Quantum Boltzmann equation of composite fermions interacting with a gauge field

Transport properties in non-Fermi liquid phases of nodal-point semimetals

In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid (NFL) phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable NFL phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g. optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-calledLuttinger-Abrikosov-Benelavskii phaseof isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity.

Ultraviolet-Infrared Mixing in Marginal Fermi Liquids

When Fermi surfaces (FSs) are subject to long-range interactions that are marginal in the renormalization-group sense, Landau Fermi liquids are destroyed, but only barely. With the interaction further screened by particle-hole excitations through one-loop quantum corrections, it has been believed that these marginal Fermi liquids (MFLs) are described by weakly coupled field theories at low energies. In this Letter, we point out a possibility in which higher-loop processes qualitatively change the picture through UV-IR mixing, in which the size of the FS enters as a relevant scale. The UV-IR mixing effect enhances the coupling at low energies, such that the basin of attraction for the weakly coupled fixed point of a (2+1)-dimensional MFL shrinks to a measure-zero set in the low-energy limit. This UV-IR mixing is caused by gapless virtual Cooper pairs that spread over the entire FS through marginal long-range interactions. Our finding signals a possible breakdown of the patch description for the MFL and questions the validity of using the MFL as the base theory in a controlled scheme for non-Fermi liquids that arise from relevant long-range interactions.

Higher-Spin Theory of the Magnetorotons

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions ν=N/(2N+1) at large N. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are O(N) neutral excitations, each carrying a well-defined spin that runs integer values 2,3,…. The mixing of modes at nonzero momentum q leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at qℓ_{B}=z_{i}/(2N+1), where ℓ_{B} is the magnetic length and z_{i} are the zeros of the Bessel function J_{1}, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.

Holographic non-Fermi-liquid fixed points

Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this 'holographic duality', various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS(2)) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.

Quantum Boltzmann equation study for the Kondo breakdown quantum critical point

We develop the quantum Boltzmann equation approach for the Kondo breakdown quantum critical point, involved with two bands for conduction electrons and localized fermions. Particularly, the role of vertex corrections in transport is addressed, crucial for non-Fermi liquid transport with temperature linear dependence. Only one band of spinons may be considered for scattering with gauge fluctuations, and their associated vertex corrections are introduced in the usual way, where the divergence of self-energy corrections is cancelled by that of vertex corrections, giving rise to a physically meaningful result in the gauge invariant expression for conductivity. On the other hand, two bands should be taken into account for scattering with hybridization excitations, giving rise to coupled quantum Boltzmann equations. We find that vertex corrections associated with hybridization fluctuations turn out to be irrelevant due to the heavy mass of spinons in the so called decoupling limit, consistent with the diagrammatic approach showing non-Fermi liquid transport.

U(1) gauge theory of the Hubbard model: spin liquid states and possible application to kappa-(BEDT-TTF)2Cu2(CN)3

We formulate a U(1) gauge theory of the Hubbard model in the slave-rotor representation. From this formalism it is argued that spin liquid phases may exist near the Mott transition in the Hubbard model on triangular and honeycomb lattices at half filling. The organic compound kappa-(BEDT-TTF)2Cu2(CN)3 is a good candidate for the spin liquid state on a triangular lattice. We predict a highly unusual temperature dependence for the thermal conductivity of this material.