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In this article, we propose the Artificial Intelligence Security Taxonomy to systematize the knowledge of threats, vulnerabilities, and security controls of machine-learning-based (ML-based) systems. We first classify the damage caused by attacks against ML-based systems, define ML-specific security, and discuss its characteristics. Next, we enumerate all relevant assets and stakeholders and provide a general taxonomy for ML-specific threats. Then, we collect a wide range of security controls against ML-specific threats through an extensive review of recent literature. Finally, we classify the vulnerabilities and controls of an ML-based system in terms of each vulnerable asset in the system's entire lifecycle.

The link between the metamagnetic transition and novel spin-triplet superconductivity of UTe$_2$ was discussed thermodynamically through magnetostriction measurements in a pulsed-magnetic field. We revealed a discontinuous magnetostriction across the metamagnetic transition at $\mu_0H_{\rm m}\approx 35$~T for the applied magnetic fields along the crystallographic $b$ axis in the orthorhombic structure. The resultanting volume magnetostriction of $\Delta V/V \approx-5.9\times 10^{-4}$ gives the initial pressure dependence of $H_{\rm m}$ by employing the Clausius-Clapeyron's equation, which agrees with previous pressure experiments. Further, significant anisotropic magnetostriction (AMS), derived by subtracting the averaged linear magnetostriction, was revealed. Contrary to the weakly field-dependent AMS along the $a$ axis, those along the $b$ and $c$ axes show strong field dependences with a similar magnitude but with opposite signs, indicating its lattice instability. The relationship between characteristic energy scales of magnetic fields and temperatures was discussed in terms of the Gr\"uneisen parameters compared to the other $f$-electron systems. The volume shrinkage in UTe$_2$ at $H_{\rm m}$, contrary to the volume expansion in typical heavy fermion metamagnets, pushes to invoke the link with the valence instability related to the itinerant-localized dual nature of the U magnetism., Comment: 6 pages, 5 figures, including supplemental material. To be published in Journal of Physical Society of Japan

It is discussed from theoretical viewpoint why the aspects of enhancements in the A-coefficient in the resistivity\cite{Knafo}and the Sommerfeld constant \gamma \cite{AtsushiMiyake,Imajo} observed in UTe2 around the metamagnetic transition at H=H_m are so different. In particular, the discussions are focused on the reason why the H dependence of the A-coefficient reported in Ref.\citen{Knafo} and \gamma reported in Ref.\citen{AtsushiMiyake}is almost symmetric around H=H_{\rm m}, while \gamma(H) at H\gsim H_m, reported in Ref.\citen{Imajo}, is considerably suppressed compared to that at H\lsim H_m. A key point to solve this seeming paradox is to take properly into account the difference in time scales of probes used in those measurements of pulsed magnetic field method with different time scales. Another crucial effect is the time dependent non-uniform magnetic fluctuations remaining in a certain period of time after the first-order metamagnetic transition has occurred. Indeed, the time scales of former measurements in Refs.\citen{Knafo,AtsushiMiyake} are far shorter than that of the latter one in Ref.\citen{Imajo}, which can solve the above paradox., Comment: 9 pages, 1 figure

The mechanism underlying the enhancement of the Sommerfeld coefficient of quasiparticles at the first-order metamagnetic transition in UTe_2, reported by Miyake et al. in J. Phys. Soc. Jpn. 88, 063706 (2019), is discussed theoretically by taking into account the ferromagnetic order-parameter fluctuations on the basis of the Landau theory of phase transition. We find that the enhanced ferromagnetic spin fluctuation gives rise to the enhancement of the effective mass of the quasiparticles or the Sommerfeld coefficient \gamma,which is consistent with the experimental observations. At the same time, the Kadowaki-Woods type scaling around the metamagnetic transition, reported by Imajo et al.in J. Phys. Soc. Jpn. 88, 083705 (2019) and Knafo et al. in J. Phys. Soc. Jpn. 88, 063705 (2019), is also understood semi-quantitatively by assuming reasonable values of parameters of Landau-type free energy reproducing key quantities characterizing the metamagnetic transition., Comment: Accepted for publication in J. Phys. Soc. Jpn

The effect of pressure on the unique electronic state of the antiferromagnetic (AF) compound EuCu2Ge2 has been measured in a wide temperature range from 10 mK to 300 K by electrical resistivity measurements up to 10 GPa. The Neel temperature of TN = 15 K at ambient pressure increases monotonically with increasing pressure and becomes a maximum of TN = 27 K at 6.2 GPa but suddenly drops to zero at Pc = 6.5 GPa, suggesting the quantum critical point (QCP) of the valence transition of Eu from a nearly divalent state to that with trivalent weight. The rhomag0 and A values obtained from the low-temperature electrical resistivity based on the Fermi liquid relation of rhomag = rhomag0 + AT^2 exhibit huge and sharp peaks around Pc. The exponent n obtained from the power law dependence rhomag = rhomag0 + BT^n is clearly less than 1.5 at P = Pc = 6. 5 GPa, which is expected at the AF-QCP. These results indicate that Pc coincides with Pv, corresponding to the quantum criticality of the valence transition pressure Pv. The electronic specific heat coefficient, estimated from the generalized Kadowaki-Woods relation, is about 510 mJ/mol K^2 around Pc, suggesting the formation of a heavy-fermion state., Comment: 12 pages, 5 figures

It was reported by Shiino et al in J. Phys. Soc. Jpn. 86, 123705 (2017) that Ce_xLa_{1-x} Cu_{5.62} Au_{0.38} (x=0.02-0.10) exhibits a new type of quantum criticality in both magnetic and thermal properties, which is the same as that observed in a series of materials exhibiting quantum critical valence fluctuations (QCVF), such as \beta-YbAlB_4, Yb_{15}Al_{34}Au_{51}, and so on. However, the temperature (T) dependence in the resistivity rho(T) for T<0.5K is quite anomalous, i.e., \rho(T)\propto (const.-T^{n}) with n \simeq 0.75 at x=0.05. We find that this anomalous exponent is given by n=2(1-\zeta), with zeta being the weakly temperature dependent (0.5 \lsim \zeta \lsim 0.7) critical exponent for the QCVF.The observed critical exponent n\simeq 0.75 at x=0.05 is reproduced by choosing \zeta\simeq 0.63 which is consistent with the divergent behavior observed in the uniform magnetic susceptibility \chi\propto T^{-\zeta} with \zeta\simeq 0.67 at x=0.02., Comment: 7 pages, 2 figures, International Conference on Strongly Correlated Systems (SCES2019)

The excess increase of the local field distribution width $\Delta H\equiv\sigma/\gamma_{\mu}$ (with $\gamma_{\mu}=135.5\,$MHz/T being the gyromagnetic ratio of $\mu^{+}$), and/or the spontaneous magnetic field $H_{\rm spon}$, have been reported in the superconducting state of a series of compounds more than 10 by $\mu$SR (muon spin rotation or relaxation) experiment. Sizes of these quantities are of the order of 1G on the whole. We propose that the increase of the local field distribution $\Delta H$ in those compounds, including ions with strong spin-orbit interaction of 5d electrons, such as La in LaNiGa$_2$ or Re in Re$_6$Zr, is possible through the cooperation of the spin-orbit coupling between the quasiparticles and ionic vibrations (phonons) and the conventional quasiparticles-phonon coupling, inducing the spin-triplet p-wave pairing with helical symmetry breaking superconducting state with chiral super spin current around stopped $\mu^{+}$ site. The size of $\Delta H$ is estimated as of the order of 1G, in consistent with experimental observations., Comment: 9 pages, 2 figures, Proceedings of J-Physics 2019: International Conference on Multipole Physics and Related Phenomena

A theory for treating the unconventional non-Fermi liquid temperature dependence of physical quantities, such as the resistivity, in the Pr-based two-channel Anderson impurities system is developed. It is shown that their temperature dependences are essentially the same as those in the pure lattice system except for the case of extremely low concentration of Pr ions that is difficult to realize by a controlled experiments. This result is consistent with recent observations in diluted Pr-1-2-20 system Y$_{1-x}$Pr$_x$Ir$_2$Zn$_{20}$ ($x=0.024,\,0.044,\,0.085,$ and $0.44$) reported in Yamane $et\ al$. Phys. Rev. Lett. ${\bf 121}$, 077206 (2018), and is quite different from that in the case of single-channel Anderson impurities system in which the crossover between behaviors of the local Fermi liquid and heavy Fermi liquid occurs at around moderate concentration of impurities as observed in Ce-based heavy fermion system La$_{1-x}$Ce$_x$Cu$_6$., Comment: 32 pages, 8 figures

The mechanism of not diverging Gr\"{u}neisen parameter in the quantum critical heavy-fermion quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed. We construct the formalism for calculating the specific heat $C_V(T)$, the thermal-expansion coefficient $\alpha(T)$, and the Gr\"{u}neisen parameter $\Gamma(T)$ near the quantum critical point of the Yb valence transition. By applying the framework to the QC, we calculate $C_V(T)$, $\alpha(T)$, and $\Gamma(T)$, which explains the measurements. Not diverging $\Gamma(T)$ is attributed to the robustness of the quantum criticality in the QC under pressure. The difference in $\Gamma(T)$ at the lowest temperature between the QC and approximant crystal is shown to reflect the difference in the volume derivative of characteristic energy scales of the critical Yb-valence fluctuation and the Kondo temperature. Possible implications of our theory to future experiments are also discussed., Comment: 13 pages, 5 figures

Complete expressions of the thermal-expansion coefficient $\alpha$ and the Gr\"{u}neisen parameter $\Gamma$ are derived on the basis of the self-consistent renormalization (SCR) theory. By considering zero-point as well as thermal spin fluctuation under the stationary condition, the specific heat for each class of the magnetic quantum critical point (QCP) specified by the dynamical exponent $z=3$ (FM) and $z=2$ (AFM) and the spatial dimension ($d=3$ and $2$) is shown to be expressed as $C_{V}=C_a-C_b$, where $C_a$ is dominant at low temperatures, reproducing the past SCR criticality endorsed by the renormalization group theory. Starting from the explicit form of the entropy and using the Maxwell relation, $\alpha=\alpha_a+\alpha_b$ (with $\alpha_a$ and $\alpha_b$ being related to $C_a$ and $C_b$, respectively) is derived, which is proven to be equivalent to $\alpha$ derived from the free energy. The temperature-dependent coefficient found to exist in $\alpha_b$, which is dominant at low temperatures, contributes to the crossover from the quantum-critical regime to the Curie-Weiss regime and even affects the quantum criticality at 2d AFM QCP. Based on these correctly calculated $C_{V}$ and $\alpha$, Gr\"{u}neisen parameter $\Gamma=\Gamma_a+\Gamma_b$ is derived, where $\Gamma_a$ and $\Gamma_b$ contain $\alpha_a$ and $\alpha_b$, respectively. The inverse susceptibility coupled to the volume $V$ in $\Gamma_b$ gives rise to divergence of $\Gamma$ at the QCP for each class even though characteristic energy scale of spin fluctuation $T_0$ is finite at the QCP, which gives a finite contribution in $\Gamma_a=-\frac{V}{T_0}\left(\frac{\partial T_0}{\partial V}\right)_{T=0}$. General properties of $\alpha$ and $\Gamma$ including their signs as well as the relation to $T_0$ and the Kondo temperature in temperature-pressure phase diagrams of Ce- and Yb-based heavy electron systems are discussed., Comment: 30 pages, 12 figures

Charge-transfer effect under odd-parity crystalline electric field (CEF) is analyzed theoretically. In quantum-critical metal $\beta$-YbAlB$_4$, seven-fold configuration of B atoms surrounding Yb atom breaks local inversion symmetry at the Yb site, giving rise to the odd-parity CEF. Analysis of the CEF on the basis of hybridization picture shows that admixture of 4f and 5d wave functions at Yb with pure imaginary coefficient occurs, which makes magnetic-toroidal (MT) and electric-dipole (ED) degrees of freedom active. By constructing the minimal model for periodic crystal $\beta$-YbAlB$_4$, we show that the MT as well as ED fluctuation is divergently enhanced at the quantum critical point of valence transition simultaneously with critical valence fluctuations., Comment: 10 pages, 3 figures, proceedings of the J-Physics2019 conference

The thermal expansion coefficient $\alpha$ and the Gr\"{u}neisen parameter $\Gamma$ near the magnetic quantum critical point (QCP) are derived on the basis of the self-consistent renormalization (SCR) theory of spin fluctuation. From the SCR entropy, the specific heat $C_{V}$, $\alpha$, and $\Gamma$ are shown to be expressed in a simple form as $C_{V}=C_{\rm a}-C_{\rm b}$, $\alpha=\alpha_{\rm a}+\alpha_{\rm b}$, and $\Gamma=\Gamma_{\rm a}+\Gamma_{\rm b}$, respectively, where $C_{\rm i}$, $\alpha_{\rm i}$, and $\Gamma_{\rm i}$ $({\rm i}={\rm a}, {\rm b})$ are related with each other. As the temperature $T$ decreases, $C_{\rm a}$, $\alpha_{\rm b}$, and $\Gamma_{\rm b}$ become dominant in $C_{V}$, $\alpha$, and $\Gamma$, respectively. The inverse susceptibility of spin fluctuation coupled to the volume $V$ in $\Gamma_{\rm b}$ is found to give rise to the divergence of $\Gamma$ at the QCP for each class of ferromagnetism and antiferromagnetism (AFM) in spatial dimensions $d=3$ and $2$. This $V$-dependent inverse susceptibility in $\alpha_{b}$ and $\Gamma_{\rm b}$ contributes to the $T$ dependences of $\alpha$ and $\Gamma$, and even affects their criticality in the case of the AFM QCP in $d=2$. $\Gamma_{\rm a}$ is expressed as $\Gamma_{\rm a}(T=0)=-\frac{V}{T_0}\left(\frac{\partial T_0}{\partial V}\right)_{T=0}$ with $T_0$ being the characteristic temperature of spin fluctuation, which has an enhanced value in heavy electron systems., Comment: 7 pages, 2 figures

Progress of theories and experiments of the quantum valence criticality is overviewed focusing on recent discoveries of direct evidence of quantum critical point of valence transitions in periodic crystal $\alpha$-YbAl$_{1-x}$Fe$_x$B$_4$ at $x=0.014$ and quasicrystal Yb$_{15}$(Al$_{1-x} $Ga$_{x}$)$_{34}$(Au$_{1-y}$Cu$_{y}$)$_{51}$ at $x=y=0$. The common quantum criticality as well as $T/B$ scaling behavior in the magnetization observed in the periodic crystal $\beta$-YbAlB$_4$ and quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ is shown to be explained from the theory of critical Yb-valence fluctuations starting from the Hamiltonians for describing the low-energy electronic states in both systems., Comment: 12 pages, 4 figures, proceedings of SCES2019 conference

A novel property of the quantum critical heavy fermion superconductor $\beta$-YbAlB$_4$ is revealed theoretically. By analyzing the crystalline electronic field (CEF) on the basis of the hybridization picture, odd parity CEF is shown to exist because of sevenfold configuration of B atoms around Yb, which breaks the local inversion symmetry. This allows onsite admixture of 4f and 5d wavefunctions with a pure imaginary coefficient, giving rise to the magnetic toroidal (MT) degree of freedom. By constructing a realistic minimal model for $\beta$-YbAlB$_4$, we show that onsite 4f-5d Coulomb repulsion drives charge transfer between the 4f and 5d states at Yb, which makes the MT fluctuation as well as the electric dipole fluctuation diverge simultaneously with the critical Yb-valence fluctuation at the quantum critical point of the valence transition., Comment: 5 pages, 3 figures

The density of low energy particle-hole excitations is non-analytic in a singular Fermi-liquid, but it is altered on entering a superconducting state in which, in the pure limit, it vanishes asymptotically at the chemical potential and in general is analytic. The single-particle excitations in the superconducting states are then quasi-particles so that a form of Landau theory may be constructed for thermodynamic and transport properties in the superconducting state. In this theory, the renormalization of measurable properties due to quasi-particle interactions, such as specific heat, compressibility, magnetic susceptibility, superfluid density, etc. changes in a temperature dependent fashion from the non-interacting theory. This is illustrated by showing the renormalization of these quantities and the relation between the parameters introduced to account for their temperature dependence. When the renormalizations in the normal state are large or singular, temperature dependence of properties in the superconducting states are then in general not useful for identifying the nodal character or symmetry of the superconducting state except for measurements at very low temperatures, upper limits of which are specified. The results obtained are expected to be useful in interpreting the experimental results for the temperature dependence of various properties in the superconducting state born of singular Fermi liquids.

A theory for anomalous enhancement of NMR relaxation rate $1/T_{1}T$ of $^{125}$Te toward zero temperature observed in Pb$_{1-x}$Tl$_{x}$Te ($x$=0.01) is presented on the idea of the charge Kondo effect of valence skipping element Tl. It is found that such enhancement in $1/T_{1}T$ is caused through enhancement of the pair-hopping and inter-orbital interactions between 6s electrons localized on Tl site and conduction electrons doped in the hole band the semiconductor PbTe, which is the heart of the charge Kondo effect. It is also found that the Knight shift is not influenced in the temperature region where the relaxation rate is enhanced which is consistent with the experimental observation showing that the Korringa relation is apparently broken., Comment: 28 pages, 12 figures, ver.2, to be submitted to J. Phys. Soc. Jpn

To get an insight into a new type of quantum critical phenomena recently discovered in the quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ and approximant crystal (AC) Yb$_{14}$Al$_{35}$Au$_{51}$ under pressure, we discuss the property of the crystalline electronic field (CEF) at Yb in the AC and show that uneven CEF levels at each Yb site can appear because of the Al/Au mixed sites. Then we construct the minimal model for the electronic state on the AC by introducing the onsite Coulomb repulsion between the 4f and 5d orbitals at Yb. Numerical calculation for the ground state shows that the lattice constant dependence of the Yb valence well explains the recent measurement done by systematic substitution of elements of Al and Au in the quasicrystal and AC, where the quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ is just located at the point from where the Yb-valence starts to change drastically. Our calculation convincingly demonstrates that this is indeed the evidence that this material is just located at the quantum critical point of the Yb-valence transition., Comment: 12 pages, 8 figures, Invited Paper in the 26th International Conference on High Pressure Science & Technology (AIRAPT 26)

Despite almost 40 years of research, the origin of heavy-fermion superconductivity is still strongly debated. Especially, the pressure-induced enhancement of superconductivity in CeCu$_2$Si$_2$ away from the magnetic breakdown is not sufficiently taken into consideration. As recently reported in CeCu$_2$Si$_2$ and several related compounds, optimal superconductivity occurs at the pressure of a valence crossover, which arises from a virtual critical end point at negative temperature $T_{\rm cr}$. In this context, we did a meticulous analysis of a vast set of top-quality high-pressure electrical resistivity data of several Ce-based heavy fermion compounds. The key novelty is the salient correlation between the superconducting transition temperature $T_{\rm c}$ and the valence instability parameter $T_{\rm cr}$, which is in line with theory of enhanced valence fluctuations. Moreover, it is found that, in the pressure region of superconductivity, electrical resistivity is governed by the valence crossover, which most often manifests in scaling behavior. We develop the new idea that the optimum superconducting $T_{\rm c}$ of a given sample is mainly controlled by the compound's $T_{\rm cr}$ and limited by non-magnetic disorder. In this regard, the present study provides compelling evidence for the crucial role of critical valence fluctuations in the formation of Cooper pairs in Ce-based heavy fermion superconductors besides the contribution of spin fluctuations near magnetic quantum critical points, and corroborates a plausible superconducting mechanism in strongly correlated electron systems in general., Comment: Supplementary Material follows after the bibliography

The local magnetic field induced by $\mu^{+}$ trapped at an interstitial site in a chiral superconductor with $p$-wave symmetry, such as Sr$_2$RuO$_4$, is discussed by solving the Bogoliubov-de Gennes equation on the two-dimensional square lattice. In the model Hamiltonian, the effect of the trapped $\mu^{+}$ extracting the electrons at surrounding Ru sites is phenomenologically taken into account as a non-magnetic impurity potential which locally destroys the chiral superconducting order with $p$-wave symmetry giving rise to local circulating current around $\mu^{+}$ site. It is shown that the size of the induced local magnetic field in the case with periodic boundary condition is far smaller compared to the case with open boundary condition without $\mu^{+}$, in which the surface current induced by destruction of superconducting order at the surface boundary gives contribution corresponding to the intrinsic angular momentum of the order of $\hbar N_{\rm s}/2$, with $N_{\rm s}$ being the number of superconducting electrons. This result qualitatively explains why the magnetic field $\simeq0.5$G measured by $\mu$SR in Sr$_2$RuO$_4$ is far smaller than the expected intrinsic magnetic field $\simeq 50$G which is nearly the same as the lower critical field $H_{{\rm c}1}\simeq 50$G., Comment: 6 pages, 5 figures, submitted to J. Phys. Soc. Jpn

Recently, it was reported by MacLaughlin et al. in Phys. Rev. B 93, 214421 (2016) that \alpha-YbAl_{0.986}Fe_{0.014}B_4 exhibits an anomalous temperature dependence in the relaxation rate 1/T_{1} of $\mu$SR, and stressed that such temperature dependence cannot be understood by the scenario based on the quantum critical valence transition (QCVT) while this compound exhibits a series of the non-Fermi liquid behaviors explained by the theory of the QCVT. In this paper, we point out that the anomalous temperature dependence in 1/T_{1} can be understood semi-quantitatively by assuming that the attraction of a screening cloud of conduction electrons about the \mu^{+} induces a local magnetic moment arising from a 4f hole on the Yb ion, giving rise to the Kondo effect between heavy quasiparticles., Comment: 16 pages, 7 figures

Unconventional quantum critical phenomena observed in Yb-based periodic crystals such as YbRh$_2$Si$_2$ and $\beta$-YbAlB$_4$ have been one of the central issues in strongly correlated electron systems. The common criticality has been discovered in quasicrystal Yb$_{15}$Au$_{51}$Al$_{34}$, which surprisingly persists under pressure at least up to $P=1.5$ GPa. The $T/H$ scaling where the magnetic susceptibility can be expressed as a single scaling function of the ratio of temperature $T$ and magnetic field $H$ has been discovered in the quasicrystal, which is essentially the same as that observed in $\beta$-YbAlB$_4$. Recently, the $T/H$ scaling as well as the common criticality has been also observed even in the approximant crystal Yb$_{14}$Au$_{51}$Al$_{35}$ under pressure. The theory of critical Yb-valence fluctuation gives a natural explanation for these striking phenomena in a unified way., Comment: 17 pages, 5 figures, Invited review paper in the 17th International Conference on High Pressure in Semiconductor Physics (HPSP-17) & Workshop on High-pressure Study on Superconducting (WHS)

To get insight into the mechanism of emergence of unconventional quantum criticality observed in quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$, the approximant crystal Yb$_{14}$Al$_{35}$Au$_{51}$ is analyzed theoretically. By constructing a minimal model for the approximant crystal, the heavy quasiparticle band is shown to emerge near the Fermi level because of strong correlation of 4f electrons at Yb. We find that charge-transfer mode between 4f electron at Yb on the 3rd shell and 3p electron at Al on the 4th shell in Tsai-type cluster is considerably enhanced with almost flat momentum dependence. The mode-coupling theory shows that magnetic as well as valence susceptibility exhibits $\chi\sim T^{-0.5}$ for zero-field limit and is expressed as a single scaling function of the ratio of temperature to magnetic field $T/B$ over four decades even in the approximant crystal when some condition is satisfied by varying parameters, e.g., by applying pressure. The key origin is clarified to be due to the strong locality of the critical Yb-valence fluctuation and small Brillouin zone reflecting the large unit cell, giving rise to the extremely-small characteristic energy scale. This also gives a natural explanation for the quantum criticality in the quasicrystal corresponding to the infinite limit of the unit-cell size., Comment: 5 pages, 4 figures

It is shown by the Wilson numerical renormalization group method that a strongly correlated impurity with a crystalline-electric-field singlet ground state in the f^2-configuration exhibits an anomalous local Fermi liquid state in which the static magnetic susceptibility remains an uncorrelated value while the NMR relaxation rate is enhanced in proportion to the square of the mass enhancement factor. Namely, the Korringa-Shiba relation is apparently broken. This feature closely matches the anomalous behaviors observed in UPt_3, i.e., the coexistence of an unenhanced value of the Knight shift due to quasiparticles contribution (the decrease across the superconducting transition) and the enhanced relaxation rate of NMR. Such an anomalous Fermi liquid behavior suggests that the Fermi liquid corrections for the susceptibility are highly anisotropic., Comment: 20 pages, 11 figures

Exact formulas of diagonal conductivity $\sigma_{xx}$ and Hall conductivity $\sigma_{xy}$ are derived from the Kubo formula in hybridized two-orbital systems with arbitrary band dispersions. On the basis of the theoretical framework for the Fermi liquid based on these formulas, the ground-state properties of the periodic Anderson model with electron correlation and weak impurity scattering are studied on the square lattice. It is shown that imbalance of the mass-renormalization factors in $\sigma_{xx}$ and $\sigma_{xy}$ causes remarkable increase in the valence-fluctuation regime as the f level increases while the cancellation of the renormalization factors causes slight increase in $\sigma_{xx}$ and $\sigma_{xy}$ in the Kondo regime. The Hall coefficient $R_{\rm H}$ shows almost constant behavior in both the regimes. Near half filling, $R_{\rm H}$ is expressed by the total hole density as $R_{\rm H}=1/(\bar{n}_{\rm hole}e)$ while $R_{\rm H}$ approaches zero near quarter filling, which reflects the curvature of the Fermi surface. These results hold as far as the damping rate for f electrons is less than about $10~\%$ of the renormalized hybridization gap. From these results we discuss pressure dependence of residual resistivity and normal Hall effect in Ce- and Yb-based heavy electron systems., Comment: 17 pages, 18 figures

The intrinsic magnetic moment (IMM) and intrinsic angular momentum (IAM) of a chiral superconductor with $p$-wave symmetry on a two-dimensional square lattice are discussed on the basis of the Bogoliubov-de Gennes equation. The the IMM and IAM are shown to be on the order of $\mu_{\rm B}N$ and $\hbar N$, respectively, $N$ being the total number of particles, without an extra factor $(T_{\rm c}/T_{\rm F})^{\gamma}$ ($\gamma=1,2$), and parallel to the pair angular momentum. They arise from the current in the surface layer with a width on the order of the coherence length $\xi_{0}$, the size of Cooper pairs. However, in a single-band model, they are considerably canceled by the contribution from the Meissner surface current in a layer with the width of the penetration depth $\lambda$, making it difficult to observe them experimentally. In the case of multi-band metals with both electron-like and hole-like bands, however, considerable cancellation still occurs for the IMM but not for the IAM, making it possible to observe the IAM selectively because the effect of the Meissner current becomes less important. As an example of a multi-band metal, the case of the spin-triplet chiral superconductor Sr$_2$RuO$_4$ is discussed and experiments for observing the IAM are proposed., Comment: 27 pages, 15 figures

The Ginzburg-Landau formalism is constructed for Fermi superfluidity based on the 2n-body condensation in parallel with the usual Ginzburg-Landau formalism for the Cooper pair condensation. By this formalism, the transition temperature of the 2n-body condensation is given compactly by the zero of coefficient of the quadratic term in the 2n-body condensed order parameter without counting complicated Feynman diagrams for the 2n-body condensation susceptibility. It is shown that the 2n-body condensed state is stabilized in the intermediate- or strong-coupling regime against the BCS state based on the Cooper pair condensation. This theory is applied to the case of the possible superfluid state of cold atomic gases such as $^9$Be and $^{173}$Yb; the quartet state is possible in the former case, while the sextet state is expected in the latter case. It is predicted that the $^{173}$Yb atomic gas so far attained satisfies the condition for the sextet condensed state to be realized., Comment: 48 pages, 13 figures, published in September issue of JPSJ 2014 (i.e., one year old)

On the basis of the Luttinger-Ward formalism for the thermodynamic potential, the specific heat of single-component interacting fermion systems with fixed chemical potential is compactly expressed in terms of the fully renormalized Matsubara Green function., Comment: 10 pages, 1 figure, published in JPSJ online on August 18

We theoretically investigate electronic states and physical properties in a two-channel Anderson lattice model to understand the non-Fermi liquid behaviors observed in PrV$_2$Al$_{20}$ and PrIr$_2$Zn$_{20}$ whose ground state of the crystalline electric field for local $f$-electron is the $\Gamma_3$ non-Kramers doublet of $f^2$-configuration and excited state is the $\Gamma_7$ Kramers doublet of $f^1$-configuration. We use the expansion from the limit of large degeneracy $N$ of the ground state ($1/N$-expansion), with $N$ being the spin-orbital degeneracy. Inclusion of the self-energy of the conduction electrons up to the order of $O(1/N)$ leads to heavy electron with channel and spin-orbit degeneracies. We find that the electrical resistivity is proportional to temperature $T$ in the limit of $T\to0$ and follows $\sqrt{T}$-law in the wide region of temperature, i.e., $T_x

It is shown that an asymmetric spin-orbit interaction is appreciably renormalized by the effect of critical spin fluctuations. As an explicit example, the Rashba-type interaction is predicted to be suppressed by anti-ferromagnetic critical fluctuations near the hot line (or point), leading to a deformation of the Fermi surface near the hot line (or point) around which the band splitting is decreased, while ferromagnetic critical fluctuations are shown to enhance the Rashba-type interaction everywhere on the Fermi surface, leading to an increase in the band splitting. It is also found that the many-body mass renormalization, which diverges towards the magnetic quantum critical point, is in the opposite sign for the two split bands by the Rashba-type interaction. These predictions are observable by the de Haas-van Alphen (dHvA) effect in principle., Comment: Published as an article in the Letter section of J. Phys. Soc. Jpn.; 11 pages, 2 figures; Supplemental Materials (20 pages) is referred as Ref. 23 in the main text

The Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover in the two-dimensional attractive Hubbard model under the magnetic field is discussed at the half-filling at T=0 K on the basis of the formalism of Eagles and Leggett. It is shown that the so-called Fulde-Ferrel-Larkin-Ovchinikov-like state with a non-zero center-of-mass wave vector ${\bf q}\not=0$ is not stabilized in the weak-coupling (BCS) region, while such a state with ${\bf q}\not=0$ is stabilized against that with ${\bf q}=0$ even in a wide strong-coupling (BEC) region where di-fermion molecules are formed. The physical implication of this surprising result is discussed., Comment: 10 pages, 7 figures

The mechanism of the emergence of robust quantum criticality in the heavy-electron quasicrystal Yb15Al34Au51 is analyzed theoretically. By constructing a minimal model for the quasicrystal and its crystalline approximant, which contain concentric shell structures with Yb and Al-Au clusters, we show that a set of quantum critical points of the first-order valence transition of Yb appears as spots in the ground-state phase diagram. Their critical regions overlap each other, giving rise to a wide quantum critical region. This well explains the robust criticality observed in Yb15Al34Au51 under pressure, and predicts the emergence of the common criticality in the crystalline approximant under pressure. The wider critical region in the quasicrystal than that in the crystalline approximant in the T-P phase diagram and the field-induced valence-crossover "region" in the T-H phase diagram are predicted to appear., Comment: 6 pages, 3 figures, conference proceedings based on the talk at SCES2014 constituted of partly published results in section 2 (J. Phys. Soc. Jpn. 83 (2013) 061006) and new results in section 3 as the self-contained form

The scaling behavior over four decades of the ratio of temperature T to magnetic field B observed in the magnetization in beta-YbAlB4 is theoretically examined. By developing a theoretical framework that exhibits the quantum critical phenomena of Yb-valence fluctuations under a magnetic field, we show that the T/B-scaling behavior can appear near the quantum critical point of the valence transition. The emergence of the T/B scaling indicates the presence of the small characteristic energy scale of critical Yb-valence fluctuations. It is argued that the quantum valence criticality offers a unified explanation for the unconventional quantum criticality as well as the T/B scaling in beta-YbAlB4., Comment: 12 pages, 2 figures

Quantum criticality due to the valence transition in some Yb-based heavy fermion metals has gradually turned out to play a crucial role to understand the non-Fermi liquid properties that cannot be understood from the conventional quantum criticality theory due to magnetic transitions. Namely, critical exponents giving the temperature (T) dependence of the resistivity \rho(T), the Sommerfeld coefficient, C(T)/T, the magnetic susceptibility, \chi(T), and the NMR relaxation rates, 1/(T_{1}T), can be understood as the effect of the critical valence fluctuations of f electrons in Yb ion in a unified way. There also exist a series of Ce-based heavy fermion metals that exhibit anomalies in physical quantities, enhancements of the residual resistivity \rho_{0} and the superconducting critical temperature (T_c) around the pressure where the valence of Ce sharply changes. Here we review the present status of these problems both from experimental and theoretical aspects., Comment: Published in "Special Topics: Advances in Physics of Strongly Correlated Electron Systems" of J. Phys. Soc. Jpn. based on an invited talk at SCES2013. Free access for one month from now through the link of J. Phys. Soc. Jpn.; http://journals.jps.jp/journal/jpsj

It is shown that an extra magnetization is induced by an onset of the equal-spin-pairing of spin triplet superconductivity if the energy dependence of the density of states of quasiparticles exists in the normal state. It turns out that the effect is observable in Sr_2RuO_4 due to the existence of van Hove singularity in the density of states near the Fermi level, explaining the extra contribution in the Knight shift reported by Ishida et al. It is also quite non-trivial that this effect exists even without external magnetic field, which implies that the time reversal symmetry is spontaneously broken in the spin space., Comment: published in J. Phys. Soc. Jpn. online on April 10, 2014; free access for one month

The mechanism of emergence of robust quantum criticality in Yb- and Ce-based heavy electron systems under pressure is analyzed theoretically. By constructing a minimal model for quasicrystal Yb15Al34Au51 and its approximant, we show that quantum critical points of the first-order valence transition of Yb appear in the ground-state phase diagram with their critical regimes being overlapped to be unified, giving rise to a wide quantum critical regime. This well explains the robust unconventional criticality observed in Yb15Al34Au51 under pressure. We also discuss broader applicability of this mechanism to other Yb- and Ce-based systems such as beta-YbAlB4 showing unconventional quantum criticality., Comment: 11 pages, 3 figures, to appear in Journal of the Physical Society of Japan

The effects of a spin-orbit interaction on transition-metal ions of (4d)^3- and (5d)^3 -based oxides in which three electrons occupy t_{2g} orbitals are studied. The amplitude of the magnetic moment of d electrons on the 5d and 4d orbitals is estimated by numerical diagonalization. It is found that the magnetic moment is reduced by the spin-orbit interaction. It is suggested that (4d)^3- and (5d)^3 -based oxides are located in the middle of the L-S and J-J coupling schemes., Comment: 4 pages, 6 figures

We investigate properties below T_c of odd-frequency pairing which is realized by antiferromagnetic critical spin fluctuations or spin wave modes. It is shown that \Delta(\epsilon_n) becomes maximum at finite \epsilon_n, and \Delta(\pi T) becomes maximum at finite T. Implications of the present results to the experimental results of CeCu_2Si_2 and CeRhIn_5 are given., Comment: Since the paper published in J. Phys. Soc. Jpn. includes a lot of typos, we would appreciate it if readers could refer to this airXiv version although the result remains essentially valid

A new microscopic model of the charge Kondo effect is proposed, and is studied on the basis of a numerical renormalization group calculations. It is shown that the charge Kondo effect is caused by a pair hopping interaction between the conduction band and the localized band. It is found that the formation of a charge Kondo-Yosida singlet due to its mechanism corresponds to the appearance of valence skipping phenomenon, and that the charge Kondo-Yosida singlet and the spin Kondo-Yosida singlet state coexist for a tuned parameter set, because the charge and spin degrees of freedom are separated in this model. Then, it is also found that the Sommerfeld coefficient is enhanced by the competition between these two singlet states., Comment: 4 pages, 5 figures, Accepted for publication in J. Phys. Soc. Jpn