Recent experimental work has brought the twin issues of the origin of non-Lifshitz-Kosevich scaling in de Haas van Alphen (dHvA) and its precise relation to anomalously broad non-quasiparticle spectral features in "strange" metals, to the forefront. Here, we revisit these issues in the specific context of a "local" quantum critical phase in an extended periodic Anderson model (EPAM). In contrast to the famed Kondo-RKKY scenarios for local quantum criticality, strong local valence fluctuations cause Kondo destruction in the EPAM. We uncover a common underlying element, namely, the Kondo-destruction-driven infra-red continuum branch-cut behavior in the one-electron propagator, as the relevant feature that governs both non-Lifshitz-Kosevich scaling in dHvA and anomalously broad non-quasiparticle spectral responses in such a "strange" metal. Employing a non-perturbative scheme to treat effects of non-magnetic disorder in this version of a local strange metal, we propose a modified Dingle scaling that can also be used to test "local" criticality scenarios. Thus, our findings potentially afford an internally consistent description of novel fermiology expected to manifest in strange metals arising as a result of Kondo-destruction coming from an underlying orbital-selective Mott transition.
We present a Quantum Monte Carlo (QMC) study of the 1D Kondo lattice at non-integer filling, i.e. a one-dimensional version of a heavy electron metal. For this special system the minus-sign problem turns out to be strongly reduced, which allows QMC simulations for temperatures as low as 1% of the conduction electron bandwidth. The single particle Green's function shows and intricate network of low-energy bands at low temperature, with a Fermi surface volume that comprises both c and f-electrons. As temperature increases the system evolves through two distinct crossover temperatures into a very…
Angle resolved photoemission spectroscopy (ARPES) enables direct observation of the Fermi surface and underlying electronic structure of crystals---the basic concepts to describe all the electronic properties of solids and to understand the key electronic interactions involved. The method is the most effective to study quasi-2D metals, to which the subjects of almost all hot problems in modern condensed matter physics have happened to belong. This has forced incredibly the development of the ARPES method which we face now. The aim of this paper is to introduce to the reader the state-of-the-ar…
Noble metal surfaces (Au, Ag and Cu etc.) have been extensively studied for the Shockley type surface states (SSs). Very recently, some of these Shockley SSs have been understood from the topological consideration, with the knowledge of global properties of electronic structure. In this letter, we show the existence of Dirac like excitations in the elemental noble metal Ru, Re and Os based on symmetry analysis and first principle calculations. The unique SSs driven Fermi arcs have been investigated in details for these metals. Our calculated SSs and Fermi arcs are consistent with the previous …
The antiferromagnetic Ruddlesden-Popper ruthenate Ca$_3$Ru$_2$O$_7$ is a model polar metal, combining inversion symmetry breaking with metallic conductivity; however, its low temperature ($T < 48$ K) crystal structure and Fermi surface topology remain ambiguous despite numerous measurements and theoretical studies. Here we perform both first principles calculations with static correlations and angle resolved photoelectron spectroscopy experiments to construct a complete model of Ca$_3$Ru$_2$O$_7$, reconciling inconsistencies among interpretations of electrical transport, thermopower measuremen…
The Fermi surface topology plays an important role in the macroscopic properties of metals. It can be particularly sensitive to electron correlation, which appears to be especially significant for the weak itinerant ferromagnet ZrZn$_{2}$. Here, we look at the differences in the predicted Fermi surface sheets of this metallic compound in its paramagnetic phase for both density functional theory (DFT) and the combination of DFT with dynamical mean field theory (DFT+DMFT). The theoretical spectral functions evaluated at the Fermi level were used along with calculations of the electron-positron m…
The quantum oscillatory effect and superconductivity in a non-tetrachalcogenafulvalene (TCF) structure based organic superconductor beta-(BDA-TTP)_2SbF_6 are studied. Here the Shubnikov-de Haas effect (SdH) and angular dependent magnetoresistance oscillations (AMRO) are observed. The oscillation frequency associated with a cylindrical Fermi surface is found to be about 4050 tesla, which is also verified by the tunnel diode oscillator (TDO) measurement. The upper critical field Hc2 measurement in a tilted magnetic field and the TDO measurement in the mixed state reveal a highly anisotropic supe…
Fermiology of the kagome compound LuNb6Sn6 probed by de Haas-van Alphen oscillations
National High Magnetic Field Laboratory, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室国家高磁场实验室）；Materials Science and Technology Division, Oak Ridge National Laboratory（橡树岭国家实验室材料科学与技术分部）
Quantum oscillation measurements can provide important information about the Fermi surface (FS) properties of strongly correlated metals. Here, we report a Shubnikov-de Haas (SdH) effect study on the pnictide parent compounds EuFe$_{2}$As$_{2}$ (Eu122) and BaFe$_{2}$As$_{2}$ (Ba122) grown by In-flux. Although both members are isovalent compounds with approximately the same density of states at the Fermi level, our results reveal subtle changes in their fermiology. Eu122 displays a complex pattern in the Fourier spectrum, with band splitting, magnetic breakdown orbits, and effective masses sist…
The surface states of Weyl semi-metals (SM's) consist of disjointed Fermi-arcs. This unusual surface-Fermiology provides a fingerprint of the topological features of the bulk Weyl-phase. Using a combination of semiclassical and numerical methods, we show that, in contrast to naive expectation, there are closed magnetic orbits involving the open- surface Fermi-arcs. Below a critical field strength that depends on sample thickness, these orbits produce periodic quantum oscillations of the density of states in a magnetic field, enabling a variety of experimental probes of the unconventional Fermi…
Unconventional metallic states which do not support well defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a non-perturbative solution to the low-energy th…
We develop U(1) slave spin-rotor theory, suggesting a metal-metal transition from Landau's Fermi-liquid state to a bad metal phase, as U(1) slave charge-rotor theory [Phys. Rev. B {\bf 70}, 035114 (2004)] describes a metal-insulator transition from Landau's Fermi-liquid state to a spin-liquid phase. U(1) slave spin-rotor formulation allows us to generalize Hertz-Moriya-Millis theory for ferromagnetic quantum phase transitions, replacing Landau's Fermi-liquid state with an incoherent metallic phase. As a result, we argue that localized magnetic moments emerge to govern quantum critical physics …
We determine the pre-asymptotic critical behavior at the quantum ferromagnetic transition in strongly disordered metals. We find that it is given by effective power laws, in contrast to the previously analyzed asymptotic critical behavior, which is valid only in an unobservably small region. The consequences for analyzing experiments are discussed, in particular ways to distinguish between critical behavior and Griffiths-phase effects.
Motivated by recent experimental realizations of polar metals with broken inversion symmetry, we explore the emergence of strong correlations driven by criticality when the polar transition temperature is tuned to zero. Overcoming previously discussed challenges, we demonstrate a robust mechanism for coupling between the critical mode and electrons in multiband metals. We identify and characterize several novel interacting phases, including non-Fermi liquids, when band crossings are close to the Fermi level and present their experimental signatures for three generic types of band crossings.
Analysis on very detailed measurements of resistivity ($ ρ$) and thermoelectric power (S) of magnetic impurity (Co) substituted iron silicide (FeSi) has been presented in this report. The impurity valence electrons of Co dominate the whole physical properties at low temperatures below 35 K, below the critical concentration x$_{c}$. The negative thermopower and the positive slope in the resistivity at low temperatures are exotic and show that the system is not entirely insulator below the critical concentration of MIT (x$_{c}$). So, due to the external impurity electrons, the system's magnetic …
When a metal undergoes a continuous quantum phase transition, non-Fermi liquid behaviour arises near the critical point. It is standard to assume that all low-energy degrees of freedom induced by quantum criticality are spatially extended, corresponding to long-wavelength fluctuations of the order parameter. However, this picture has been contradicted by recent experiments on a prototype system: heavy fermion metals at a zero-temperature magnetic transition. In particular, neutron scattering from CeCu$_{6-x}$Au$_x$ has revealed anomalous dynamics at atomic length scales, leading to much debate…
Finding microscopic models for metallic states that exhibit quantum critical properties such as $ω/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $χ(T,ω)$ for a Hubbard model at half filling using Dynamical Mean-Field Theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite temperature critical point. The signature of the latter is $ω/T$ scaling where $T$ is the temperature.…
Divergent carrier-density fluctuations equivalent to the critical opalescence of gas-liquid transitions emerge around a metal-insulator critical point at a finite temperature. In contrast to the gas-liquid transitions, however, the critical temperature can be lowered to zero, which offers a challenging quantum phase transition. We present a microscopic description of such quantum critical phenomena in two dimensions. The conventional scheme of phase transitions by Ginzburg, Landau and Wilson is violated and an unconventional universality appears. It offers a clear insight into the criticalitie…
We analyze general properties of the perturbation expansion for two-dimensional quantum critical metals with singular forward scattering, such as metals at an Ising nematic quantum critical point and metals coupled to a U(1) gauge field. We derive asymptotic properties of fermion loops appearing as subdiagrams of the contributing Feynman diagrams -- for large and small momenta. Substantial cancellations are found in important scaling limits, which reduce the degree of divergence of Feynman diagrams with boson legs. Implementing these cancellations we obtain improved power-counting estimates th…
At certain quantum critical points in metals an entire Fermi surface may disappear. A crucial question is the nature of the electronic excitations at the critical point. Here we provide arguments showing that at such quantum critical points the Fermi surface remains sharply defined even though the Landau quasiparticle is absent. The presence of such a critical Fermi surface has a number of consequences for the universal phenomena near the quantum critical point which are discussed. In particular the structure of scaling of the universal critical singularities can be significantly modified from…
This paper reports thermopower and conductivity measurements through the metal-insulator transition for 2-dimensional electron gases in high mobility Si-MOSFETs. At low temperatures both thermopower and conductivity show critical behaviour as a function of electron density. When approaching the critical density from the metallic side the diffusion thermopower appears to diverge and the conductivity vanishes. On the insulating side the thermopower shows an upturn with decreasing temperature. These features have much in common with those expected for an Anderson transition.
In contrast to the first-order correlation-driven Mott metal-insulator transition (MIT), contin- uous disorder-driven transitions are intrinsically quantum critical. Here, we investigate transport quantum criticality in the Falicov-Kimball model, a representative of the latter class in the "strong disorder" category. Employing cluster-dynamical mean-field theory (CDMFT), we find clear and anomalous quantum critical scaling behavior manifesting as perfect mirror symmetry of scaling curves on both sides of the MIT. Surprisingly, we find that the beta-function, \b{eta}(g), scales like log(g) deep…
Perfect $T$-linear resistivity associated with universal scattering rate: $1/τ=αk_B T/\hbar$ with $α\sim 1$, so-called Planckian metal state, has been observed in the normal state of a variety of strongly correlated superconductors close to a quantum critical point. However, the microscopic origin of this intriguing phenomena and its link to quantum criticality still remains an outstanding open problem. In this work, we observe the quantum-critical $T/B$-scaling of the Planckian metal state in the resistivity and heat capacity of heavy-electron superconductor Ce$_{1-x}$Nd$_x$CoIn$_5$ in magnet…
The critical electron density for the metal-insulator transition in a two-dimensional electron gas can be determined by two distinct methods: (i) a sign change of the temperature derivative of the resistance, and (ii) vanishing activation energy and vanishing nonlinearity of current-voltage characteristics as extrapolated from the insulating side. We find that in zero magnetic field (but not in the presence of a parallel magnetic field), both methods give equivalent results, adding support to the existence of a true zero-field metal-insulator transition.
The dc-conductivity of electrons on a square lattice interacting with a local repulsion in the presence of disorder is computed by means of quantum Monte Carlo simulations. We provide evidence for the existence of a transition from an Anderson insulator to a correlated disordered metal with a universal value of the critical dc-conductivity σ_{dc,crit} = (1.18 \pm 0.06) e^{2}/h at the transition.
We calculate analytically the conductivity of weakly disordered metals close to a "ferromagnetic" quantum critical point in the low temperature regime. Ferromagnetic in the sense that the effective carrier potential $V(q,ω)$, due to critical fluctuations, is peaked at zero momentum $q=0$. Vertex corrections, due to both critical fluctuations and impurity scattering, are explicitly considered. We find that only the vertex corrections due to impurity scattering, combined with the self-energy, generate appreciable effects as a function of the temperature $T$ and the control parameter $a$, which m…
We report on the dramatic slowing down of the charge carrier dynamics in a quasi-two-dimensional organic conductor, which can be reversibly tuned through the Mott metal-insulator transition (MIT). At the finite-temperature critical endpoint we observe a divergent increase of the resistance fluctuations accompanied by a drastic shift of spectral weight to low frequencies, demonstrating the critical slowing down of the order parameter (doublon density) fluctuations. The slow dynamics is accompanied by non-Gaussian fluctuations, indicative of correlated charge carrier dynamics. A possible explana…
Heavy fermion metals typically exhibit unconventional quantum critical point or quantum critical phase at zero temperature due to competition of Kondo effect and magnetism. Previous theories were often based on certain local type of assumptions and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice and introduce the concept of nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram co…
We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as "Stripe Loop Metals" where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different conti…
Anomalous metals are observed in numerous experiments on disordered two-dimensional systems proximate to superconductivity. A characteristic feature of an anomalous metal is that its low temperature conductivity has a weakly temperature dependent value, significantly higher than that of a disordered Fermi liquid. We propose a dynamical mean-field model of an anomalous metal: interacting electrons similar in structure to that of the well-studied universal Hamiltonian of mesoscopic metallic grains, but with independent random interactions between pairs of sites, involving Cooper pair hopping and…
We revisit the problem of two dimensional metals in the vicinity of a quantum phase transition to incommensurate $\mathbf{Q}=2k_F$ charge density wave order, where the order parameter wave vector $\mathbf{Q}$ connects two hot spots on the Fermi surface with parallel tangents. Earlier theoretical works argued that such critical points are potentially unstable, if the Fermi surface at the hot spots is not sufficiently flat. Here we perform a controlled, perturbative renormalization group analysis and find a stable fixed point corresponding to a continuous quantum phase transition, which exhibits…
A fundamental challenge to our current understanding of metals is the frequent observation of qualitative departures from Fermi liquid behavior. The standard view attributes such non-Fermi liquid phenomena to the scattering of electrons off quantum critical fluctuations of an underlying order parameter. While the possibility of non-Fermi liquid behavior isolated from the border of magnetism has long been speculated, no experimental confirmation has been made. Here we report on the observation of a strange metal region in the absence of a magnetic instability in an ultrapure single crystal. In …
We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for $U$ larger than a critical value $U_c$, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-f…
Anomalous quasiparticle lifetime in geometric quantum critical metals
McMaster University（麦克马斯特大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
We study finite temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent $z=2$, in contrast to $z=3$ found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to $Ω/γ(T)$ at small momenta, where $γ(T)$ is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte-…
We show how the collapse of an energy scale in a quantum critical metal can lead to physics beyond the weak-field limit usually used to compute transport quantities. For a density-wave transition we show that the presence of a finite magnetic field at the critical point leads to discontinuities in the transport coefficients as temperature tends to zero. The origin of these discontinuities lies in the breakdown of the weak field Jones-Zener expansion which has previously been used to argue that magneto-transport coefficients are continuous at simple quantum critical points. The presence of pote…
The low-temperature dc conductivities of barely metallic samples of p-type Si:B are compared for a series of samples with different dopant concentrations, n, in the absence of stress (cubic symmetry), and for a single sample driven from the metallic into the insulating phase by uniaxial compression, S. For all values of temperature and stress, the conductivity of the stressed sample collapses onto a single universal scaling curve. The scaling fit indicates that the conductivity of si:B is proportional to the square-root of T in the critical range. Our data yield a critical conductivity exponen…
A bilayer system comprising a Kondo insulator coupled to a simple metal (KI-M) is considered. Employing the framework of dynamical mean field theory, the model system is shown to exhibit a surface of quantum critical points (QCPs), that separates a Kondo screened, Fermi liquid phase from a local moment, Mott insulating phase. The quantum critical nature of these Mott transitions is characterized by the vanishing of (a) the coherence scale on the Fermi liquid side, and (b) the Mott gap on the MI side. In contrast to the usual `large to small' Fermi surface (FS) QCPs in heavy fermion systems, th…
Ubiquity of unconventional phenomena observed in a series of heavy fermion metals is discussed on the basis of an idea of critical valence fluctuations. After surveying experimental aspects of these unconventional behaviors in prototypical compounds, CeCu_2(Si,Ge)_2, under pressure, we propose that sharp valence crossover phenomena are realized in CeCu_6, CeRhIn_5, and Ce(Ir,Rh)Si_3 by tuning the pressure and the magnetic field simultaneously, on the basis of previous results for an extended Anderson lattice model with the Coulomb repulsion U_fc between localized f-electron and itinerant condu…
Bad-Metal (BM) behavior featuring linear temperature dependence of the resistivity extending to well above the Mott-Ioffe-Regel (MIR) limit is often viewed as one of the key unresolved signatures of strong correlation. Here we associate the BM behavior with the Mott quantum criticality by examining a fully frustrated Hubbard model where all long-range magnetic orders are suppressed, and the Mott problem can be rigorously solved through Dynamical Mean-Field Theory. We show that for the doped Mott insulator regime, the coexistence dome and the associated first-order Mott metal-insulator transiti…
We propose a holographic theory to explain numbers of anomalous critical phenomena observed in certain heavy-fermion metals, e.g. $\mathrm{CeCu_{5.9}Au_{0.1}}$ and $\mathrm{YbRh_{2}(Si_{0.95}Ge_{0.05}})_{2}$, which are incompatible with any conventional spin-density-wave quantum critical point theory. We show that the non-Gaussian nature of the fixed point from holography plays an essential role in the physics of these materials near a quantum critical point, which is not in the same universality class of the spin-density-wave type fixed point. The critical spin fluctuations at the non-Gaussia…
We provide evidence for the existence of a {\em quantum critical point} at the metallization of magnetite Fe$_{3}$O$_{4}$ at an applied pressure of $p_{c} \approx 8$ GPa. We show that the present ac magnetic susceptibility data support earlier resistivity data. The Verwey temperature scales with pressure $T_{V}\sim (1-p/p_{c})^ν$, with $ν\sim 1/3$. The resistivity data shows a temperature dependence $ρ(T)=ρ_{0}+AT^{n}$, with $n\simeq 3$ above and 2.5 at the critical pressure, respectively. This difference in $n$ with pressure is a sign of critical behavior at $p_{c}$. The magnetic susceptibili…
The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction $U$ at the $d$-orbital and the charge-transfer energy $Δ$ between the $d$- and $p$-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of $U$ and $Δ$. The analytic results are in good agreement with the numerical results of the exact …
We compute the Hall angle and the magnetoresistance of the spin-fermion model, which is a successful phenomenological theory to describe the physics of the cuprates and iron-based superconductors within a wide range of doping regimes. We investigate both the role of the spin-fermion interaction that couples the large-momentum antiferromagnetic fluctuations to the so-called "hot-spots" at the Fermi surface and also of an effective higher-order composite operator in the theory. The latter operator provides a scattering mechanism such that the momentum transfer for the fermions close to the Fermi…
A magnetic field applied to a three-dimensional antiferromagnetic metal can destroy the long-range order and thereby induce a quantum critical point. Such field-induced quantum critical behavior is the focus of many recent experiments. We investigate theoretically the quantum critical behavior of clean antiferromagnetic metals subject to a static, spatially uniform external magnetic field. The external field does not only suppress (or induce in some systems) antiferromagnetism but also influences the dynamics of the order parameter by inducing spin precession. This leads to an exactly marginal…
Quantum criticality of metal-insulator transitions in correlated electron systems is shownto belong to an unconventional universality class with violation of Ginzburg-Landau-Wilson(GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square latticesare capable…
It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo scre…
In a clean quantum critical metal, and in the absence of umklapp, most d.c. conductivities are formally infinite due to momentum conservation. However, there is a particular combination of the charge and heat currents which has a finite, universal conductivity. In this paper, we describe the physics of this conductivity $σ_Q$ in quantum critical metals obtained by charge doping a strongly interacting conformal field theory. We show that it satisfies an Einstein relation and controls the diffusivity of a conserved charge in the metal. We compute $σ_Q$ in a class of theories with holographic gra…
Using recent insights obtained in heavy fermion physics on the thermodynamic singularity structure associated with quantum phase transitions, we present here an experimental strategy to establish if the zero-temperature transition in the disordered two dimensional gas is a real quantum phase transition. We derive a overcomplete set of scaling laws relating the density and temperature dependence of the chemical potential and the effective mass, which are in principle verifyable by experiment.
We present a field theory for a structurally disordered magnetic system coupled to a metallic environment near a quantum critical point. We show that close to the magnetic quantum critical point droplets are formed due to the disorder and undergo dissipative quantum dynamics. We show that the problem has a characteristic energy scale, the droplet Kondo temperature, that determines the crossover energy scale from weak to strong coupling. Our results have direct significance for the Griffiths-McCoy singularities of itinerant magnets.
The standard description of quantum critical points takes into account only fluctuations of the order parameter, and treats quantum fluctuations as extra dimensions of classical fluctuations. This picture can break down in a qualitative fashion in quantum critical metals: non-Fermi liquid electronic excitations are formed precisely at the quantum critical point and appear as a part of the quantum-critical spectrum. In the case of heavy fermion metals, it has been proposed that the non-Fermi liquid behavior is characterized by the destruction of the Kondo effect. The latter invalidates Hertz's …
The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic {\it metal} is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to $24\times 24$ sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recent…
Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this article, we review the status of the understanding of metallic quantum criticality, and the recent p…
We compute the transition temperature $T_c$ and the Ginzburg temperature $T_{\rm G}$ above $T_c$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron system. Our calculation is based on a renormalization group analysis of the Hertz action with a scalar order parameter. We provide analytic expressions for $T_c$ and $T_{\rm G}$ as a function of the non-thermal control parameter for the quantum phase transition, including logarithmic corrections. The Ginzburg regime between $T_c$ and $T_{\rm G}$ occupies a sizable…
We use the dynamical mean-field approximation to study singularities in the self-energy and a two-particle irreducible vertex induced by the metal-insulator transition of the disordered Falicov-Kimball model. We set general conditions for the existence of a critical metal-insulator transition caused by a divergence of the imaginary part of the self-energy. We calculate explicitly the critical behavior of the self-energy for the symmetric and asymmetric disorder distributions. We demonstrate that the metal-insulator transition is preceded by a pole in a two-particle irreducible vertex. We show …
