We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson φ, which undergoes a continuous transition towards nematic order with a d-wave form factor. We consider two cases: (a) when φ is a soft collective mode of fermions near a Pomeranchuk instability, and (b) when it is an independent critical degree of freedom, such as a composite spin order parameter. In both cases, the order parameter is not a conserved quantity and the d-wave fermionic polarization Π(q,Ω) remains finite even at q=0.

Tunneling of electrons into a two-dimensional electron system is known to exhibit an anomaly at low bias, in which the tunneling conductance vanishes due to a many-body interaction effect. Recent experiments have measured this anomaly between two copies of the half-filled Landau level as a function of in-plane magnetic field, and they suggest that increasing spin polarization drives a deeper suppression of tunneling.

Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized.

Samarium hexaboride is a classic three-dimensional mixed valence system with a high-Temperature metallic phase that evolves into a paramagnetic charge insulator below 40 K. A number of recent experiments have suggested the possibility that the low-Temperature insulating bulk hosts electrically neutral gapless fermionic excitations.

We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform (Q=0) Ising nematic quantum critical point of d-wave symmetry. The nematic order parameter is not a conserved quantity, and this permits a nonzero value of the fermionic polarization in the d-wave channel even for vanishing momentum and finite frequency: Π(q=0,Ωm)≠0.

We develop a theory of quantum oscillations in insulators with an emergent Fermi sea of neutral fermions minimally coupled to an emergent U(1) gauge field. As pointed out by Motrunich [Phys. Rev. B 73, 155115 (2006)PRBMDO1098-012110.1103/PhysRevB.73.155115], in the presence of a physical magnetic field the emergent magnetic field develops a nonzero value leading to Landau quantization for the neutral fermions. We focus on the magnetic field and temperature dependence of the analog of the de Haas-van Alphen effect in two and three dimensions.

We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron-field operators inherits a light-cone-like growth, arising from an interplay of a growth (Lyapunov) exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder.

The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with N components in the (2+1)-dimensional O(N) nonlinear sigma model to leading order in 1/N. The system is taken to be in thermal equilibrium at a temperature T above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted λL.

In this work we study the effect of static disorder on the growth of commutators - a probe of information scrambling in quantum many-body systems - in a variety of contexts. We find generically that disorder slows the onset of scrambling and, in the case of a many-body localized (MBL) state, partially halts it. In the MBL state, we show using a fixed point Hamiltonian that operators exhibit slow logarithmic growth under time evolution and compare the result with the expected growth of commutators in (de)localized noninteracting disordered models.

We review ideas on the nature of the metallic states of the hole-doped cuprate high temperature superconductors, with an emphasis on the connections between the Luttinger theorem for the size of the Fermi surface, topological quantum field theories (TQFTs), and critical theories involving changes in the size of the Fermi surface.We begin with the derivation of the Luttinger theorem for a Fermi liquid, using momentum balance during a process of flux insertion in a lattice electronic model with toroidal boundary conditions.