This talk will briefly review the challenges posed to our understanding of the normal metallic state posed by heavy fermion metals. I shall contrast, magnetic, quantum critical and Fermi liquid phases of these materials and discuss the difficulties posed by current theoretical models.

ABSTRACT TBA.

Quantum criticality (QC) in heavy fermion systems has been studied mainly for Kondo lattice systems with integer valence where a quantum critical point is usually expected to be on the border of magnetism. On the other hand, the first Yb-based heavy fermion superconductor ∼beta-YbAlB4 provides a unique example of QC in the mixed valent compounds. In addition, the QC cannot be explained by the standard spin fluctuation mechanism and emerges without tuning any control parameter, indicating formation of a strange metal phase. Indeed, recent resistivity measurements under pressure has revealed that a non-Fermi liquid phase is stable over a finite pressure range up to ~ 0.4 GPa and separated from a magnetic order by a Fermi liquid phase. Here we review such novel phenomena observed in beta-YbAlB4 as well as those found in its isostructural polymorph alpha-YbAlB4, discussing a possible role of valence fluctuation and anisotropy in hybridization gap for the prominent non-Fermi liquid behavior.

Pronounced deviations from Fermi-liquid behaviors are found over broad temperature, pressure and magnetic field ranges in the heavy-fermion compounds CeRhIn5 and CeCoIn5. These behaviors appear to arise from unusual types of quantum-critical points, a magneto-superconducting QCP in CeCoIn5 and two magnetic QCPs accompanied by a reconstruction of the Fermi surface in CeRhIn5. The nature of these quantum critical points, or perhaps more appropriately lines, is not captured in conventional theories and points to the need to consider the role of critical fermionic degrees of freedom. Preliminary studies of a related compound CePt2In7 suggest that its quantum-criticality also may be unconventional.

The emergence of a heavy fermion state in a Kondo lattice system and how this complex electronic state transforms into other correlated states such as superconductivity and other "hidden order" states continues to be at the forefront of condensed matter physics. Through a series of spectroscopic mapping experiments with the scanning tunneling microscope (STM) we have unraveled the emergence of heavy fermions in URu2Si2 and in CeCoIn5 and have followed the evolution of this state into the hidden order state, unconventional metallic phase, and nodal superconducting phase. Our measurements provide direct evidence for the composite nature of heavy quasi-particles and direct experimental evidence of their heavy energy-momentum characteristics. In the superconducting state of CeCoIn$_5$, we provide direct evidence for a d_$x^2-y^2$ pairing symmetry of this compound and show how superconductivity occurs with a band of heavy and correlated composite excitations.

ABSTRACT TBA.

We perform a systematic study of incoherent transport in the high temperature crossover region of the half filled one-band Hubbard model. We demonstrate that the family of resistivity curves displays characteristic quantum critical scaling of the form ρ(T,δU)=ρc(T)f(T/T0(δU)), with T0(δU)∼|δU|zν, and ρc(T)∼T. The corresponding β function displays a “strong coupling” form β∼ln⁡(ρc/ρ), reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticality may be acting as the fundamental mechanism behind the unusual transport phenomena in many systems near the metal-insulator transition.

ABSTRACT TBA.

I will provide the session overview of experiments and related theories on Gapless Spin Liquids.

The Mott transitions of an antiferromagnet and a spin liquid in quasi-triangular lattice organics are compared. A generallized Mott transition in a doped system is proposed for another organics.

ABSTRACT TBA. I'd like to present our recent work of thermal-transport and magnetic torque measurements to study the low-lying excitation of two-dimensional quantum spin liquid state found in the organic Mott-insulator EtMe3Sb[Pd(dmit)2]2.

Quantum spin liquids are new states of matter that are characterized by long-range entanglement and support exotic excitations. Herbertsmithite, a spin-1/2 kagome lattice antiferromagnet, is a leading candidate for having a quantum spin liquid (QSL) ground state. Our success in crystal growth has allowed us to perform detailed studies of the low temperature properties. In particular, inelastic neutron scattering measurements reveal that the spin excitations are fractionalized, a hallmark of the the QSL state. Additional measurements on our samples further corroborate the identification of a QSL and allow us to quantify the deviations from pristine spin Hamiltonians.

The discovery of Herbertsmithite, ZnCu3(OH)6Cl2, has triggered an intense activity on new kagome materials and related theories for the ground state of the quantum kagome Heisenberg antiferromagnet. I will illustrate some of our research thrusts in tracking down quantum spin liquid physics in Cu2+ S=1/2 materials and will discuss the experimental phase diagrams which result from deviations from the pure Heisenberg case. If time permits, I’ll present a new route to this physics with a novel Vanadium-based oxyfluoride kagome family.

ABSTRACT TBA.

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau’s celebrated Fermi liquid theory is of central importance to many outstanding problems in condensed matter physics. Here, we present a theory for a specific example of a strange metal, which we term the “d-wave metal.” Using variational wave functions, gauge theoretic arguments, and ultimately large-scale DMRG calculations, we establish compelling evidence that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian: the venerable t-J model supplemented with a frustrated electron ring exchange term.

I will show how it is possible to design a large class of SU(N) spin models on bipartite lattices to be free of the notorious sign problem of Monte Carlo simulations. These designer models turn out to be the best examples of microscopic spin Hamiltonians that harbor unconventional "deconfined" quantum critical points, which go beyond naive applications of the classic Landau paradigm of phase transitions, because of uncompensated Berry phases. Detailed numerical studies and comparisons with large-N computations have established that the universality class of these critical points is described by U(1) gauge theories with gapless scalar matter fields.

In this talk, I will discuss about two examples of non-Fermi liquids which can be understood in controlled manners. The first example is based on a dimensional regularization scheme, where the co-dimension of Fermi surface is extended such that the Yukawa coupling between a critical boson and Fermi surface is stabilized at a finite but small value. In the second example, I will discuss about chiral non-Fermi liquid states in two space dimensions, which can be realized on the surfaces of stacks of quantum Hall layers. Although the theories flow to strongly interacting field theories at low energies, one can prove the stability of the states and extract exact critical exponents thanks to chirality.

States of matter with a sharp Fermi-surface but no well-defined Landau quasiparticles are expected to arise in a number of physical systems. Examples include i) quantum critical points associated with the onset of order in metals, ii) the spinon Fermi-surface (U(1) spin-liquid) state of a Mott insulator and iii) the Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this talk, I will use renormalization group techniques to investigate possible instabilities of such non-Fermi-liquids to pairing. I will show that for a large class of phase transitions in metals, the attractive interaction mediated by order parameter fluctuations always leads to a superconducting instability, which preempts the non-Fermi-liquid effects. On the other hand, the spinon Fermisurface and the Halperin-Lee-Read states are stable against pairing for a....

ABSTRACT TBA.

I present quantum oscillation measurements in underdoped YBa2Cu3O6+x and YBa2Cu4O8, where the normal ground state is accessed using high applied magnetic fields up to 100 T. Charge-bond order is found to create nodal Fermi pockets in the normal ground state, from which superconducting pairs subsequently emerge. Superconductivity is further found to grow more robust as the optimal and lower quantum critical points are approached by quantum oscillation measurements.

A comprehensive phenomenology is an important starting point for microscopic understanding in complex materials such as the cuprate high temperature superconductors. We have performed a high-resolution laser ARPES study as a function of temperature and momentum, spanning most of the doping range where Bi2Sr2CaCuO8+d (Bi-2212) can be grown. These data were supplemented by synchrotron ARPES experiments to gain access to the antinode, and we find three distinct phase regions inside the superconducting dome. These are interpreted as the regime where superconductivity exists alone (p>0.19), the regime where superconductivity exists with the pseudogap (0.076

Using high resolution ARPES we analyze the electronic scattering rates of cuprate superconductors as a function of temperature, energy, and doping. We show the smooth and continual evolution from the heavily overdoped Fermi liquid limit to the optimally doped Marginal Fermi liquid limit and beyond, with these results showing a new type of universality for these non-Fermi liquid interactions. These results are also very relevant for discussions of the pseudogap as well as quantum-criticality under the dome. Time permitting, I may make connections to recent data on doped Mott insulating iridates.

The normal and superconducting states of iron based high temperature superconductors exhibit many unusual properties. Among them, the quantum critical point, nematic phase in iron pnictides and BCS-BEC crossover in iron chalcogenides will be discussed.

ABSTRACT TBA.

Iridium oxides comprise a new class of correlated materials poised at the boundary between insulating and conducting behavior and strongly influenced by substantial spin-orbit coupling. I will discuss a minimal model for the electronic structure of the pyrochlore iridates, how interaction effects give rise to non-Fermi liquid and unusual quantum criticality in this model, and the implications of this for experiments.

Geometrical frustration suppresses magnetic order, leading to spin liquid state, and therefore, frustrated materials can be close to quantum phase transition between magnetically ordered and spin liquid states. Increasing number of candidate materials of spin liquid have made possible to investigate their exotic properties and we have studied variety of frustrated systems, ranging from insulating hyper-kagome Na4Ir3O8, semi-metallic spin ice Pr2Ir2O7 and heavy-fermion frustrated Kondo lattice YbAgGe. We have investigated quantum criticality of above materials down to low temperatures (~30mK) by means of thermodynamic quantities. Divergence and quantum critical scaling of magnetic Grueneisen parameter of these systems prove near-by quantum critical point and importance of critical free energy. In Pr2Ir2O7, our data show that critical behavior is closely related to magnetic monopole excitations. In quasi-kagome Kondo lattice YbAgGe, we propose that the geometrical frustration sets the system close to a quantum bicritical point, inducing the....

The emergence, stability and decay of skyrmions and the associated emergent electrodynamics in chiral magnets is reviewed. The non-zero topological winding in these systems corresponds to precisely one quantum of emergent magnetic flux that mediates an extremely efficient coupling between the conduction electrons and the magnetic properties. This emergent flux leads to a topological Hall signal, spin transfer torques at ultra-low current densities and emergent electric fields. Additionally skyrmions are characterised by an exceptional stability, which cannot be simply suppressed under large hydrostatic pressures. In fact, measurements of the Hall effect suggest the survival of a topological winding akin that of skyrmions in a non-Fermi iquid regime at high pressures, where neutron scattering suggests the absence of long-range magnetic order.

In this talk, I will present a short review of experimental results for the quantum phase transition in metallic ferromagnets with focus on two specific materials: the quasi-1D heavy-fermion YbNi4P2 and the transition metal compound NbFe2.

ABSTRACT TBA.

I will describe some recent work from my group on the problem of scattering in correlated electron metals. I will show that if an analysis is restricted to situations in which the resistivity varies linearly with temperature in materials with known quasiparticle parameters, a rate of approximately k_B / h_bar per kelvin is observed in a surprisingly wide range of circumstances. The implications of this will be discussed in the context of electrons in metals, and compared empirically with observations on other quantum fluids.

In this talk, I will review our experimental studies of the transport properties of different correlated metals exhibiting non-Fermi-liquid behaviour at low to intermediate temperatures, including the phenomenon of extended or anomalous criticality in cuprates and the curious behavior of the quasi-one-dimensional purple bronze, lithium molybdate.

We reconsider the quantum fluctuation around an AFM quantum critical point in two dimensions. We find that the quantum fluctuations lead to the emergence of a pseudo gap with a composite order parameter fluctuating between a checkerboard charge order and superconducting pairing. Relevance for the pseudo-gap phase of cuprate superconductors will be discussed.

I will argue for a quasi-hydrodynamic description of transport in the absence of quasiparticles. Topics to be discussed from this perspective will include the Wiedemann-Franz law and metal-insulator transitions.

ABSTRACT TBA.

Strong correlations can lead to new phases of quantum matter with striking features, such as emergent fermions and photons in a system composed only of bosons, or even phases where the excitations are neither fermions, nor bosons. Given their scarcity, a fundamental question is: when are such exotic phases stable? In this talk, I will discuss how the quantum entanglement, which is the key property that makes such phases unique in the first place, also allows one to determine the stability of a large class of gapless quantum spin-liquids. I will also discuss the characterization of spin-liquids via their entanglement properties.

At a quantum critical point (QCP) in two or more spatial dimensions, leading-order contributions to the scaling of entanglement entropy typically follow the "area" law, while sub-leading behavior contains universal physics. Different universal functions can be access through entangling subregions of different geometries. For example, for polygonal shaped subregions, quantum field theories have demonstrated that the sub-leading scaling is logarithmic, with a universal coefficient dependent on the number of vertices in the polygon. Although such universal quantities are routinely studied in non-interacting field theories, it requires numerical simulation to access them in interacting theories. In this talk, we discuss numerical calculations of the Renyi entropies at QCPs in 2D quantum lattice models. We calculate the universal coefficient of the vertex-induced logarithmic scaling term, and compare to non-interacting field theory calculations. Also, we examine the shape dependence of the Renyi entropy for finite-size lattices with smooth subregion boundaries. Such geometries provide a sensitive probe of the gapless wavefunction in the thermodynamic limit, and give new universal quantities that could be examined by field-theoretical studies in 2+1D.

Understanding the real time dynamics of systems near quantum critical points at non-zero temperatures constitutes an important yet challenging problem, especially in two spatial dimensions where interactions are strong. We present detailed quantum Monte Carlo results for two separate realizations of the superfluid-insulator transition of bosons on a lattice: their low-frequency conductivities are found to have the same universal dependence on imaginary frequency and temperature. We then use the structure of the real time dynamics of conformal field theories described by the holographic gauge/gravity duality to make progress on the difficult problem of analytically continuing the Monte Carlo data to real time. Our method yields quantitative and experimentally testable results on the frequency-dependent conductivity at the quantum critical point, and on the spectrum of quasinormal modes in the vicinity of the superfluid-insulator quantum phase transition. Extensions to other observables and universality classes are discussed.