arXiv subjects

Takafumi Kita

Publications and source records attributed to Takafumi Kita.

At least 19 recordsLinked to original sources

arXiv2025

Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles

A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a $π$-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively.

quant-ph↗

arXiv2025

Hidden Bose-Einstein Singularities in Correlated Electron Systems: III. Thermodynamic Signals

We study thermodynamic consequences of the hidden Bose-Einstein singularities, which have been predicted to cause a pseudogap phase, based on quantum field theory of ordered phases. Starting from the Luttinger-Ward functional for the grand thermodynamic potential, we derive expressions of the Helmholtz free energy, internal energy, entropy, and heat capacity in a form suitable for numerical studies. They are applied to the weakly attractive Hubbard model in three dimensions to calculate the thermodynamic potentials numerically and continuously for the normal, pseudogap, and superconducting phases on the same footing. It is shown that the entry into the pseudogap phase is detectable as singularities of thermodynamic potentials, especially a discontinuity in the heat capacity.

cond-mat.str-el↗

arXiv2025

Hidden Bose-Einstein Singularities in Correlated Electron Systems: II. Pseudogap Phase in the Weakly Attractive Hubbard Model

The hidden Bose-Einstein singularities of correlated electron systems, whose possible existence has been pointed out in a previous paper based on quantum field theory of ordered phases [T. Kita, J. Phys. Soc. Jpn. {\bf 93}, 124704 (2024)], are studied in more detail in terms of the attractive Hubbard model, for which the mean-field theory predicts that spin-singlet superconductivity is realized at low enough temperatures for any band structure and interaction strength. It is shown that incorporating correlation effects should change the mean-field superconducting solution substantially and qualitatively even in the weak coupling, implying that the system lies in the strong-coupling region perturbatively. The hidden singularity is found to be present around the mean-field superconducting temperature $T_{{\rm c}0}$, below which the standard self-consistent treatment by quantum field theory cannot be used due to divergences in the zero Matsubara frequency branch obeying Bose-Einstein statistics. Our method to recover the applicability with a Lagrange multiplier predicts that the singularity is a physical entity signaling the threshold of a pseudogap phase with a characteristic V-shape structure in the density of states near zero energy, which lies above the superconducting phase and originates from the emerging one-particle-reducible structure in the self-energy.

cond-mat.str-el↗

arXiv2024

Hidden Bose-Einstein Singularities in Correlated Electron Systems

Hidden singularities in correlated electron systems, which are caused by pair fluctuations of electron-electron or electron-hole bubbles obeying Bose-Einstein statistics, are clarified theoretically. The correlation function of each pair fluctuation is shown to have a bound in the zero Matsubara frequency branch, similarly to the chemical potential of ideal Bose gases. Once the bound is reached, the self-energy starts to acquire a component proportional to Green's function itself, i.e., the structure called one-particle reducible, to keep the correlation function within the bound. The singularities are closely related to, but distinct from, phase transitions with broken symmetries. Passing down through them is necessarily accompanied by a change in the single-particle density of states around the excitation threshold, such as the pseudogap behavior found here for the negative-$U$ Hubbard model above the superconducting transition temperature.

cond-mat.supr-con↗

arXiv2023

How Infrared Singularities Affect Nambu-Goldstone Bosons at Finite Temperatures

Ordered phases realized through broken continuous symmetries embrace long-range order-parameter fluctuations as manifest in the power-law decays of both the transverse and longitudinal correlations, which are similar to those at the second-order transition point. We calculate the transverse one-loop correction to the dispersion relation of nonrelativistic Nambu-Goldstone (NG) bosons at finite temperatures, assuming that they have well-defined dispersion relations with some integer exponents. It is found that the transverse correlations make the lifetime of the NG bosons vanish right on the assumed dispersion curve below three dimensions at finite temperatures. Combined with the vanishing of the longitudinal "mass", the result indicates that the correlations generally bring both an intrinsic lifetime to the excitations and a qualitative change in the dispersion relation at long wavelengths below three dimensions at finite temperatures, unless it is protected by some conservation law. A more detailed calculation performed specifically on a single-component Bose-Einstein condensate reveals that the gapless Bogoliubov mode predicted by the perturbative treatment is modified substantially after incorporating the correlations to have (i) an intrinsic lifetime and (ii) a peak shift at long wavelengths from the linear dispersion relation. Thus, the NG bosons may be fluctuating intrinsically into and out of the ordered "vacuum" to maintain the order temporally.

cond-mat.quant-gas↗

arXiv2022

Legendre Transformation of the Luttinger-Ward Functional from the Bare Interaction Vertex to the Renormalized One

On the basis of the Luttinger-Ward functional for interacting many-body systems given in terms of full Green's function $G$ and the bare interaction vertex $Γ^{(0)}$, we develop a novel Legendre transformation to express the grand thermodynamic potential $Ω$ as a functional of $G$ and the renormalized interaction vertex $Γ$ so that (i) $G$ and $Γ$ obey the stationarity conditions $δΩ/δG=0$ and $δΩ/δΓ=0$ and (ii) $Γ$ reduces to $Γ^{(0)}$ in the weak-coupling limit. The formalism enables us to perform microscopic studies of thermodynamic, single-particle, and two-particle properties in a unified self-consistent conserving framework.

cond-mat.str-el↗

arXiv2022

Charging in the vortex lattice of type-II superconductors

We study the magnetic-field dependence of the vortex-core charge in the Abrikosov lattice of an $s$-wave superconductor based on the augmented quasiclassical equations, where we incorporate the pair-potential gradient (PPG) terms characteristic of charging in superconductors besides the well-known Lorentz force. Our numerical results at $T=0.2 T_{\rm c}$ and $0.5 T_{\rm c}$ reveal that periodic charge redistribution is superimposed on the magnetic flux-line lattice with different spatial patterns at different fields. The PPG terms are dominant at weak fields over the Lorentz force for accumulating charge in the vortex cores, whereas the Lorentz force prevails at higher fields to give rise to a peak structure in the core charge around $H\sim \frac{1}{2}H_{{\rm c}2}$. We estimate the peak value of the core charge at $T=0.2 T_{\rm c}$ using parameters appropriate for cuprates to obtain a large value of $Q \sim 10^{-2} |e|$ in the core region of radius $0.2 ξ_0$ in the $ab$ plane and length $1 \ {\rm nm}$ along the $c$ axis.

cond-mat.supr-con↗

arXiv2021

Quantum Field Theory of Correlated Bose-Einstein condensates: I. Basic Formalism

Quantum field theory of equilibrium and nonequilibrium Bose-Einstein condensates is formulated so as to satisfy three basic requirements: the Hugenholtz-Pines relation; conservation laws; identities among vertices originating from Goldstone's theorem I. The key inputs are irreducible four-point vertices, in terms of which we derive a closed system of equations for Green's functions, three- and four-point vertices, and two-particle Green's functions. It enables us to study correlated Bose-Einstein condensates with a gapless branch of single-particle excitations without encountering any infrared divergence. The single- and two-particle Green's functions are found to share poles, i.e., the structure of the two-particle Green's functions predicted by Gavoret and Nozières for a homogeneous condensate at $T=0$ is also shown to persist at finite temperatures, in the presence of inhomogeneity, and also in nonequilibrium situations.

cond-mat.quant-gas↗

arXiv2021

Quantum Field Theory of Correlated Bose-Einstein condensates: II. Ward-Takahashi Identities and Correlation Functions

We derive Ward-Takahashi identities for correlated Bose-Einstein condensates based on the expressions of the first-order variations $(δΨ,δG)$ due to perturbations obtained in the preceding paper [T. Kita, J. Phys. Soc. Jpn. $\bf 90$, 024001 (2021)] for the condensate wave function $Ψ$ and Green's function $G$. They enable us to obtain several exact results on the density and current correlation functions $K_{νν'}^{}$, and also express $K_{νν'}^{}$ in terms of low-energy Green's functions and vertices. The latter expressions open up the possibility of constructing theory of superfluid Bose liquids in the same way as that for fermions at low temperatures. The vertices are found to have different limits depending on which of frequency $ω$ and wavenumber $q$ is set equal to zero first.

cond-mat.quant-gas↗

arXiv2020

Zero-Field Surface Charge Due to the Gap Suppression in $d$-Wave Superconductors

We perform a microscopic study on the redistribution of electric charge near the surface of a model $d$-wave superconductor cut along the [110] direction, with a Fermi surface appropriate for cuprate superconductors, using the augmented quasiclassical equations. We identify two possible mechanisms for the redistribution of charged particles different from the well-known magnetic Hall effect, namely; the pair potential gradient (PPG) force due to surface effects on the pair potential and the pressure difference between the normal and superconducting regions arising from the slope of the density of states (SDOS) in the normal states at the Fermi level. Our present results show that in spite of the absence of supercurrents, electric charge is induced around the surface. Moreover, the charging effect due to the SDOS pressure dominates over that due to the PPG force for all the realistic electron-fillings $n=0.8$, $0.9$, and $1.15$, at all temperatures. In addition, for the filling $n=1.15$, the PPG force and the SDOS pressure contributions have the same negative signs, which gives a larger total surface charge i.e., both the sign and amount of the surface charge depends greatly on the Fermi-surface curvature. We have also calculated the local density of states (LDOS) within the augmented quasiclassical theory. Spatially varying local particle-hole asymmetry appears in the LDOS, which suggests the presence of electric charge.

cond-mat.supr-con↗

arXiv2020

Drastic enhancement of the thermal Hall angle in a $d$-wave superconductor

A drastic enhancement of the thermal Hall angle in $d$-wave superconductors was observed experimentally in a cuprate superconductor and in CeCoIn$_5$ at low temperatures and very weak magnetic field [Phys. Rev. Lett. $\bf 86$, 890 (2001); Phys. Rev. B $\bf 72$, 214515 (2005)]. However, to the best of our knowledge, its microscopic calculation has not been performed yet. To study this microscopically, we derive the thermal Hall coefficient in extreme type-II superconductors with an isolated pinned vortex based on the augmented quasiclassical equations of superconductivity with the Lorentz force. Using it, we can confirm that the quasiparticle relaxation time and the thermal Hall angle are enhanced in $d$-wave superconductors without impurities of the resonant scattering because quasiparticles around the gap nodes which become dominant near zero temperature are restricted to the momentum in a specific orientation. This enhancement of the thermal Hall angle may also be observed in other nodal superconductors with large magnetic-penetration depth.

cond-mat.supr-con↗

arXiv2019

A Renormalization-Group Study of Interacting Bose-Einstein Condensates: II. Anomalous Dimension $η$ for $d\lesssim 4$ at Finite Temperatures

We study the anomalous dimension $η$ of homogeneous interacting single-component Bose-Einstein condensates at finite temperatures for $d\lesssim 4$ dimensions. This $η$ is defined in terms of the one-particle density matrix $ρ({\bf r})\equiv \langle \hatψ^\dagger({\bf r}_1)\hatψ({\bf r}_1+{\bf r})\rangle$ through its asymptotic behavior $ρ({\bf r})\rightarrow N_{\bf 0}/V+C r^{-d+2-η}$ for $r\rightarrow \infty$, where $N_{\bf 0}/V$ is the condensate density and $C$ is a constant. It is shown that the anomalous dimension is given by $η=0.181ε^2$ to the leading order in $ε\equiv d-4$. The change of the prefactor $0.181$ from the value $0.02$ at the transition point of the ${\rm O}(2)$ symmetric $ϕ^4$ model is attributed to the emergence of three-point vertices and the anomalous Green's function when $N_{\bf 0}$ acquires a finite value.

cond-mat.quant-gas↗

arXiv2019

Variational Approach to Many-Body Problems Incorporating Many-Body Effects at Finite Temperature

We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this formalism to weakly interacting Bose-Einstein condensates to incorporate the dynamical 3/2-body processes, which are considered important in the dynamical properties. The processes lower the free energy below the mean-field Hartree--Fock--Bogoliubov's value in the same way as a previous zero-temperature formalism. From our numerical results, the pair creation or annihilation processes neglected in the Popov--Shohno approximation are enhanced, particularly in the long wavelength region, owing to the many-body effects. Because the 3/2-body correlations give a finite contribution to the self-energy of quasiparticles, they may change the microscopic properties qualitatively, even in the weak-coupling region.

cond-mat.quant-gas↗

arXiv2019

A Renormalization-Group Study of Interacting Bose-Einstein condensates: Absence of the Bogoliubov Mode below Four ($T>0$) and Three ($T=0$) Dimensions

We derive exact renormalization-group equations for the $n$-point vertices ($n=0,1,2,\cdots$) of interacting single-component Bose-Einstein condensates based on the vertex expansion of the effective action. They have a notable feature of automatically satisfying Goldstone's theorem (I), which yields the Hugenholtz-Pines relation $Σ(0)-μ=Δ(0)$ as the lowest-order identity. Using them, it is found that the anomalous self-energy $Δ(0)$ vanishes below $d_{\rm c}=4$ ($d_{\rm c}=3$) dimensions at finite temperatures (zero temperature), contrary to the Bogoliubov theory predicting a finite "sound-wave" velocity $v_{\rm s}\propto [Δ(0)]^{1/2}>0$. It is also argued that the one-particle density matrix $ρ({\bf r})\equiv\langle\hatψ^\dagger({\bf r}_1)\hatψ({\bf r}_1+{\bf r})\rangle$ for $d 0$. The anomalous dimension $η$ at finite temperatures is predicted to behave for $d=4-ε$ dimensions ($0<ε\ll 1$) as $η\proptoε^2$. Thus, the interacting Bose-Einstein condensates are subject to long-range fluctuations similar to those at the second-order transition point, and their excitations in the one-particle channel are distinct from the Nambu-Goldstone mode with a sound-wave dispersion in the two-particle channel.

cond-mat.quant-gas↗

arXiv2018

Variational Wave Function for Inhomogeneous Bose--Einstein Condensate with 3/2-Body Correlations

We construct a variational wave function for inhomogeneous weakly interacting Bose--Einstein condensates beyond the mean-field approximation by incorporating $3/2$-body correlations. From our numerical results calculated for a system trapped by a one-dimensional harmonic oscillator, the $3/2$-body correlations give a contribution comparable to the mean- field energy toward lowering the ground-state energy.

cond-mat.quant-gas↗

arXiv2018

Number-Phase Fluctuations in Isolated Superconductors

We improve the Bardeen-Cooper-Schrieffer wave function with a fixed particle number so as to incorporate many-body correlations beyond the mean-field treatment. It is shown that the correlations lower the ground-state energy far more than Cooper-pair condensation in the weak-coupling region. Moreover, they naturally bring a superposition over the number of condensed particles. Thus, Cooper-pair condensation is special among the various bound-state formations of quantum mechanics in that number fluctuations are necessarily present in the condensate through the dynamical exchange of particles with the non-condensate reservoir. On the basis of this result, we propose $\varDelta N_{\rm con}\cdot \varDelta ϕ\gtrsim 1$ as the uncertainty relation relevant to the number-phase fluctuations in superconductors and superfluids, where the number of condensed particles $N_{\rm con}$ is used instead of the total particle number $N$. The formula implies that a macroscopic phase $ϕ$ can be established even in number-fixed superconductors and superfluids since $\varDelta N_{\rm con}\gg 1$.

cond-mat.supr-con↗

arXiv2018

Charging in a Superconducting Vortex Due to the Three Force Terms in Augmented Eilenberger Equations

We derive augmented Eilenberger equations that incorporate the following missing force terms: (i) the Lorentz force, (ii) the pair-potential gradient (PPG) force, and (iii) the pressure difference arising from the slope in the density of states (DOS). Recently, augmented Eilenberger equations with the Lorentz and PPG forces have been derived microscopically by studying the Hall and charging effects in superconductors, but the pressure due to the slope in the DOS has not yet been considered in augmented Eilenberger equations, despite phenomenological indications that it is a charging mechanism in a vortex of type-II superconductors. This newly added pressure is called "the SDOS pressure". We calculate the charging in an isolated vortex of an s-wave superconductor with a spherical Fermi surface using the augmented Eilenberger equations incorporating the Lorentz force, PPG force, and SDOS pressure. When we compare the charge densities due to the three force terms in the augmented Eilenberger equations, the vortex-core charging due to the SDOS pressure is larger than that due to the other forces near the superconducting transition temperature. Thus, when we calculate the charging in an isolated vortex of a superconductor with a finite slope in the DOS, we should consider not only the Lorentz and PPG forces but also the SDOS pressure.

cond-mat.supr-con↗

arXiv2018

Ground-State Wave Function with Interactions between Different Species in $M$-Component Miscible Bose-Einstein Condensates

We construct a variational ground-state wave function of weakly interacting M-component Bose-Einstein condensates beyond the mean-field theory by incorporating the dynamical 3/2-body processes, where one of the two colliding particles drops into the condensate and vice versa. Our numerical results with various masses and particle numbers show that the 3/2-body processes between different particles make finite contributions to lowering the ground-state energy, implying that many-body correlation effects between different particles are essential even in the weak-coupling regime of the Bose--Einstein condensates. We also consider the stability condition for $2$-component miscible states using the new ground-state wave function. Through this calculation, we obtain the relation $U^{2}_{AB}/U_{AA}U_{BB}<1+α$, where $U_{ij}$ is the effective contact potential between particles $i$ and $j$ and $α$ is the correction, which originates from the $3/2$-body and $2$-body processes.

cond-mat.quant-gas↗