Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session X45: Beyond Fermi Liquids II |
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Sponsoring Units: DCMP Chair: Sriram Shastry, Univ of California-Santa Cruz Room: LACC 505 |
Friday, March 9, 2018 8:00AM - 8:12AM |
X45.00001: Transport in the t-t'-J model in 2-d using the Extremely Correlated Fermi Liquid theory Sriram Shastry, Peizhi Mai We present the low energy transport functions of the t-t'-J model in 2-dimensions, relevant for understanding cuprate superconductors. The calculations are based on recent progress in the extremely correlated Fermi liquid theory, applicable to strong coupling models. The spectral functions, the resistivity ρ(T) and Hall conductivities can be obtained at various density, t' and J. The quasiparticle weight Z is typically very small for n ≥ 0.8. The spectral properties display a remarkable thermal sensitivity, with an effective Fermi temperature lower than the bare bandwidth by two orders of magnitude. At low T flipping the sign of t' also flips the curvature of the ρ(T) ↔ T curves, from convex to concave. These resemble the observed curvature flips in hole-doped versus electron-doped systems. At low T, the cotangent Hall angle behaves as T2. It also displays a bending (i.e. kink) at higher T, signifying a crossover from a (Gutzwiller correlated) Fermi liquid to a strange metal. |
Friday, March 9, 2018 8:12AM - 8:24AM |
X45.00002: High order λ expansion in the t-J model using Extremely Correlated Fermi Liquid theory. Edward Perepelitsky, Michael Arciniaga, Sriram Shastry The results of the λ expansion for the Green's function in the t-J model to high orders are reported in two and infinite spatial dimensions. This expansion is defined through the Schwinger equation of motion, in which (0≤λ≤1) provides continuity between the Fermi gas and the fully correlated model. In recent work, we have formulated a systematic set of rules for the "Schwinger diagrams" which arise from this expansion. These include a set of standard Feynman diagrams, in which the band dispersion εk, and the superexchange Jk, play the role of the interaction, as well as a set of "Meta-Feynman" diagrams. The earlier λ expansion results, taken to second order, reliably reproduce the low-frequency part of the spectral function (in the immediate vicinity of the quasiparticle). The results of the higher order diagrams display a marked improvement in the features at high energies. |
Friday, March 9, 2018 8:24AM - 8:36AM |
X45.00003: The Electron Green's Function for the t-t'-J Model in 1,2 … ∞ Dimensions Peizhi Mai, Steven White, Sriram Shastry By combining the extremely correlated Fermi liquid (ECFL) theory and the density matrix renormalization group (DMRG) method, we present an overview of the electron propagator of the t-t'-J model in any dimension for various parameters of the model and electron densities. In 1-d the DMRG method gives essentially exact numerical results, which are shown to compare quite well with the ECFL method. In particular the momentum dependence can be checked against the exact DMRG result. We use a closed set of equations from ECFL theory that are valid in all dimensions. Their application to infinite dimension has been checked against dynamical mean field theory earlier. These equations have also been applied to recently 2-d. The present study fills the remaining gap, thus giving an overview of the solution in all dimensions. In 1-d at low energies we find clear signatures of spin-charge separation in both calculations. At higher energies the spectral functions resemble those in higher dimensions. |
Friday, March 9, 2018 8:36AM - 8:48AM |
X45.00004: Dynamic spin and charge susceptibilities of a Fermi liquid Prachi Sharma, Vladimir Zyuzin, Dmitrii Maslov Motivated by recent observation of the charge susceptibility of superconducting cuprates [1], we study the dynamic spin and charge susceptibilities of a Fermi liquid beyond the random phase approximation (RPA) for a screened Coulomb interaction. Taking into account the self-energy (SE) and vertex (V) diagrams, which describe an excitation of two particle-hole pairs, gives a non-zero contribution to the imaginary part of the spin susceptibility, χs''(q,ω), beyond the continuum boundary. The resulting profile of χs''(q,ω) has two peaks, one is due to the damped spin mode below the continuum and another one is due to the non-RPA corrections above the continuum boundary. The tail of χs''(q,ω) falls off as q2/ω for frequencies far above the continuum boundary. In a Galilean-invariant system, the SE and V contributions to the charge susceptibility, χc(q,ω), are canceled by the Aslamazov-Larkin diagrams, and the tail of resulting χc''(q,ω) falls off as q4/ω. We also study an interplay between the plasmon peak and non-RPA corrections in χc''(q,ω). |
Friday, March 9, 2018 8:48AM - 9:00AM |
X45.00005: ‘Metallic’ phase in a system of spin-orbit coupled bosons Shouvik Sur, Kun Yang We study a system of interacting bosons in the presence of isotropic spin-orbit coupling in two space dimensions. An isotropic spin-orbit coupling leads to a highly degenerate band-minima that lie along a ring in momentum space. Further, the density of states of the non-interacting system diverges as the ring is approached in analogy to one dimensional bosonic systems and fermionic systems at van Hove filling. A large number of low energy states enhances the effects of interaction which is expected to strongly dress the non-interacting system. Indeed, many candidate ground states have been proposed that differ from conventional Bose-Einstein condensate or superfluid state. Here we show that it is possible to stabilize a critical phase that does not break any symmetries of the non-interacting system, and resembles a Tomonaga-Luttinger liquid. We also identify the leading instability, and obtain a phase diagram. |
Friday, March 9, 2018 9:00AM - 9:12AM |
X45.00006: Constraints on the Fermi liquid scaling of the optical conductivity in MnSi Laleh Mohtashemi, F. Bartram, Amir Farahani, Eric Karhu, Theodore Monchesky, J. Steven Dodge We have developed a new method of terahertz time-domain spectroscopy (THzTDS) analysis to test the frequency-temperature scaling relation of Fermi-liquid theory, ρ(ν,T) = [σ(ν,T)]-1=ρ0+Α[(hν)2+(pπkBT)2], where p=2. We apply this to THzTDS measurements of MnSi thin films over a temperature range T = 5-300 K and a frequency range ν = 0.1-3 THz. |
Friday, March 9, 2018 9:12AM - 9:24AM |
X45.00007: Magnetotransport in a Model of a Disordered Strange Metal Aavishkar Patel, John McGreevy, Daniel Arovas, Subir Sachdev We engineer a microscopic model of two-dimensional itinerant electrons locally and randomly scattering off point-like impurities which are described by Sachdev-Ye-Kitaev (SYK) models. For a particular choice of the scattering interaction, this model realizes a controlled description of a diffusive marginal Fermi liquid without momentum conservation, which has a linear-in-T resistivity. By tuning the strength of the scattering interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-T crossover to a fully incoherent regime that also has a linear-in-T resistivity. We describe the magnetotransport properties of this model. We then consider a macroscopically disordered sample with domains of such marginal Fermi liquids with varying electron and impurity densities. Using an effective medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the applied transverse magnetic field B at large B. The resistance also scales linearly in T at small B, and as T f(B/T) at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates. |
Friday, March 9, 2018 9:24AM - 9:36AM |
X45.00008: Near field optical microscopy of Luttinger liquid plasmons in single walled carbon nanotubes Sheng Wang, Feng Wang Quantum-confined electrons in one dimension (1D) behave as Luttinger liquid, which features charge spin separation and other intriguing properties in dramatic contrast to Fermi liquid. The strong electron electron interaction in Luttinger liquid dominates its properties and is characterized by a single Luttinger liquid parameter. Metallic single walled carbon nanotubes (SWNTs) is one of the best candidates to explore such Luttinger-liquid physics. Recently developed scanning near field optical microscopy (SNOM) has made it possible to extract this Luttinger liquid parameter quantitatively from its plasmon wavelength by a single scanning. With this quantitative information enabled by SNOM, we performed systematic study of this Luttinger liquid plasmons and how they are modified by extrinsic factors. This study provides more fundamental understanding of Luttinger liquid behaviours in carbon nanotubes and also facilitates the applications of nanophotonic devices based on remarkably confined and high quality factor carbon nanotube plasmons. |
Friday, March 9, 2018 9:36AM - 9:48AM |
X45.00009: Anomalous Thermal Diffusivity in Bad Metals Jiecheng Zhang, Eli Levenson-Falk, Erik Kountz, Brad Ramshaw, Doug Bonn, Ruixing Liang, Walter Hardy, Richard Greene, Sean Hartnoll, Aharon Kapitulnik Local measurements of thermal diffusivity are used to analyze the transport of heat in the bad metallic regime of several strongly correlated materials. Thermal diffusivity was measured for several curate systems in their so-called bad metal regime. For underdoped YBCO, we find that the thermal anisotropy is comparable to reported values of the electrical resistivity anisotropy and drops sharply below the charge order transition, suggesting that both anisotropies have the same origin. For some electron-doped cuprates the inverse diffusivity is found to be proportional to temperature, again similar to the behavior of the electrical resistivity. We interpret our results through a strong electron-phonon scattering picture where both electron and lattice system saturates a quantum scattering time bound of ~h/kBT. Our results suggest that neither well-defined electron nor phonon quasiparticles might be present in these systems, and that thermal transport is carried out by a collective ”soup” of strongly coupled electrons and phonons. |
Friday, March 9, 2018 9:48AM - 10:00AM |
X45.00010: High temperature transport in a Hubbard model with screened Coulomb interactions Connie Mousatov, Ilya Esterlis, Sean Hartnoll We demonstrate that the Hubbard model with screened Coulomb interactions can be treated perturbatively in the hopping parameter t at temperatures and interaction strengths T, U >>t. This allows high temperature transport to be studied using classical Monte Carlo methods. Performing a Monte Carlo simulation, we map out the phase diagram for this two-dimensional electron system as a function of doping and T/U. It exhibits multiple signatures of non-Fermi liquid behavior, including linear-in-temperature resistivity across a large range of temperatures and a Lorentz ratio which fails to obey the Wiedemann-Franz law. We compare the transport and thermodynamic properties of our model to those measured experimentally in various strongly correlated materials. |
Friday, March 9, 2018 10:00AM - 10:12AM |
X45.00011: Strange metals and strange insulators with coherent Fermi surface Sujay Ray, Tanmoy Das In a conventional metallic (insulating) phase, resistivity increases (decreases) with temperature, and a coherent Fermi surface exists (does not exist). In a ‘strange’ metal, the Fermi surface is partially or fully incoherent (non-Fermi liquid), and the resistivity increases linearly with temperature. Here we introduce two opposite concepts. (i) We introduce a ‘strange metal’ state where the resistivity features non-Fermi-liquid behavior, but the Fermi-surface is coherent and analytic. (ii) We also introduce insulating-like transport properties, even in the presence of coherent Fermi-surface. Both results are obtained analytically, as well as numerically within the momentum-resolved density-fluctuation (MRDF) theory in a single band Hubbard model. We calculate self-energy due to itinerant-localized density fluctuations (self-consistently) and find their generic strong momentum-dependence. We demonstrate that both the above results are a manifestation of the momentum-dependence of the self-energy, but at different values of the Hubbard interaction. The results highlight the importance of the non-local self-energy effects in correlated materials, giving unusual results as seen in various experiments. |
Friday, March 9, 2018 10:12AM - 10:24AM |
X45.00012: Due-diligence to interpreting the Wiedemann-Franz law measurement Kin Chung Fong Considerable interest has arisen to understand the non-Fermi liquid behavior in strongly correlated systems by the Wiedemann-Franz law. Experimentally, this simple law holds remarkably well in wide ranges of carrier densities and masses as long as the collisions are elastic. This robustness makes the violation of the WF law a strong indicator for non-Fermi liquid behavior if it is not trivially broken. However, testing the WF law is a challenging experiment because it requires the measurement of the electronic thermal conductivity without contributions from other channels, i.e. phonons. The inevitable electrical contact resistance would also contaminate the Lorenz number measurement. Specifically, would the experimental test give a false positive or negative error due to the finite contact resistance? We will answer this question using a simple model in order to perform the due-diligence to interpreting the experimental results. |
Friday, March 9, 2018 10:24AM - 10:36AM |
X45.00013: Thermal diffusivity and chaos in holographic metals Richard Davison, Subir Sachdev, Mike Blake We study the thermal diffusivity in holographic models of strange metals. The properties of these metals are related to the properties of gravitational theories in a higher-dimensional curved spacetime. Near generic infra red fixed points of these models, we find that the thermal diffusivity is related to the parameters characterising many-body chaos. This is true independently of the charge density, magnetic field, or periodic potential strength, and is a consequence of a universal feature of certain black hole horizons. |
Friday, March 9, 2018 10:36AM - 10:48AM |
X45.00014: Trial wave functions for a Composite Fermi liquid on a torus Mikael Fremling, Niall Moran, Johannes Slingerland, Steven Simon We study the two-dimensional electron gas in a magnetic field at filling fraction ν = 2 1 . At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions. |
Friday, March 9, 2018 10:48AM - 11:00AM |
X45.00015: Derivation of effective Hubbard models by unitary transformation based on numerical optimization using Hubbard ground state YIFAN TIAN, Steven White The effective low-energy models of Hubbard model are usually derived from perturbation theory. Here we derive the effective model of Hubbard model in spin space and t-J space using a unitary transformation from numerical optimization. We represent the Hamiltonian as Matrix product state(MPO). We represent the unitary transformation using gates according to tensor network methods. We obtain this unitary transformation by optimizing the unitary transformation between the ground state of Hubbard model and the projection of Hubbard model ground state into spin space and t-J space. The ground state is computed using DMRG(Density matrix renormalization method). In half filling case, the optimization can reach a very high accuracy using a three-sites gate. We then analyze systems of different numbers of particles using t-J space. The unitary transformation we get from numerical optimization gives rise to effective models that are in line with perturbation theories. This numerical optimization method starting from ground state energy provides another approach to analyze effective low-energy models of strongly correlated electron systems. |
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