Local Quantum Criticality Research Articles

On the universality of AdS2 diffusion bounds and the breakdown of linearized hydrodynamics

The chase of universal bounds on diffusivities in strongly coupled systems and holographic models has a long track record. The identification of a universal velocity scale, independent of the presence of well-defined quasiparticle excitations, is one of the major challenges of this program. A recent analysis, valid for emergent IR fixed points exhibiting local quantum criticality, and dual to IR AdS2 geometries, suggests to identify such a velocity using the time and length scales at which hydrodynamics breaks down — the equilibration velocity. The latter relates to the radius of convergence of the hydrodynamic expansion and it is extracted from a collision between a hydrodynamic diffusive mode and a non-hydrodynamic mode associated to the IR AdS2 region. In this short note, we confirm this picture for holographic systems displaying the spontaneous breaking of translational invariance. Moreover, we find that, at zero temperature, the lower bound set by quantum chaos and the upper one defined by causality and hydrodynamics exactly coincide, determining uniquely the diffusion constant. Finally, we comment on the meaning and universality of this newly proposed prescription.

Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling

Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastable insulator at the boundary of metal-insulator coexistence region, which can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures and hence difficult to access numerically, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a \emph{different} power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. We connect our findings to experiments on tunable Mott materials.

Translationally Invariant Non-Fermi-Liquid Metals with Critical Fermi Surfaces: Solvable Models

We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<\infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.

Quantum criticality associated with dimensional crossover in the iso-electronic series Ca2−xSrxRuO4

The iso-electronic series, Ca2−xSrxRuO4, is studied within the GGA (and spin-orbit coupled GGA) plus DMFT formalism using the hybridization expansion of continuous time Quantum Monte Carlo (CT-QMC) impurity solver. GGA+DMFT, along with CT-QMC impurity solver we used, provides insights into the retarded electronic correlations at finite temperatures. We use GGA+U and energy considerations at T = 0 for complementary understanding of the ground state structural and electronic properties. While the dynamical correlations make Sr2RuO4 a Hund’s metal, they drive Ca2RuO4 to a Mott insulating ground state. We study the single-particle and two-particle responses at three different points (x = 2.0, 0.5, 0.0) to understand the anomalous cross-over from Hund’s metal (x = 2.0 ) to a Mott insulator (x = 0) and observe that a structural distortion is likely to be responsible. Further, dynamical correlations reveal that the band-width (W) of the Hund’s metal is larger than its effective local Hubbard U, and a finite Hund’s coupling JH helps it remain in a bad metallic and nearly spin-frozen state over a large temperature range. Ca2RuO4, though, is driven to the proximity of a Mott transition by the narrowing of band width (U/W > 1.5). We show that there is a critical end point of second-order structural transition at x = 0.5, where spin fluctuations become critical and follow the scaling of local quantum criticality. We argue that this critical end point of quasi-3D nature is associated with an effective dimensional cross-over from the quasi-2D structures of x = 2.0 and x = 0.0 end-members. Finally we draw an electronic and magnetic phase diagram in T-x plane with these novel inputs, with a fan like region starting from the quantum critical end point at x = 0.5.

Local quantum criticality of a one-dimensional Kondo insulator model

The continuous quantum phase transition and the nature of quantum critical point (QCP) in a modified Kondo lattice model with Ising anisotropic exchange interactions is studied within the density-matrix renormalization group algorithm. We investigate the effect of quantum fluctuations on critical Kondo destruction QCP, by probing static and dynamic properties of the magnetic order and the Kondo effect. In particular, we identify that local Kondo physics itself becomes critical at the magnetic phase transition point, providing unbiased evidences for local quantum criticality between two insulators without resorting to the change of Fermi surface.

Steady-State Dynamics and Effective Temperature for a Model of Quantum Criticality in an Open System.

We study the thermal and nonthermal steady-state scaling functions and the steady-state dynamics of a model of local quantum criticality. The model we consider, i.e., the pseudogap Kondo model, allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points. In the vicinity of each fixed point we establish the existence of an effective temperature-different at each fixed point-such that the equilibrium fluctuation-dissipation theorem is recovered. Most notably, steady-state scaling functions in terms of the effective temperatures coincide with the equilibrium scaling functions. This result extends to higher correlation functions as is explicitly demonstrated for the Kondo singlet strength. The nonlinear charge transport is also studied and analyzed in terms of the effective temperature.

Kondo destruction in heavy fermion quantum criticality and the photoemission spectrum of YbRh2Si2

Heavy fermion metals provide a prototype setting to study quantum criticality. Experimentally, quantum critical points have been identified and studied in a growing list of heavy fermion compounds. Theoretically, Kondo destruction has provided a means to characterize a class of unconventional quantum critical points that goes beyond the Landau framework of order-parameter fluctuations. Among the prominent evidence for such local quantum criticality have been measurements in YbRh2Si2. A rapid crossover is observed at finite temperatures in the isothermal field dependence of the Hall coefficient and other transport and thermodynamic quantities, which specifies a T*B line in the temperature (T)–magnetic field (B) phase diagram. Here, we discuss what happens when temperature is raised, by analyzing the ratio of the crossover width to the crossover position. With this ratio approaching unity at T≳0.5K, YbRh2Si2 at zero magnetic field belongs to the quantum-critical fluctuation regime, where the single-particle spectral function has significant weight at both the small and large Fermi surfaces. This implies that, in this temperature range, any measurements sensitive to the Fermi surface will also see a significant spectral weight at the large Fermi surface. The angle-resolved photoemission spectroscopy experiments recently reported for YbRh2Si2 at T>1K are consistent with this expectation, and therefore support the association of the T*B line with the physics of Kondo destruction.

Local quantum criticality in the two-dimensional dissipative quantum XY model

We use quantum Monte-Carlo simulations to calculate the phase diagram and the correlation functions for the quantum phase transitions in the two-dimensional dissipative XY model with and without four-fold anisotropy. Without anisotropy, the model describes the superconductor to insulator transition in two-dimensional dirty superconductors. With anisotropy, the model represents the loop-current order observed in the under-doped cuprates and its fluctuations, as well as the fluctuations near the ordering vector in simple models of itinerant antiferromagnets. These calculations test an analytic solution of the model which re-expressed it in terms of topological excitations - the vortices with interactions only in space but none in time, and warps with leading interactions only in time but none in space, as well as sub-leading interactions which are both space and time-dependent. For parameters for which the proliferation of warps dominates the phase transition, the critical fluctuations as a function of the deviation of the dissipation parameter $\alpha$ from its critical value $\alpha_c$ are scale-invariant in imaginary time $\tau$ as the correlation length in time $\xi_{\tau} = \tau_c e^{|\alpha_c/(\alpha_c-\alpha)|^{1/2}}$ diverges. On the other hand, the spatial correlations develop with a correlation length $\xi_x \approx \xi_0 \log{(\xi_{\tau})}$, with $\xi_0$ of the order of a lattice constant. The dynamic correlation exponent $z$ is therefore $\infty$. These results are consistent with the phenomenology proposed for the strange metal properties of the cuprates. The Monte-Carlo calculations also directly show warps and vortices. Their density and correlations across the various transitions in the model are calculated and related to those of the order parameter in the original model.

Emergence of localized magnetic moments near antiferromagnetic quantum criticality

We revisit an antiferromagnetic quantum phase transition with $\mathbit{Q}=2{\mathbit{k}}_{F}$, where $\mathbit{Q}$ is an ordering wave vector and ${\mathbit{k}}_{F}$ is a Fermi momentum. Reformulating the Hertz-Moriya-Millis theory within the strong-coupling approach to diagonalize the spin-fermion coupling term and performing the scaling analysis for an effective-field theory with quantum corrections in the Eliashberg approximation, we propose an interacting fixed point for this antiferromagnetic quantum phase transition, where antiferromagnetic spin fluctuations become locally critical to interact with renormalized electrons. The emergence of local quantum criticality suggests a mechanism of $\ensuremath{\omega}/T$ scaling for antiferromagnetic quantum criticality, generally forbidden in the context of the Hertz-Moriya-Millis theory.

Quantum Criticality and Lifshitz Transition in the Ising System CeRu2Si2: Comparison with YbRh2Si2

New thermoelectric power (TEP) measurements on prototype heavy-fermion compounds close to magnetic quantum criticality are presented. The highly sensitive technique of TEP is an unique tool to reveal Fermi surface instabilities, referred here as Lifshitz transitions. The first focus is on the Ising CeRu2Si2 series. Doping CeRu2Si2 with Rh produces a decoupling between the first order metamagnetic transition and the pseudo-metamagnetism observed in the pure compound. Comparison is made with the case of YbRh2Si2 which is often considered as the archetype of local quantum criticality by contrast to CeRu2Si2, taken as an example of spin-density wave criticality. Up to now for ferromagnetic materials showing ferromagnetic wings, no simple case appears where the Fermi surface is preserved between the ferromagnetic and paramagnetic phases. An open issue is the consequence of Lifshitz transitions on superconductivity in these multiband systems.

Novel Metallic Phase Emerging from Quantum Criticality: We Couldn��t Observe Electrons at Low Energies

The emergence of non-Fermi liquids near metallic quantum criticality is an essential feature in the system of strongly correlated electrons, where electron quasiparticles decay into other types of collective excitations. As a result, novel metallic phases appear without electrons, showing various exotic non-Fermi liquid physics beyond the Landau Fermi-liquid theory. In this review, we discuss what electrons disintegrate into, which allows us to classify theories for quantum critical metals into the Hertz-Moriya-Millis, Kondo breakdown, and local quantum criticality scenarios. We discuss both the goodness and the weakness of each theoretical framework, recalling experimental aspects for heavy-fermion quantum criticality.

Stoner Instability Revisited: Emergence of Local Quantum Criticality?

We revisit Stoner instability, an old problem but in a modern point of view. An idea is to extract out dynamics of directional fluctuations of spins explicitly, resorting to the CP$^{1}$ representation and integrating over their amplitude fluctuations. As a result, we derive an effective field theory for ferromagnetic quantum phase transitions in terms of bosonic spinons and fermionic holons. We show that this effective field theory reproduces overdamped spin dynamics in a paramagnetic Fermi liquid and magnon spectrum in a ferromagnetic Fermi liquid. An interesting observation is that the velocity of spinons becomes zero, approaching the ferromagnetic quantum critical point, which implies emergence of local quantum criticality. Based on this scenario, we predict the $\omega/T$ scaling behavior near ferromagnetic quantum criticality beyond the conventional scenario of the weak-coupling approach.

Quantum corrected phase diagram of holographic fermions

We study the phases of strongly correlated electron systems in two spatial dimensions in the framework of AdS${}_4$/CFT${}_3$ correspondence. The AdS (gravity) model consists of a Dirac fermion coupled to electromagnetic field and gravity. To classify the ground states of strongly correlated electrons on the CFT side and to construct the full phase diagram of the system, we construct a quantum many-body model of bulk fermion dynamics, based on the WKB approximation to the Dirac equation. At low temperatures, we find a quantum corrected approximation to the electron star where the edge is resolved in terms of wavefunctions extended fully through AdS. At high temperatures, the system exhibits a {\em first} order thermal phase transition to a charged AdS-RN black hole in the bulk and the emergence of local quantum criticality on the CFT side. This change from the third order transition experienced by the semi-classical electron star restores the intuition that the transition between the critical AdS-RN liquid and the finite density Fermi system is of van der Waals liquid-gas type.

Pressure phase diagram and quantum criticality of CePt2In7single crystals

We report the temperature-pressure (T-P) phase diagram of CePt2In7 single crystals, especially the pressure evolution of the antiferromagnetic order and the emergence of superconductivity, which have been studied by electrical resistivity and ac calorimetry under nearly hydrostatic environments. Compared with its polycrystalline counterpart, bulk superconductivity coexists with antiferromagnetism in a much narrower pressure region. The possible existence of textured superconductivity and local quantum criticality also are observed in CePt2In7, exhibiting a remarkable similarity with CeRhIn5.

Local quantum criticality out of equilibrium: Effective temperatures and scaling in the steady-state regime

We study the out-of-equilibrium steady-state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low-energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-N approach on the Keldysh contour, we study two different non-equilibrium setups: a) a finite bias voltage and b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point–dependent effective temperature, defined though the fluctuation-dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin-susceptibilities.

Local Quantum Criticality of an Iron-Pnictide Tetrahedron

Motivated by the close correlation between transition temperature (T(c)) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin-Kondo effect is suppressed to low temperatures by Hund's coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials.

Holography and condensed matter

AbstractThis is a review of recent developments in the application of AdS/CFT methods to some condensed matter problems. In particular we present the holographic description of a local quantum critical state, related to (non)‐Fermi liquids and the strange metal, that appears in large N CFTs with a gravity dual at finite density and zero temperature, and explore its properties by probing it with fermionic operators. Further we discuss possible bosonic and fermionic instabilities, leading to s‐, p‐ or d‐wave holographic superconductors and “electron stars”. Finally we present a realization of local quantum criticality with an impurity problem.

Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators

We discuss the general theoretical arguments advanced earlier for the T=0 global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing between the established and the conjectured. In addition to the well-known phase of a paramagnetic metal with a “large” Fermi surface (PL), there is also an antiferromagnetic phase with a “small” Fermi surface (AFS). We provide the details of the derivation of a quantum non-linear sigma-model (QNLσM) representation of the Kondo lattice Hamiltonian, which leads to an effective field theory containing both low-energy fermions in the vicinity of a Fermi surface and low-energy bosons near zero momentum. An asymptotically exact analysis of this effective field theory is made possible through the development of a renormalization group procedure for mixed fermion-boson systems. Considerations on how to connect the AFS and PL phases lead to a global phase diagram, which not only puts into perspective the theory of local quantum criticality for antiferromagnetic heavy fermion metals, but also provides the basis to understand the surprising recent experiments in chemically-doped as well as pressurized YbRh2Si2. We point out that the AFS phase still occurs for the case of an equal number of spin-1/2 local moments and conduction electrons. This observation raises the prospect for a global phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally, we discuss the connection between the Kondo breakdown physics discussed here for the Kondo lattice systems and the non-Fermi liquid behavior recently studied from a holographic perspective.

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.

Quantum Criticality and Scaling of the Magnetic Response in CeCu6−x Aux

The heavy-fermion system CeCu6−xAux which exhibits antiferromagnetic order for Au concentrations x>0.1, can be easily tuned to a quantum phase transition, either by chemical composition, i.e., Au concentration, or by an external magnetic field. We present extensive inelastic neutron scattering measurements in order to study the momentum and energy dependence of the critical spin fluctuations for concentration- and magnetic field-tuned CeCu6−xAux. The quasi-2D fluctuations, observed for x=0.1 at the magnetic instability, are already present in pure CeCu6 and persist to x=0.2, i.e., well into the magnetically ordered regime. This is a strong hint that disorder does not play a major role in this system. The magnetic response for quantum critical CeCu6−xAux exhibits critical slowing down and obeys scaling relations that depend on the tuning parameter. While the E/T scaling of the dynamic susceptibility in concentration-tuned CeCu5.9Au0.1 is an indication for local quantum criticality, the E/T3/2 scaling in field-tuned CeCu5.8Au0.2 points to a conventional spin-density-wave instability.