arXiv subjects

Takashi Yanagisawa

Publications and source records attributed to Takashi Yanagisawa.

At least 19 recordsLinked to original sources

arXiv2025

Superconductivity and inhomogeneous charge-ordered state in the two-Dimensional Hubbard model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model IV

We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp($-S$)-type where $S$ is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The $d$-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the $d$-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.

cond-mat.str-el↗

arXiv2025

Unconventional and anomalous magnetic field distribution in a bilayer superconductor with geometric constraints

We investigate the magnetic field distribution in multi-component superconductors. We examine a layered superconductor and a two-component one-layer superconductor. We evaluate the field distribution in the presence of a half-flux quantum vortex with a kink structure in the phase space of gap functions. We also examine the magnetic field distribution of a knot soliton which is formulated in a two-component superconductor. We investigate the effect of geometric constraints for multi-component superconductors, where the geometric constraint means that the system is compactified in one direction so that the current in this direction becomes vanishingly small. This corresponds to the gauge fixing in this direction. An unconventional magnetic field distribution takes place; here the unconventional means that the magnetic field is screened incompletely which would be called the anomalous Meissner effect. We argue that this anomalous behavior creates a massless gauge field.

cond-mat.supr-con↗

arXiv2023

From Resistance Minimum to Kondo Physics

We discuss the development of Kondo physics from the resolution of the resistance minimum by J. Kondo to recent developments in physics. The Kondo effect has given a great impact to all areas of physics. This reminds us that physics is one unified science. Kondo's pioneering work has led major developments in physics. We show brief history of the Kondo effect and discuss the Kondo effect from several points of view that appeared to be important through conversations with Prof. J. Kondo.

cond-mat.str-el↗

arXiv2023

Field resilient superconductivity in atomic layer crystalline materials

A recent study [S. Yoshizawa {\it et al}., Nature Communications {\bf 12}, 1462 (2021)] reported the occurrence of field-resilient superconductivity, that is, enhancement of the in-plane critical magnetic field $H^{||}_{\rm c2}$ beyond the paramagnetic limiting field, in atomic-layer crystalline ($\sqrt{7}\times\sqrt{3}$)-In on a Si(111) substrate. The present article elucidates the origin of the observed field-resilient noncentrosymmetric superconductivity in this highly crystalline two-dimensional material. We develop the quasiclassical theory of superconductivity by incorporating the Fermi surface anisotropy together with an anisotropic spin splitting and texture specific to atomic-layer crystalline systems. In Si(111)-($\sqrt{7}\times\sqrt{3}$)-In, a typical material with a large antisymmetric spin-orbit coupling (ASOC), we show an example where the combination of the ASOC and disorder effect suppresses the paramagnetic depairing and can lead to an enhancement of $H^{||}_{\rm c2}$ compared to an isotropic system only when a magnetic field is applied in a particular direction due to an anisotropic spin texture. We also study the parity-mixing effect to demonstrate that the enhancement of $H^{||}_{\rm c2}$ is limited in the moderately clean regime because of the fragile $s$+$p$-wave pairing against nonmagnetic scattering in the case of the dominant odd-parity component of a pair wavefunction. Furthermore, from analysis of the transition line, we identify the field-resilience factor taking account of the scattering and suppression of paramagnetic effects and discuss the origin of the field-resilient superconductivity. Through fitting of the $H^{||}_{\rm c2}$ data, the normal-state electron scattering is discussed with a prime focus on the role of atomic steps on a Si(111) surface.

cond-mat.supr-con↗

arXiv2022

Ferromagnetic diagonal stripe states in the two-dimensional Hubbard model with $U\lesssim\infty$

We have performed a variational Monte Carlo simulation to study the ground state of a two-dimensional Hubbard model on a square lattice in the strong coupling region. The energy gain of possible inhomogeneous electron states are computed as a function of $U$ when the hole density $ε=1/8$ and next nearest-neighbor hopping $t'/t=-0.30$. The bond-centered ferromagnetic diagonal stripe state is stabilized in the strong coupling region ($U/t\geq$16), which is due to the gain of both kinetic energy and on-site Coulomb interaction energy due to the holon moving over the ferromagnetic domain and the gain of kinetic-exchange-interaction energy at the antiferromagnetic domain wall.

cond-mat.str-el↗

arXiv2021

Enhancement of superconductivity due to kinetic-energy effect in the strongly correlated phase of the two-dimensional Hubbard model

We investigated kinetic properties of correlated pairing states in strongly correlated phase of the Hubbard model in two space dimensions. We employ an optimization variational Monte Carlo method, where we use the improved wave function $ψ_λ= e^{-λK}ψ_G$ for the Gutzwiller wave function $ψ_G$ with $K$ being the kinetic part of the Hamiltonian. The Gutzwiller-BCS state is stabilized as the potential energy driven superconductivity because the Coulomb interaction energy is lowered while the kinetic energy increases in this state. In contrast, we show that in the $ψ_λ$-BCS wave function $ψ_{λ-BCS}= e^{-λK}P_Gψ_{BCS}$, the Coulomb energy increases and instead the kinetic energy is lowered in the strongly correlated phase where the Coulomb repulsive interaction $U$ is large. The correlated superconducting state is realized as a kinetic energy driven pairing state and this indicates the enhancement of superconductivity due to kinetic-energy effect.

cond-mat.str-el↗

arXiv2021

Phase diagram of the three-band d-p model based on the optimization variational Monte Carlo method

The phase diagram of cuprate high-temperature superconductors is investigated on the basis of the three-band d-p model. We use the optimization variational Monte Carlo method, where improved many-body wave functions have been proposed to make the ground-state wave function more precise. We investigate the stability of antiferromagnetic state by changing the band parameters such as the hole number, level difference $Δ_{dp}$ between $d$ and $p$ electrons and transfer integrals. We show that the antiferromagnetic correlation weakens when $Δ_{dp}$ decreases and the pure $d$-wave superconducting phase may exist in this region. We present phase diagrams including antiferromagnetic and superconducting regions by varying the band parameters. The phase diagram obtained by changing the doping rate $x$ contains antiferromagnetic, superconducting and also phase-separated phases. We propose that high-temperature superconductivity will occur near the antiferromagnetic boundary in the space of band parameters.

cond-mat.str-el↗

arXiv2021

Renormalization group theory of generalized multi-vertex sine-Gordon model

We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by $\cos(k_j\cdot ϕ)$ where $k_j$ ($j=1,2,\cdots,M$) are momentum vectors and $ϕ$ is an $N$-component scalar field. The beta functions are calculated for the sine-Gordon model with multi cosine interactions. The second-order correction in the renormalization procedure is given by the two-point scattering amplitude for tachyon scattering. We show that new vertex interaction with momentum vector $k_{\ell}$ is generated from two vertex interactions with vectors $k_i$ and $k_j$ when $k_i$ and $k_j$ meet the condition $k_{\ell}=k_i\pm k_j$ called the triangle condition. Further condition $k_i\cdot k_j=\pm 1/2$ is required within the dimensional regularization method. The renormalization group equations form a set of closed equations when $\{k_j\}$ form an equilateral triangle for $N=2$ or a regular tetrahedron for $N=3$. The Wilsonian renormalization group method gives qualitatively the same result for beta functions.

hep-th↗

arXiv2020

Phase diagram and mechanism of superconductivity in a strongly correlated electron system

We investigate the phase diagram of two-dimensional (2D) Hubbard model by employing the optimization variational Monte Carlo method. The 2D Hubbard model is the most simple electronic model for cuprate high-temperature superconductors. The phase diagram consists of three regions; they are antiferromagnetic insulator (AFI) region, superconducting (SC) region and the coexistent region of superconductivity and antiferromgantism. The phase diagram obtained by numerical calculations well agrees with the experimental phase diagram for high-temperature cuprates. We mainly focused on the effect of $t'$ on the antiferromagnetic (AF) correlation and the AFI region. The area of the AF phase increases when we include $t'$ and thus the pure $d$-wave SC phase decreases. The AFI phase near half filling decreases as $|t'|$ increases.

cond-mat.str-el↗

arXiv2020

Zero-energy modes, fractional fermion numbers and the index theorem in a vortex-Dirac fermion system

Physics of topological materials have attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological superconductors. A zero-energy mode exists when Dirac fermions couple to objects with soliton-like structure such as kinks, vortices, monopoles, strings and branes. We discuss a system of Dirac fermions interacting with a vortex and a kink. This kind of systems will be realized on the surface of topological insulators where Dirac fermions exist. The fermion number is fractionalized and this is related to the presence of fermion zero-energy excitation modes. A zero-energy mode can be regarded as a Majorana fermion mode when the chemical potential vanishes. Our discussion includes the case where there is a half-flux quantum vortex associated with a kink in a magnetic field in a bilayer superconductor. A normalizable wave function of fermion zero-energy mode does not exist in the core of the half-flux quantum vortex. The index of Dirac operator and the fermion number have additional contributions when a soliton scalar field has a singularity.

hep-th↗

arXiv2019

Fractional skyrmion and absence of low-lying Andreev bound states in a micro fractional-flux quantum vortex

We investigate quasi-particle excitation modes and the topological number of a fractional-flux quantum vortex in a layered (multi-component) superconductor. The Bogoliubov equation for a half-flux quantum vortex is solved to show that there is no low-lying Andreev bound state near zero energy in the core of a quantum vortex, which is surprisingly in contrast to the result for an inter-flux vortex. Related to this result, there are singular excitation modes that have opposite angular momenta, moving in the opposite direction around the core of the vortex. The topological index (skyrmion number) for a fractional-flux quantum vortex becomes fractional since the topological index is divided into two parts where one from the vortex (bulk) and the other from the kink (domain wall, boundary). The topological numbers for both the vortex and the kink (domain wall) are fractional, and their sum becomes an integer. This shows an interesting analogy between this result and the index theorem for manifolds with boundary. We argue that fractional-flux quantum vortices are not commutative each other and follow non-abelian statistics. This non-abelian statistics of vortices is different from that in p-wave superconductors.

cond-mat.supr-con↗

arXiv2019

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

It is very important to elucidate the mechanism of superconductivity for achieving room temperature superconductivity. This paper is a short review article on the mechanism of high-temperature superconductivity. In the first half of this paper, we give a brief review on mechanisms of superconductivity in many-electron systems. We believe that high-temperature superconductivity may occur in a system with interaction of large-energy scale. Empirically, this is true for superconductors that have been found so far. In the second half of this paper, we discuss cuprate high-temperature superconductors. We argue that superconductivity of high temperature cuprates is induced by the strong on-site Coulomb interaction, that is, the origin of high-temperature superconductivity is the strong electron correlation. We show the results on the ground state of electronic models for high temperature cuprates on the basis of the optimization variational Monte Carlo method. A high-temperature superconducting phase will exist in the strongly correlated region.

cond-mat.str-el↗

arXiv2019

Antiferromagnetism, Superconductivity and Phase Diagram in the Two-Dimensional Hubbard Model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model III --

We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion $U$, the band parameter $t'$ and the electron density $n_e$. We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.

cond-mat.str-el↗

arXiv2019

Green's functions of Nambu-Goldstone modes and Higgs modes in superconductors

We examine fundamental properties of Green's functions of Nambu-Goldstone and Higgs modes in superconductors with multiple order parameters. Nambu-Goldstone and Higgs modes are determined once the symmetry of the system and that of the order parameters are specified. Multiple Nambu-Goldstone modes and Higgs modes exist when we have multiple order parameters. The Nambu-Goldstone Green function $D(ω,{\bf q})$ has the form $1/(gN(0))^2\cdot (2Δ)^2/(ω^2-c_s^2{\bf q}^2)$ with the coupling constant $g$ and $c_s=v_F/\sqrt{3}$ for small $ω$ and ${\bf q}$, with a pole at $ω=0$ and ${\bf q}=0$ indicating the existence of a massless mode. It is shown, based on the Ward-Takahashi identity, that the massless mode remains massless in the presence of intraband scattering due to nonmagnetic and magnetic impurities. The pole of $D(ω,{\bf q})$, however, disappears as $ω$ increases as large as $2Δ$: $ω\sim 2Δ$. The Green function $H(ω,{\bf q})$ of the Higgs mode is given by $H(ω,{\bf q})\propto (2Δ)^2/((2Δ)^2-\frac{1}{3}ω^2+\frac{1}{3}c_s^2{\bf q}^2)$ for small $ω$ and ${\bf q}$. $H(ω,{\bf q})$ is proportional to $1/(gN(0))^2\cdot Δ/\sqrt{ (2Δ)^2+c_s^2{\bf q}^2-ω^2}$ for $ω\sim 2Δ$ and $ω< ω({\bf q})$. This behavior is similar to that of the $σ$-particle Green function in the Gross-Neveu model. That is, the Higgs Green function $H(ω, {\bf q})$ has the same singularity as the Green function of the $σ$ boson of the Gross-Neveu model. The constant part of the action for the Higgs modes is important since it determines the coherence length of a superconductor. There is the case that it has a large eigenvalue, indicating that the large upper critical field $H_{c2}$ may be realized in a superconductor with multiple order parameters.

cond-mat.supr-con↗

arXiv2019

Renormalization group analysis of the hyperbolic sine-Gordon model -- Asymptotic freedom from cosh interaction --

We present a renormalization group analysis for the hyperbolic sine-Gordon (sinh-Gordon) model in two dimensions. We derive the renormalization group equations based on the dimensional regularization method and the Wilson method. The same equations are obtained using both these methods. We have two parameters $α$ and $β\equiv \sqrt{t}$ where $α$ indicates the strength of interaction of a real salar field and $t=β^2$ is related with the normalization of the action. We show that $α$ is renormalized to zero in the high-energy region, that is, the sinh-Gordon theory is an asymptotically free theory. We also show a non-renormalization property that the beta function of $t$ vanishes in two dimensions.

hep-th↗

arXiv2018

Massless and quantized modes of kinks in the phase space of superconducting gaps

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory.

cond-mat.supr-con↗

arXiv2018

Renormalization group theory of effective field theory models in low dimensions

This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We consider the models that are universal and frequently appear in physics, both in high-energy physics and condensed-matter physics. They are the non-linear sigma model, the $ϕ^4$ model and the sine-Gordon model. We use the dimensional regularization method to regularize the divergence and derive the renormalization group equations called the beta functions. The dimensional method is described in detail.

cond-mat.stat-mech↗

arXiv2017

Nambu-Goldstone bosons characterized by the order parameter in spontaneous symmetry breaking

We present explicitly a relation between the Nambu-Goldstone boson and the order parameter in non-relativistic systems with spontaneous symmetry breaking. We show that the Nambu-Goldstone bosons are characterized by transformation property of the order parameter under symmetry transformation of a system. We give an explicit formula for the Nambu-Goldstone boson for a general Lie group $G$, and then the number of the Nambu-Goldstone boson is derived straightforwardly from the symmetry of the order parameter, i.e. the type of symmetry breaking. We show that the Ward-Takahashi identity is modified in the presence of the Nambu-Goldstone boson, where the generalized Ward-Takahashi identity includes the coupling (the vertex function) between fermions and Nambu-Goldstone bosons. The closed equation for the Green's functions of Nambu-Goldstone bosons is derived by introducing the fermion-Nambu-Goldstone boson vertex function. Examples are given for $G=SU(2)$ (ferromagnetic), $U(1)$ (superconductor) and $SU(3)$ symmetry breaking.

hep-th↗