Session J22: Theory of Non Fermi Liquids

Resistivity of a non-Galilean Fermi liquid near Pomeranchuk Quantum Criticality

We analyze the effect of the electron-electron interaction on the resistivity of a metal near a Pomeranchuk quantum critical point (QCP). We show that Umklapp processes are not effective near a QCP, and one must consider the interplay between interaction and disorder. By power counting, the correction to the residual resistivity at low $T$ scales as $AT^{(D+2)/3}$ at QCP ($T^{4/3}$ in 2D). We show, however, that that $A=0$ for a simply connected and convex Fermi surface in 2D due to hidden integrability of the electron motion. We argue that $A >0$ in a two-band ($s-d$) model with light and heavy carriers, and propose this model as an explanation for the observed $T^{(D+2)/3}$ behavior.   

Transport Properties near Quantum Critical Point in 2D Hubbard Model

We obtain high quality estimates of the self energy $\Sigma(K,\omega)$ by {\em{direct}} analytic continuation of $\Sigma(K,i\omega_n)$ obtained from Continuous-Time Quantum Monte Carlo. We use these results to investigate the transport properties near the quantum critical point found in the 2D Hubbard model at finite doping. Resistivity, thermal conductivity, Wiedemann-Franz Law, and thermopower are examined in the Fermi liquid, Marginal Fermi liquid (MFL), and pseudo-gap regions. $\Sigma''(k,\omega)$ with $k$ along the nodal direction displays temperature-dependent scaling similar to that seen in the experiment. A next-nearest neighbor hopping $t'<0$ increases the doping region where MFL character is found.   

Quantum Phase Transition in Interacting Quantum Wires

We consider the quantum phase transition of interacting electrons in a quantum wire from a one-dimensional (1D) to a quasi-1D state as a function of an external gate voltage. At weak interactions, a Lifshitz transition occurs when electrons start filling the second subband of transverse quantization. The physics in the vicinity of the transition is characterized by pronounced correlations as interactions in the second subband are effectively strong due to the diverging density of states close to the band bottom. Inter-subband interactions lead to the formation of polarons, but the nature of the transition is unchanged, i.e., one finds a Lifshitz transition of impenetrable polarons. By contrast, strongly interacting electrons form a (quasi-)1D Wigner crystal, and the transition corresponds to the linear crystal splitting into a zigzag crystal. This Ising transition in the charge sector is decoupled from the spin excitations in the system.   

Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances

We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of $e^2/h$ for spinless electrons, and the total resistance is independent of the Luttinger parameter $K_W$ of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interaction regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a three-wire junction, there are two families of such matrices; we find that the conductance matrix depends on $K_W$ for one family but is independent of $K_W$ for the other family.   

Holographic metals and fractionalized Fermi liquids

I show that there is a close correspondence between the physical properties of holographic metals near charged black holes in anti-de Sitter (AdS) space, and the fractionalized Fermi liquid phase of the lattice Anderson model. The latter phase has a ``small'' Fermi surface of conduction electrons, along with a spin liquid of local moments. This correspondence implies that certain mean-field gapless spin liquids are states of matter at non-zero density which realize the near-horizon, AdS$_2 \times$R$^2$ physics of Reissner-Nordstrom black holes. I will also go beyond this mean-field theory, and discuss connections between gauge theories of fractionalized Fermi liquids and holographic theories.   

Dynamically Generated Gap from Holography: Mottness from a Black Hole

In the fermionic sector of top-down approaches to holographic systems, one generically finds that the fermions are coupled to gravity and gauge fields in a variety of ways, beyond minimal coupling. In this paper, we take one such interaction -- a Pauli, or magnetic dipole, interaction -- and study its effects on fermion correlators. We find that this interaction modifies the fermion spectral density in a remarkable way. As we change the strength of the interaction, we find that spectral weight is transferred between bands, and beyond a critical value, a hard gap emerges in the fermion density of states. A possible interpretation of this bulk interaction then is that it drives the dynamical formation of a (Mott) gap, in the absence of any symmetry breaking.   

Quantum phase transitions in the pseudogap Anderson Holstein model

We study a pseudogap Anderson-Holstein model of a magnetic impurity level that (1) hybridizes with a conduction band whose density of states vanishes in power-law fashion at the Fermi energy, and (2) couples, via its charge, to a nondispersive bosonic mode (e.g., an optical phonon). The model exhibits quantum phase transitions (QPTs) of different types depending on the strength $\lambda$ of the impurity-boson coupling. For small $\lambda$, the suppression of the density of states near the Fermi energy leads to QPTs between strong-coupling (Kondo) and local-moment phases. A sufficiently large $\lambda$, however, transforms the bare Coulomb repulsion between a pair of electrons in the impurity level into an effective attraction, leading to QPTs between strong-coupling (charge-Kondo) and local-charge phases. Critical exponents characterizing the response to a local magnetic field (for small $\lambda$) or electric potential (for large $\lambda$) suggest that the QPTs belong to the same universality class as the QPT of the previously studied pseudogap Anderson model. One specific case of the pseudogap Anderson-Holstein model may be realized in a double-quantum-dot device, where the QPTs manifest themselves in the finite- temperature linear electrical conductance.   

Statistical fluxes and the sodium cobaltate Curie-Weiss metal

A central pursuit in the study of quantum matter is whether non Fermi liquid states exist, as invoked in trying to explain e.g. high-$T_{c}$ superconductivity. A quite different context is the search for thermodynamic materials in energy applications, which require at the same time a very large thermopower and a low resistivity. Here we predict a new state of matter that descends from a strongly interacting microscopy described by a t-J model on a triangular lattice. Due to the altered role of quantum statistics the spins are ``localized'' in statistical Landau orbits, while the charge carriers form a Bose metal that feels the spins through random gauge fields. In contrast to the Fermi-liquid state, this state naturally exhibits a Curie-Weiss susceptibility, large thermopower, and linear-temperature resistivity, explaining the physics of \textrm{Na}$_{x}$\textrm {CoO}$_{2}$ at $x>0.5.$ A ``smoking gun'' prediction for neutron scattering is presented.   

Spin-incoherent behavior in the ground state of strongly correlated systems

It is commonly believed that strongly interacting one-dimensional Fermi systems with gapless excitations are effectively described by Luttinger liquid theory. However, when the temperature of the system is high compared to the spin energy, but small compared to the charge energy, the system becomes ``spin-incoherent.'' We present numerical evidence showing that the one-dimensional ``t-J-Kondo'' lattice, consisting of a t-J chain interacting with localized spins, displays all the characteristic signatures of spin-incoherent physics, but in the ground state. We argue that similar physics may be present in a wide range of strongly interacting systems.   

DMRG study of the Phase Diagram of the Infinite U Hubbard Model

Despite decades of discussion, the phase diagram of the paradigmatic Hubbard model in the strong coupling limit remains uncertain. Here, we study Hubbard ladders with infinite on site repulsion and electron density ranging from n=0 to n=1 per site. DMRG calculations shows that the phase diagrams of two, three and four-leg laddders share the following similarities: as a function of decreasing n a fully polarized (half metallic ferromagnetic phase is followed by a partially polarized ferromagnetic metallic state, and finally by a paramagnetic (unpolarized) phase for n less than a critical value of roughly n $\sim $ 0.5, but which differs somewhat depending on the number of legs. Unexpectedly, the ferromagnetic metal phase is reentrant in the sense that it is interrupted at a special commensurate density (n=0.75 for the two-leg and 4-leg ladders and n=0.8 for the three leg) by an incompressible commensurate density wave phase with zero net ferromagnetic moment. All results appear to extrapolate smoothly to the limit of infinite ladder length. We conclude with some speculations about the phase diagram of the 2D infinite U Hubbard model.   

Mobile impurities in ferromagnetic liquids

Recent work has shown that mobile impurities in one dimensional interacting systems may exhibit behaviour that differs strongly from that predicted by standard Tomonaga-Luttinger liquid theory, with the appearance of power-law divergences in the spectral function signifying sublinear diffusion of the impurity. Using time-dependent matrix product states, we investigate a range of cases of mobile impurities in systems beyond the analytically accessible examples to assess the existence of a new universality class of low-energy physics in one-dimensional systems. \newline\newline Correspondence: Adrian.Kantian@unige.ch   

Nonlinear Collective Field Theory for models with inverse square interaction and exchange

We present fully nonlinear dynamics [1] in inverse square models such as spin-Calogero model and Haldane-Shastry model. Hydrodynamic equations of motion are written for these models in the regime where gradient corrections to the exact hydrodynamic formulation of the theory may be neglected. We then show how this collective field theory allows to calculate correlation functions [2] that cannot be considered with conventional bosonization. We will also present the case of including external harmonic confinement [3] and show that the Calogero family is strikingly similar to models with delta (short-ranged) interaction and can be used as a toy model for cold atom experiments. Including harmonic trap usually ends up destroying integrability. However, Calogero family is special in this regard and the system remains integrable. In addition, we will present results of collective field theory which include gradient corrections thereby enabling us to go beyond gradient catastrophe.\\[4pt] [1] M. Kulkarni, F. Franchini, A. G. Abanov, Phys. Rev. B 80, 165105 (2009)\\[0pt] [2] F. Franchini, M. Kulkarni, Nucl. Phys. B, 825, 320 (2010)\\[0pt] [3] M. Kulkarni, A. G. Abanov, arXiv:1006.0966   

Renyi entropy of gapless spin liquids

Spin liquids are exotic quantum states that do not break any symmetry. Though much is known about gapped spin-liquids, critical spin-liquids with strongly interacting gapless excitations in two and three spatial dimensions are less understood. Candidate ground state wave-functions for such states however can be constructed using the Gutzwiller projection method. We use bipartite entanglement entropy, in particular the Renyi entropy $S_2$ to investigate the quantum structure of these wave-functions. Using the Variational Monte-Carlo technique, we calculate the Renyi entropy of a critical spin liquid - the projected Fermi sea state on the triangular lattice. We find a violation of the boundary law, with $S_2$ enhanced by a logarithmic factor, an unusual result for a bosonic wave-function reflecting the presence of emergent spinons that form a Fermi surface. The Renyi entropy for algebraic spin liquids is found to obey the area law, consistent with the presence of emergent Dirac fermions in the system. Projection is found to completely alter the entanglement properties of nested Fermi surface states. These results show that the Renyi entropy calculations could serve as a diagnostic for gapless fractionalized phases.   

Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Parton Fermi Surface

We study bond energy correlation functions in an exactly solvable quantum spin model of Kitaev type on the kagome lattice with stable Fermi surface of partons proposed recently by Chua {~\textit{et~al.}}, Ref. [arXiv:1010.1035]. Even though any spin correlations are ultra-short ranged, we find that the bond energy correlations have power law behavior with a $1/r^{3}$ envelope and oscillations at incommensurate wavevectors. We determine the corresponding singular surfaces in momentum space, which provide a gauge-invariant characterization of this gapless spin liquid.