, antiferromagnetic and stripe phases, phase separation in the underdoped region, and also novel magnetism in the heavily-overdoped region. Our four-band $d$-$p$ model with neighbouring intersite interactions is a minimal model to describe the phase diagram comprehensively. The presence of $p$ orbitals is critical to the charge-stripe features, which induce two types of stripe phases with $s'$-wave and $d$-wave bond stripe. On the other hand, the presence of $d_{z^2}$ orbital is indispensable to material dependence of the superconducting transition temperature ($T_{\mathrm{c}}$), and enhances local magnetic moment as a source of novel magnetism in the heavily-overdoped region as well. These findings beyond one-band description could provide a major step toward a full explanation of unconventional normal state and high $T_{\mathrm{c}}$ in cuprate supercondutors.

cond-mat.supr-con↗

arXiv2023

Parametrized quantum circuit for weight-adjustable quantum loop gas

Motivated by the recent success of realizing the topologically ordered ground state of the exactly solvable toric code model by a quantum circuit on the real quantum device [K. J. Satzinger {\it et al}., Science \textbf{374}, 1237 (2021)], here we propose a parametrized quantum circuit (PQC) with the same real-device-performable optimal structure to represent quantum loop gas states with adjustably weighted loop configurations. Combining such a PQC with the variational quantum eigensolver, we obtain the accurate quantum circuit representation for the toric code model in an external magnetic field with any field strength, where the system is not exactly solvable. The topological quantum phase transition in this system is further observed in the optimized circuits by measuring the magnetization and topological entanglement entropy.

quant-ph↗

arXiv2022

Energy-filtered random-phase states as microcanonical thermal pure quantum states

We propose a method to calculate finite-temperature properties of a quantum many-body system for a microcanonical ensemble by introducing a pure quantum state named here an energy-filtered random-phase state, which is also a potentially promising application of near-term quantum computers. In our formalism, a microcanonical ensemble is specified by two parameters, i.e., the energy of the system and its associated energy window. Accordingly, the density of states is expressed as a sum of Gaussians centered at the target energy with its spread corresponding to the width of the energy window. We then show that the thermodynamic quantities such as entropy and temperature are calculated by evaluating the trace of the time-evolution operator and the trace of the time-evolution operator multiplied by the Hamiltonian of the system. We also describe how these traces can be evaluated using random diagonal-unitary circuits appropriate to quantum computation. The pure quantum state representing our microcanonical ensemble is related to a state of the form introduced by Wall and Neuhauser for the filter diagonalization method [M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995)], and therefore we refer to it as an energy-filtered random-phase state. The energy-filtered random-phase state is essentially a Fourier transform of a time-evolved state whose initial state is prepared as a random-phase state, and the cut-off time in the time-integral for the Fourier transform sets the inverse of the width of the energy window. The proposed method is demonstrated numerically by calculating thermodynamic quantities for the one-dimensional spin-1/2 Heisenberg model on small clusters up to 28 qubits, showing that the method is most efficient for the target energy around which the dense distribution of energy eigenstates is found.

quant-ph↗

arXiv2022

Variational counterdiabatic driving of the Hubbard model for ground-state preparation

Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protocol engages an approximated AGP expressed as a series of nested commutators. We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coefficients are given by the squared Frobenius norms of these commutators. We devise an exact algorithm that escapes the formidable iterative matrix-vector multiplications and evaluates the nested commutators and the CD Hamiltonian in analytic representations. We then examine the CD driving of the one-dimensional Hubbard model up to $L = 14$ sites with driving order $l \leqslant 3$. Our results demonstrate the usefulness of the variational CD protocol to the Hubbard model and permit a possible route towards fast ground-state preparation for many-body systems.

cond-mat.str-el↗

arXiv2022

Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary operators involving only single-qubit rotations, at the cost of the sum over the auxiliary fields. To perform the sum over the auxiliary fields, we introduce two approaches that have complementary features. The first approach employs a linear-combination-of-unitaries circuit, which enables one to probabilistically prepare the Gutzwiller wave function on a quantum computer, while the second approach uses importance sampling to estimate observables stochastically, similar to a quantum Monte Carlo method in classical computation. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model. Furthermore, we perform quantum simulations using a real quantum device, demonstrating that the proposed scheme can reproduce the exact ground-state energy of the two-site Fermi-Hubbard model within error bars.

quant-ph↗

arXiv2022

Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer

We propose an extended version of the symmetry-adapted variational-quantum-eigensolver (VQE) and apply it to a two-component Fermi-Hubbard model on a bipartite lattice. In the extended symmetry-adapted VQE method, the Rayleigh quotient for the Hamiltonian and a parametrized quantum state in a properly chosen subspace is minimized within the subspace and is optimized among the variational parameters implemented on a quantum circuit to obtain variationally the ground state and the ground-state energy. The corresponding energy derivative with respect to a variational parameter is expressed as a Hellmann-Feynman-type formula of a generalized eigenvalue problem in the subspace, which thus allows us to use the parameter-shift rules for its evaluation. The natural-gradient-descent method is also generalized to optimize variational parameters in a quantum-subspace-expansion approach. As a subspace for approximating the ground state of the Hamiltonian, we consider a Krylov subspace generated by the Hamiltonian and a symmetry-projected variational state, and therefore the approximated ground state can restore the Hamiltonian symmetry that is broken in the parametrized variational state prepared on a quantum circuit. We show that spatial symmetry operations for fermions in an occupation basis can be expressed as a product of the nearest-neighbor fermionic swap operations on a quantum circuit. We also describe how the spin and charge symmetry operations, i.e., rotations, can be implemented on a quantum circuit. By numerical simulations, we demonstrate that the spatial, spin, and charge symmetry projections can improve the accuracy of the parametrized variational state, which can be further improved systematically by expanding the Krylov subspace without increasing the number of variational parameters.

quant-ph↗

arXiv2022

Local multiplet formation around a single vacancy in graphene: an effective Anderson model analysis based on the block-Lanczos DMRG method

To better understand the electronic structure of a single vacancy in graphene, we study the ground state property of an effective Anderson model, consisting of three dangling $sp^2$ orbitals of the surrounding carbon atoms around the vacancy and the $π$ orbitals of carbon atoms that form the honeycomb lattice with a single vacancy. Employing the block-Lanczos density-matrix renormalization group method, we show that there are two phases in the relevant parameter space, i.e., a nonmagnetic phase in the weak coupling region and a free magnetic moment phase in the realistic parameter region. The systematic analysis finds that, in the free magnetic moment phase, local multiplets of the doubly degenerate irreducible representation of the $\mathcal{C}_3$ point group with spin 1 become dominant in the ground state, and approximately half of this local spin 1 is screened by electrons in the surrounding $π$ orbitals, indicating the emergence of the residual spin-1/2 free magnetic moment. Furthermore, we find that the emergence of the free magnetic moment is robust against carrier doping, which is in sharp contrast to the case of graphene with an adatom, thus explaining the qualitative difference observed experimentally in these two classes of systems. We also find the enhancement of the spin correlation function between $π$ electrons around the vacancy and those in the conduction band away from the vacancy in the undoped case, as compared to that in the doped case, while the spin correlation function between the $σ$ electrons in the $sp^2$ dangling orbitals around the vacancy and the $π$ electrons in the conduction band remains large in both undoped and doped cases. Our calculations thus support qualitatively the previous experiment that suggests the emergence of free magnetic moment with two distinct origins.

cond-mat.str-el↗

arXiv2021

Automatic quantum circuit encoding of a given arbitrary quantum state

We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state $\vert Ψ\rangle$ onto an optimal quantum circuit $\hat{\mathcal{C}}$ with a finite number of single- and two-qubit quantum gates. The proposed algorithm employs as an objective function the absolute value of fidelity $F = \langle 0 \vert \hat{\mathcal{C}}^{\dagger} \vert Ψ\rangle$, which is maximized iteratively to construct an optimal quantum circuit $\hat{\mathcal{C}}$ with controlled accuracy. The key ingredient of the algorithm is the sequential determination of a set of optimal two-qubit unitary operators one by one via the singular value decomposition of the fidelity tensor. Once the optimal unitary operators are determined, including the location of qubits on which each unitary operator acts, elementary quantum gates are assigned algebraically. With noiseless numerical simulations, we demonstrate the algorithm to encode a ground state of quantum many-body systems, including the spin-1/2 antiferromagnetic Heisenberg model and the spin-1/2 XY model. The results are also compared with the quantum circuit encoding of the same quantum state onto a quantum circuit in a given circuit structure. Moreover, we demonstrate that the algorithm can also be applied to construct an optimal quantum circuit for classical data such as a classical image that is represented as a quantum state by the amplitude encoding. Finally, we also experimentally demonstrate that a quantum circuit generated by the AQCE algorithm can indeed represent the original quantum state reasonably on a noisy real quantum device.

quant-ph↗