arXiv subjects

Takeru Yokota

Publications and source records attributed to Takeru Yokota.

At least 19 recordsLinked to original sources

arXiv2025

Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids

In our previous work [Phys. Rev. E 104, 014124 (2021)], we developed a method for analyzing classical liquids using the functional renormalization group (FRG) without relying on a hard-core reference system. In this paper, we extend this method to three-dimensional liquids. We describe an efficient approach for performing the spatial integrals that appear in the renormalization group equations, which is essential for realizing numerical calculations in three dimensions. As a demonstration, we present its application to the Lennard-Jones liquids. Through calculations of thermodynamic quantities, we find that FRG preserves thermodynamic consistency (TC) better than traditional integral-equation methods such as the hypernetted-chain, Percus-Yevick, and Kovalenko-Hirata closures. Taking the molecular dynamics results as a benchmark, we also show that FRG can achieve an accuracy comparable to that of integral-equation methods that incorporate TC, such as the Rogers-Young closure. We further assess the accuracy of the pair distribution function and examine whether our method remains applicable below the critical temperature. Our results demonstrate that FRG provides a new method for describing classical liquids with accuracy comparable to modern liquid theories.

cond-mat.soft↗

arXiv2025

Unpolarized prethermal discrete time crystal

Prethermal discrete time crystals (DTCs) are a novel phase of periodically driven matter that exhibits robust subharmonic oscillations without requiring disorder. However, previous realizations of prethermal DTCs have relied on the presence of polarization, either spontaneous or induced. Here, we introduce a new class of prethermal DTCs termed ``unpolarized prethermal discrete time crystals'' (UPDTCs) that arise without any uniform/staggered polarization and propose an experiment to observe them in current trapped-ion quantum simulators. By studying a model of trapped ions using a quantum circuit simulator, we demonstrate that robust period-doubled dynamics can persist in the autocorrelation function of the staggered magnetization, even though its expectation value does not exhibit such dynamics. The period-doubled dynamics is not explained by the classical picture of flipping spins but by quantum fluctuations. We establish that UPDTCs are exponentially long-lived in the high-frequency driving regime, a hallmark of prethermalization. These results expand the known phenomenology and mechanism of prethermal time crystals and underscore the role of quantum effects in stabilizing novel nonequilibrium phases.

cond-mat.quant-gas↗

arXiv2024

Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees

We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its unrealistic computational costs and has been a long standing problem over decades. Thus, numerical approximations of FDEs have been developed, but they often oversimplify the solutions. To tackle these two issues, we propose a hybrid approach combining physics-informed neural networks (PINNs) with the \textit{cylindrical approximation}. The cylindrical approximation expands functions and functional derivatives with an orthonormal basis and transforms FDEs into high-dimensional PDEs. To validate the reliability of the cylindrical approximation for FDE applications, we prove the convergence theorems of approximated functional derivatives and solutions. Then, the derived high-dimensional PDEs are numerically solved with PINNs. Through the capabilities of PINNs, our approach can handle a broader class of functional derivatives more efficiently than conventional discretization-based methods, improving the scalability of the cylindrical approximation. As a proof of concept, we conduct experiments on two FDEs and demonstrate that our model can successfully achieve typical $L^1$ relative error orders of PINNs $\sim 10^{-3}$. Overall, our work provides a strong backbone for physicists, mathematicians, and machine learning experts to analyze previously challenging FDEs, thereby democratizing their numerical analysis, which has received limited attention. Code is available at \url{https://github.com/TaikiMiyagawa/FunctionalPINN}.

math.NA↗

arXiv2024

Physics-informed neural networks for solving functional renormalization group on a lattice

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even on lattices. We leverage physics-informed neural networks (PINNs) as a state-of-the-art machine learning method for solving high-dimensional partial differential equations to overcome this challenge. In a zero-dimensional O($N$) model, we numerically demonstrate the construction of an effective action on an $N$-dimensional configuration space, extending up to $N=100$. Our results underscore the effectiveness of PINN approximation, even in scenarios lacking small parameters such as a small coupling.

cond-mat.dis-nn↗

arXiv2023

Color superconductivity on the lattice -- analytic predictions from QCD in a small box

We investigate color superconductivity on the lattice using the gap equation for the Cooper pair condensate. The weak coupling analysis is justified by choosing the physical size of the lattice to be smaller than the QCD scale, while keeping the aspect ratio of the lattice small enough to suppress thermal excitations. In the vicinity of the critical coupling constant that separates the superconducting phase and the normal phase, the gap equation can be linearized, and by solving the corresponding eigenvalue problem, we obtain the critical point and the Cooper pair condensate without assuming its explicit form. The momentum components of the condensate suggest spatially isotropic s-wave superconductivity with Cooper pairs formed by quarks near the Fermi surface. The chiral symmetry in the massless limit is spontaneously broken by the Cooper pair condensate, which turns out to be dominated by the scalar and the pseudo-scalar components. Our results provide useful predictions, in particular, for future lattice simulations based on methods to overcome the sign problem such as the complex Langevin method.

hep-lat↗

arXiv2022

Functional Renormalization Group Approach to Circuit Quantum Electrodynamics

A nonperturbative approach is developed to analyze superconducting circuits coupled to quantized electromagnetic continuum within the framework of the functional renormalization group. The formalism allows us to determine complete physical pictures of equilibrium properties in the circuit quantum electrodynamics (cQED) architectures with high-impedance waveguides, which have recently become accessible in experiments. We point out that nonperturbative effects can trigger breakdown of the supposedly effective descriptions, such as the spin-boson and boundary sine-Gordon models, and lead to qualitatively new phase diagrams. The origin of the failure of conventional understandings is traced to strong renormalizations of circuit parameters at low-energy scales. Our results indicate that a nonperturbative analysis is essential for a comprehensive understanding of cQED platforms consisting of superconducting circuits and long high-impedance transmission lines.

quant-ph↗

arXiv2022

Nonperturbative Waveguide Quantum Electrodynamics

Understanding physical properties of quantum emitters strongly interacting with quantized electromagnetic modes is one of the primary goals in the emergent field of waveguide quantum electrodynamics (QED). When the light-matter coupling strength is comparable to or even exceeds energies of elementary excitations, conventional approaches based on perturbative treatment of light-matter interactions, two-level description of matter excitations, and photon-number truncation are no longer sufficient. Here we study in and out of equilibrium properties of waveguide QED in such nonperturbative regimes on the basis of a comprehensive and rigorous theoretical approach using an asymptotic decoupling unitary transformation. We uncover several surprising features ranging from symmetry-protected many-body bound states in the continuum to strong renormalization of the effective mass and potential; the latter may explain recent experiments demonstrating cavity-induced changes in chemical reactivity as well as enhancements of ferromagnetism or superconductivity. To illustrate our general results with concrete examples, we use our formalism to study a model of coupled cavity arrays, which is relevant to experiments in superconducting qubits interacting with microwave resonators or atoms coupled to photonic crystals. We examine the relation between our results and delocalization-localization transition in the spin-boson model; notably, we point out that a reentrant transition can occur in the regimes where the coupling strength becomes the dominant energy scale. We also discuss applications of our results to other problems in different fields, including quantum optics, condensed matter physics, and quantum chemistry.

quant-ph↗

arXiv2021

Color superconductivity in a small box: a complex Langevin study

It is expected that the color superconductivity (CSC) phase appears in QCD at low temperature and high density. On the basis of the lattice perturbation theory, a possible parameter region in which the CSC occurs has been predicted. In this work, we perform complex Langevin simulation on an $8^3\times 128$ lattice using four-flavor staggered fermions. We find, in particular, that the quark number has plateaux with respect to the chemical potential similar to our previous study, indicating the formation of the Fermi sphere. A diquark-antidiquark operator, which is an order parameter of color superconductivity, is formulated on the lattice using the U(1) noise. Our result for this operator is found to fluctuate violently when the Fermi surface coincides with the energy levels of quarks. We also discuss partial restoration of the chiral symmetry at high density.

hep-lat↗

arXiv2021

Flavor number dependence of QCD at finite density by the complex Langevin method

We discuss the flavor number dependence of QCD at low temperature and high density by the complex Langevin method. In our previous work, the complex Langevin method is confirmed to satisfy the criterion for correct convergence in certain regions, such as $μ_{\rm q} / T = 5.2-7.2$ on $8^3 \times 16$ and $μ_{\rm q} / T = 1.6-9.6$ on $16^3 \times 32$ using $N_{\rm f} = 4$ staggered fermion at $β= 5.7$. We extend this study to more realistic flavor cases, $N_{\rm f} = 2, 2 + 1, 3$, using Wilson fermions. We present the flavor number dependence of the validity regions of the complex Langevin method and the quark number.

hep-lat↗

arXiv2021

Construction of energy density functional for arbitrary spin polarization using functional renormalization group

We show an application of the functional-renormalization-group aided density functional theory to the homogeneous electron gas with arbitrary spin polarization, which gives the energy density functional in the local spin density approximation. The correlation energy per particle is calculated at arbitrary Wigner-Seitz radius $ r_{\rm s} $ and spin polarization $ ζ$. In the high-density region, our result shows good agreement with Monte Carlo (MC) data. The agreement with MC data is better in the case of small spin polarization, while the discrepancy increases as the spin polarization increases. The magnetic properties given by our numerical results are also discussed.

cond-mat.str-el↗

arXiv2021

Perturbative predictions for color superconductivity on the lattice

We develop a new method to investigate color superconductivity (CSC) on the lattice based on the Thouless criterion, which amounts to solving the linearized gap equation without imposing any ansatz on the structure of the Cooper pairs. We perform explicit calculations at the one-loop level with the staggered fermions on a $8^3 \times 128$ lattice and the Wilson fermions on a $4^3 \times 128$ lattice, which enables us to obtain the critical $β(=6/g^2)$ as a function of the quark chemical potential $μ$, below which the CSC phase is expected to appear. The obtained critical $β$ has sharp peaks at the values of $μ$ corresponding to the discretized energy levels of quarks similarly to what was observed in previous studies on simplified effective models. From the solution to the linearized gap equation, one can read off the flavor and spatial structures of the Cooper pairs at the critical $β$. In the case of massless staggered fermion, in particular, we find that the chiral $\mathrm{U}(1)$ symmetry of the staggered fermions is spontaneously broken by the condensation of the Cooper pairs.

hep-lat↗

arXiv2021

Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system

The renormalization-group approaches for classical liquids in previous works require a repulsive reference such as a hard-core one when applied to systems with short-range repulsion. The need for the reference is circumvented here by using a functional renormalization group approach for integrating the hierarchical flow of correlation functions along a path of variable interatomic coupling. We introduce the cavity distribution functions to avoid the appearance of divergent terms and choose a path to reduce the error caused by the decomposition of higher order correlation functions. We demonstrate using an exactly solvable one-dimensional models that the resulting scheme yields accurate thermodynamic properties and interatomic distribution at various densities when compared to integral-equation methods such as the hypernetted chain and the Percus-Yevick equation, even in the case where our hierarchical equations are truncated with the Kirkwood superposition approximation, which is valid for low-density cases.

cond-mat.stat-mech↗

arXiv2021

Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory

We show an $\textit{ab initio}$ construction of the energy density functional (EDF) for electron systems using the functional renormalization group. The correlation energies of the homogeneous electron gas given in our framework reproduce the exact behavior at high density and agree with the Monte-Carlo data in a wide range of densities. Our analytic technique enables us to get the correlation energies efficiently for various densities, which realizes the determination of EDF in the local density approximation (LDA) without any fitting for physically relevant densities. Applied to the Kohn-Sham calculation for the noble gas atoms, our EDF shows comparable results to those of other conventional ones in LDA.

cond-mat.str-el↗

arXiv2020

Microscopic derivation of density functional theory for superfluid systems based on effective action formalism

Density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and nonlocal pairing densities and demonstrate that the Hohenberg-Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from $0$ to $1$, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn-Sham potential generalized to including the pairing potentials. The resultant Kohn-Sham potential has a nice feature that it expresses the microscopic formulae of the external, Hartree, pairing, and exchange-correlation terms, separately. It is shown that our Kohn-Sham potential gives the ground-state energy of the Hartree-Fock-Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to systematically improve the correlation part.

nucl-th↗

arXiv2018

Ab-initio description of excited states of a one-dimensional nuclear matter with the Hohenberg-Kohn-theorem-inspired functional-renormalization-group method

We demonstrate for the first time that a functional-renormalization-group aided density-functional theory (FRG-DFT) describes well the characteristic features of the excited states as well as the ground state of an interacting many-body system with infinite number of particles in a unified manner. The FRG-DFT is applied to a $(1+1)$-dimensional spinless nuclear matter. For the excited states, the density--density spectral function is calculated at the saturation point obtained in the framework of FRG-DFT, and it is found that our result reproduces a notable feature of the density--density spectral function of the non-linear Tomonaga-Luttinger liquid: The spectral function has a singularity at the edge of its support of the lower-energy side. These findings suggest that the FRG-DFT is a promising first-principle scheme to analyze the excited states as well as the ground states of quantum many-body systems starting from the inter-particle interaction.

nucl-th↗

arXiv2018

Functional-renormalization-group aided density-functional analysis for the correlation energy of the two-dimensional homogeneous electron gas

The functional-renormalization-group aided density-functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius $ r_{\rm s} $ directly. We find that our correlation energy completely reproduces the exact behavior at the high-density limit. For finite density, the result of FRG-DFT shows good agreement with the Monte Carlo (MC) results in the high-density region, although the discrepancy between FRG-DFT and MC results becomes larger as the system becomes more dilute. Our study is the first example in which the FRG-DFT is applied to more-than-one-dimensional models, and shows that the FRG-DFT is a feasible and promising method even for the analysis of realistic models for quantum many-body systems.

cond-mat.str-el↗

arXiv2018

Functional renormalization-group calculation of the equation of state of one-dimensional nuclear matter inspired by the Hohenberg--Kohn theorem

We present the first successful functional renormalization group(FRG)-aided density-functional (DFT) calculation of the equation of state (EOS) of an infinite nuclear matter (NM) in (1+1)-dimensions composed of spinless nucleons. We give a formulation to describe infinite matters in which the 'flowing' chemical potential is introduced to control the particle number during the flow. The resultant saturation energy of the NM coincides with that obtained by the Monte-Carlo method within a few percent. Our result demonstrates that the FRG-aided DFT can be as powerful as any other methods in quantum many-body theory.

nucl-th↗

arXiv2017

Tachyonic instability of the scalar mode prior to QCD critical point based on Functional renormalization-group method

We establish and elucidate the physical meaning of the appearance of an acausal mode in the sigma mesonic channel, found in the previous work by the present authors, when the system approaches the $\mathrm{Z}_{2}$ critical point. The functional renormalization group method is applied to the two--flavor quark--meson model with varying current quark mass $m_q$ even away from the physical value at which the pion mass is reproduced. We first determine the whole phase structure in the three-dimensional space $(T, μ, m_q)$ consisting of temperature $T$, quark chemical potential $μ$ and $m_q$, with the tricritical point, $\mathrm{O}(4)$ and $\mathrm{Z}_{2}$ critical lines being located; they altogether make a wing-like shape quite reminiscent of those known in the condensed matters with a tricritical point. We then calculate the spectral functions $ρ_{σ, π}(ω, p)$ in the scalar and pseudoscalar channel around the critical points. We find that the sigma mesonic mode becomes tachyonic with a superluminal velocity at finite momenta before the system reaches the $\mathrm{Z}_{2}$ point from the lower density, even for $m_q$ smaller than the physical value. One of the possible implications of the appearance of such a tachyonic mode at finite momenta is that the assumed equilibrium state with a uniform chiral condensate is unstable toward a state with an inhomogeneous $σ$ condensate. No such an anomalous behavior is found in the pseudoscalar channel. We find that the $σ$-to-$2σ$ coupling due to finite $m_q$ play an essential role for the drastic modification of the spectral function.

hep-ph↗