Local Quantum Critical Point Research Articles

Emergence of non-Fermi liquid dynamics through nonlocal correlations in an interacting disordered system

We provide strong evidence of a quantum critical point (QCP) associated with the destruction of Kondo screening in the Anderson-Hubbard model for interacting electrons with quenched disorder. A unique crossover energy scale, $\omega^*$ separating the Fermi liquid and non-Fermi liquid (nFL) scattering dynamics on the metallic side of the quantum critical fan is identified. The scale vanishes at the disorder driven QCP. We interpret our results by measuring the distribution of Kondo scales and find that the QCP occurs when this distribution acquires a finite intercept, indicating a Kondo destruction scenario, albeit distinct from the local QCP picture. The nFL behavior is shown to stem from an interplay of strong electron-electron interactions and the systematic inclusion of short-range dynamical fluctuations induced by the underlying random potential. The results have been obtained through a computational framework based on the typical medium dynamical cluster approximation.

Model for a Ferromagnetic Quantum Critical Point in a 1D Kondo Lattice.

Motivated by recent experiments, we study a quasi-one-dimensional model of a Kondo lattice with ferromagnetic coupling between the spins. Using bosonization and dynamical large-N techniques, we establish the presence of a Fermi liquid and a magnetic phase separated by a local quantum critical point, governed by the Kondo breakdown picture. Thermodynamic properties are studied and a gapless charged mode at the quantum critical point is highlighted.

Large and small Fermi-surface spin density waves in the Kondo lattice model

We demonstrate the existence of metallic spin density waves (SDWs) in the Kondo lattice model on a square lattice for a wide range of parameters by means of real space dynamical mean field theory. In these SDWs, the spin polarization as well as the charge density depend on the lattice site and are modulated along one direction of the square lattice. We show that within this phase of metallic SDWs the Fermi surface changes from small to large, when the coupling strength is increased. Furthermore, the transition between the large Fermi-surface SDW phase and the paramagnetic phase is of second order, while the transition between the small Fermi-surface SDW phase and the paramagnetic phase is of first order. A local quantum critical point is thus avoided in our calculations by undergoing a first order phase transition.

Nonequilibrium dynamics across an impurity quantum critical point due to quantum quenches

Whether a small quantum mechanical system is able to equilibrate with its environment once an external local perturbation drives it out of thermal equilibrium is a central question which cuts across many different fields of science. Here we consider such a problem for a correlated quantum impurity coupled to a fermionic reservoir and driven out of equilibrium by local quantum quenches such as those recently realized in optical absorption experiments on single quantum dots. We argue that equilibration in this problem is deeply connected to the occurrence of Kondo Effect at low energy and that a highly non trivial dynamical behavior may emerge whenever a local quantum critical point intrudes between a conventional Kondo screened phase and a Kondo unscreened one. We discuss this issue in the context of the Anderson Impurity model coupled to a pseudo-gap reservoir by using a correlated time dependent variational wave function that is able to qualitatively describe this physics.

Convergence of Energy Scales on the Approach to a Local Quantum Critical Point

We find the emergence of strong correlations and universality on the approach to the quantum critical points of a two-impurity Anderson model. The two impurities are coupled by an interimpurity exchange interaction J and direct interaction U{12} and are hybridized with separate conduction channels. The low energy behavior is described in terms of renormalized parameters. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor z→0, and the renormalized parameters can be expressed in terms of a single energy scale T{*}. The values of the renormalized interaction parameters in terms of T{*} can be predicted from the condition of continuity of the spin and charge susceptibilities, and correspond to strong correlation. These predictions are confirmed by the numerical renormalization group calculations, including the case when the on site interaction U=0.

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau–Ginzburg–Wilson paradigm. The Landau–Ginzburg–Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.

Novel Duality in Disorder Driven Local Quantum Criticality

We find that competition between random Kondo and random magnetic correlations results in a quantum phase transition from a local Fermi liquid to a spin liquid. The local charge susceptibility turns out to have exactly the same critical exponent as the local spin susceptibility, suggesting a novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson symmetry breaking framework. This leads us to propose an enhanced symmetry at the local quantum critical point, described by an O(4) vector for spin and charge. The symmetry enhancement serves as a mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.

Magnetic Fluctuations at a Field-Induced Quantum Phase Transition

We report an inelastic neutron-scattering study at the field-induced magnetic quantum phase transition of CeCu5.8Au0.2. The data can be described better by the spin-density-wave scenario than by a local quantum critical point, while the latter scenario was shown to be applicable to the zero-field concentration-tuned quantum phase transition in CeCu6-xAux for x=0.1. This constitutes direct microscopic evidence for a difference in the quantum fluctuation spectra at a magnetic quantum critical point driven by different tuning parameters.

Avoided criticality in near-optimally doped high-temperature superconductors

We study the crossover from the underdoped to the overdoped regime in the t-J model.The underdoped regime is dominated by the superexchange interaction, locking the spins into singlets which weakly perturbe coherent charge carriers. In the overdoped, large carrier concentration regime, the Kondo effect dominates resulting in spin-charge composite quasiparticles which are also coherent. Separating these two Fermi liquid regimes, there is a critical doping where superexchange and Kondo interaction balance each other, bringing the system close to a local quantum critical point near the point of maximal superconducting transition temperature. At this point, particle hole symmetry is dynamically restored and physical quantities such as the optical conductivity, exhibit power law behaviour at intermediate frequencies as observed experimentally. Quantum criticality is avoided by the onset of superconductivity.

Magnetic fluctuations at the field-tuned vs. concentration-tuned quantum phase transition in [formula omitted

CeCu 6 - x Au x has become a model system to study magnetic quantum phase transitions (QPT). In this system, the QPT can be tuned by Au concentration x , pressure, or magnetic field. Previous inelastic neutron-scattering (INS) experiments have demonstrated an anomalous scaling of the dynamical susceptibility at the concentration-tuned (zero-field) QPT for x = 0.1 , i.e., χ - 1 ( q , E , T ) = c - 1 [ θ α ( q ) + ( T - i E ) α ] , where θ ( q ) is a generalized Curie–Weiss temperature. This scaling suggests local criticality, with an anomalous exponent α ≈ 0.75 . Here we report on an INS study at the field-induced magnetic QPT of CeCu 5.8 Au 0.2 where the Néel temperature is driven to zero at a critical field of B ≈ 0.4 T , supplemented by specific-heat data. The INS data can be described better by the spin-density-wave scenario, i.e., χ - 1 ( Q AF , E , T ) = a - 1 ( T 3 / 2 - i bE ) where Q AF is the antiferromagnetic ordering wave vector, than by a local quantum critical point. This constitutes direct microscopic evidence for a difference in quantum fluctuation spectra at a magnetic QPT driven by different tuning parameters.

Local Quantum Critical Point in the Pseudogap Anderson Model: Finite-T Dynamics and ω/T Scaling

The pseudogap Anderson impurity model is a paradigm for locally critical quantum phase transitions. Within the framework of the local moment approach we study its finite-T dynamics, as embodied in the single-particle spectrum, in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid (Kondo screened) and local moment phases. The scaling spectra in both phases, and at the QCP itself, are obtained analytically. A key result is that pure omega/T scaling obtains at the QCP, where the Kondo resonance has just collapsed. The connection between the scaling spectra in either phase and that at the QCP is explored in detail.

Extended dynamical mean field theory study of the periodic Anderson model.

We investigate the competition of the Kondo and the RKKY interactions in heavy fermion systems. We solve a periodic Anderson model using extended dynamical mean field theory (EDMFT) with quantum Monte Carlo method. We monitor simultaneously the evolution of the electronic and magnetic properties. As the RKKY coupling increases the heavy fermion quasiparticle unbinds and a local moment forms. At a critical RKKY coupling there is an onset of magnetic order. Within EDMFT the two transitions occur at different points and the disappearance of the magnetism is not described by a local quantum critical point.

Large-N analysis of the local quantum critical point and the spin-liquid phase

We analytically study a Kondo lattice model with an additional nearest-neighbor antiferromagnetic interaction in the framework of large-$\mathcal{N}$ theory. We find that there is a local quantum critical point between two phases, a normal Fermi liquid and a spin liquid in which the spins are decoupled from the conduction electrons. The local spin susceptibility displays a power-law divergence throughout the spin liquid phase. We check the reliability of the large-$\mathcal{N}$ results by solving with a quantum Monte Carlo simulation, the $\mathcal{N}=2$ spin-liquid problem with no conduction electrons, and we find qualitative agreement. We show that the spin-liquid phase is unstable at low temperatures, suggestive of a first-order transition to an ordered phase.

Quantum phase transitions

We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.