Jedediah Pixley

Kondo Destruction and Quantum Criticality in Kondo Lattice Systems

Considerable efforts have been made in recent years to theoretically understand quantum phase transitions in Kondo lattice systems. A particular focus is on Kondo destruction, which leads to quantum criticality that goes beyond the Landau framework of order-parameter fluctuations. This unconventional quantum criticality has provided an understanding of the unusual dynamical scaling observed experimentally. It also predicted a sudden jump of the Fermi surface and an extra (Kondo destruction) energy scale, both of which have been verified by systematic experiments. Considerations of Kondo destruction have in addition yielded a global phase diagram, which has motivated the current interest in heavy fermion materials with variable dimensionality or geometrical frustration. Here we summarize these developments, and discuss some of the ongoing work and open issues. We also consider the implications of these results for superconductivity. Finally, we address the effect of spin–orbit coupling on the global phase ...

Many-Body Localization and Quantum Nonergodicity in a Model with a Single-Particle Mobility Edge.

We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge.

Kondo destruction and valence fluctuations in an Anderson model.

Unconventional quantum criticality in heavy-fermion systems has been extensively analyzed in terms of a critical destruction of the Kondo effect. Motivated by a recent demonstration of quantum criticality in a mixed-valent heavy-fermion system, β-YbAlB(4), we study a particle-hole-asymmetric Anderson impurity model with a pseudogapped density of states. We demonstrate Kondo destruction at a mixed-valent quantum critical point, where a collapsing Kondo energy scale is accompanied by a singular charge-fluctuation spectrum. Both spin and charge responses scale with energy over temperature (ω/T) and magnetic field over temperature (H/T). Implications for unconventional quantum criticality in mixed-valence heavy fermions are discussed.

Quantum Phases of the Shastry-Sutherland Kondo Lattice: Implications for the Global Phase Diagram of Heavy-Fermion Metals

Considerable recent theoretical and experimental effort has been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in heavy-fermion compounds with geometrical frustration. These developments have motivated us to study the competition between the Ruderman-Kittel-Kasuya-Yosida and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the valence bond solid and heavy Fermi liquid. In the presence of antiferromagnetic order, our zero-temperature phase diagram is remarkably similar to the global phase diagram proposed earlier based on general grounds. We discuss the implications of our results for the experiments on Yb2Pt2Pb and related compounds.

Logarithmic entanglement lightcone in many-body localized systems

We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for quantum information propagation in many-body localized systems previously conjectured based on the existence of local integrals of motion. In addition, near the localization-delocalization transition, we find that the final states after the local quench exhibit volume-law entanglement. We also show that the local quench induces a deterministic orthogonality catastrophe for highly excited eigenstates, where the typical wave-function overlap between the pre- and post-quench eigenstates decays {\it exponentially} with the system size.

Static and dynamic properties of interacting spin-1 bosons in an optical lattice

We study the physics of interacting spin-

Critical Kondo Destruction in a Pseudogap Anderson Model: Scaling and Relaxational Dynamics

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Real-space mean-field theory of a spin-1 Bose gas in synthetic dimensions

bosons in an optical lattice using a variational Gutzwiller technique. We compute the mean-field ground state wave-function and discuss the evolution of the condensate, spin, nematic, and singlet order parameters across the superfluid-Mott transition. We then extend the Gutzwiller method to derive the equations governing the dynamics of low energy excitations in the lattice. Linearizing these equations, we compute the excitation spectra in the superfluid and Mott phases for both ferromagnetic and antiferromagnetic spin-spin interactions. In the superfluid phase, we recover the known excitation spectrum obtained from Bogoliubov theory. In the nematic Mott phase, we obtain gapped, quadratically dispersing particle and hole-like collective modes, whereas in the singlet Mott phase, we obtain a non-dispersive gapped mode, corresponding to the breaking of a singlet pair. For the ferromagnetic Mott insulator, the Gutzwiller mean-field theory only yields particle-hole like modes but no Goldstone mode associated with long range spin order. To overcome this limitation, we supplement the Gutzwiller theory with a Schwinger boson mean-field theory which captures super-exchange driven fluctuations. In addition to the gapped particle-hole-like modes, we obtain a gapless quadratically dispersing ferromagnetic spin-wave Goldstone mode. We discuss the evolution of the singlet gap, particle-hole gap, and the effective mass of the ferromagnetic Goldstone mode as the superfluid-Mott phase boundary is approached from the insulating side. We discuss the relevance and validity of Gutzwiller mean-field theories to spinful systems, and potential extensions of this framework to include more exotic physics which appears in the presence of spin-orbit coupling or artificial gauge fields.

Pairing correlations near a Kondo-destruction quantum critical point

We study the pseudogap Anderson model as a prototype system for critical Kondo destruction. We obtain finite-temperature (T) scaling functions near its quantum-critical point, by using a continuous-time quantum Monte Carlo method and also considering a dynamical large-N limit. We are able to determine the behavior of the scaling functions in the typically difficult to access quantum-relaxational regime (ℏω<k(B)T) and conclude that the relaxation rates for both the spin and single-particle excitations are linear in temperature. We discuss the implications of these results for the quantum-critical phenomena in heavy-fermion metals.

Frustration and multicriticality in the antiferromagnetic spin-1 chain

The internal degrees of freedom provided by ultracold atoms provide a route for realizing higher dimensional physics in systems with limited spatial dimensions. Nonspatial degrees of freedom in these systems are dubbed “synthetic dimensions.” This connection is useful from an experimental standpoint but complicated by the fact that interactions alter the condensate ground state. Here we use the Gross-Pitaevskii equation to study the ground-state properties of a spin-1 Bose gas under the combined influence of an optical lattice, spatially varying spin-orbit coupling, and interactions at the mean-field level. The associated phases depend on the sign of the spin-dependent interaction parameter and the strength of the spin-orbit field. We find “charge”- and spin-density-wave phases which are directly related to helical spin order in real space and affect the behavior of edge currents in the synthetic dimension. We determine the resulting phase diagram as a function of the spin-orbit coupling and spin-dependent interaction strength, considering both attractive (ferromagnetic) and repulsive (polar) spin-dependent interactions, and we provide a direct comparison of our results with the noninteracting case. Our findings are applicable to current and future experiments, specifically with ^(87)Rb, ^7Li, ^(41)K, and ^(23)Na.