Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session M22: Strongly Correlated Electron Theory II |
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Sponsoring Units: DMP Chair: Srinivas Raghu, Stanford University Room: 324 |
Wednesday, March 20, 2013 8:00AM - 8:12AM |
M22.00001: Bond Disorder Induced Criticality of the Three-Color Ashkin-Teller Model Arash Bellafard, Helmut Katzgraber, Matthias Troyer, Sudip Chakravarty An intriguing result of statistical mechanics is that a first-order phase transition can be rounded by disorder coupled to energylike variables. In fact, even more intriguing is that the rounding may manifest itself as a critical point, quantum or classical. In general, it is not known, however, what universality classes, if any, such criticalities belong to. In order to shed light on this question we examine in detail the disordered three-color Ashkin-Teller model by Monte Carlo methods. Extensive analyses indicate that the critical exponents define a new universality class. We show that the rounding of the first-order transition of the pure model due to the impurities is manifested as criticality. However, the magnetization critical exponent, $\beta$, and the correlation length critical exponent, $\nu$, are found to vary with disorder and the four-spin coupling strength, and we conclusively rule out that the model belongs to the universality class of the two-dimensional Ising model. [Preview Abstract] |
Wednesday, March 20, 2013 8:12AM - 8:24AM |
M22.00002: A multi-critical point of strongly interacting itinerant fermions with supersymmetry Liza Huijse, Bela Bauer, Erez Berg, Matthias Troyer, Kareljan Schoutens A key challenge in theoretical condensed matter physics is the study of strongly interacting fermions, for which perturbative techniques do not work. In recent years a specific model has been put forward where exact results at intermediate densities can be obtained by incorporating supersymmetry. For 2D lattices the supersymmetric model exhibits superfrustration, a strong form of quantum charge frustration, characterized by an extensive ground state entropy. In 1D the model also shows a rich structure. In particular, we discuss the supersymmetric model on the square ladder and show that it describes a multi-critical point where an Ising and a KT transition coincide. The RG equations for the continuum theory reveal an intricate flow diagram with a marginal direction that preserves supersymmetry. We will argue that these results imply that there is a whole class of models with a U(1) and a Z2 symmetry, for which the multi-critical point has emergent supersymmetry. [Preview Abstract] |
Wednesday, March 20, 2013 8:24AM - 8:36AM |
M22.00003: Two-dimensional Hubbard model on a honeycomb lattice Kun Fang, Gayana Fernando, Alexander Balatsky, Armen Kocharian, Kalum Palandage In the honeycomb lattice, a combination of nontrivial topology and electronic correlations drives a great variety of phenomena. We study the 2-dimensional fermionic Hubbard model on a honeycomb lattice using exact diagonalization method at various onsite interaction strength U values. By introducing holes in the model at different filling levels, we analyze the charge gap instability of the lattice which indicates the possibility the system going into a paired state. We further monitor the one-particle excitation spectrum and density of states at various k-points. We find that the electronic interaction introduces quasiparticle states around the Fermi level and the system can undergo a metal-insulator transition. /newline /newline The authors acknowledge the computing facilities provided by the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility at Los Alamos National Laboratory (Contract DE-AC52-06NA25396) and Sandia National Laboratories (Contract DE-AC04-94AL85000) and the Center for Functional Nanomaterials, Brookhaven National Laboratory supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No.DE-AC02-98CH10886. [Preview Abstract] |
Wednesday, March 20, 2013 8:36AM - 8:48AM |
M22.00004: Order and supersymmetry at high filling zero-energy states on the triangular lattice Dimitrios Galanakis, Chris Henley, Stefanos Papanikolaou We perform exact diagonalization studies in $d=2$ dimensions for the Fendley and Schoutens model of hard-core and nearest-neighbor excluding fermions that displays an exact non-relativistic supersymmetry. Using clusters of all possible shapes up to 46 sites, we systematically study the behavior of the ground state phase diagram as a function of filling. We focus on the highly degenerate zero-energy states found at fillings between $1/7$ and $\sim 1/5$. At the lower end of that interval, at filling $1/7$, we explicitly show that the ground states are gapped crystals. Consistent with previous suggestions, we find that the extensive entropy of zero states peaks at a filling of $\sim 0.178$. At the higher end of the interval, we find zero energy ground states at fillings above $1/5$, contrary to previous expectations; which display non-trivial amplitude degeneracies. [Preview Abstract] |
Wednesday, March 20, 2013 8:48AM - 9:00AM |
M22.00005: Toward a unified description of spin incoherent behavior at zero and finite temperatures Mohammad Soltanieh-ha, Adrian Feiguin While the basic theoretical understanding of spin-charge separation in one-dimension, known as ``Luttinger liquid theory'', has existed for some time, recently a previously unidentified regime of strongly interacting one-dimensional systems at finite temperature came to light: The ``spin-incoherent Luttinger liquid'' (SILL). This occurs when the temperature is larger than the characteristic spin energy scale. I will show that the spin-incoherent state can be written exactly as a generalization of Ogata and Shiba's factorized wave function in an enlarged Hilbert space, using the so-called ``thermo-field formalism.'' Interestingly, this wave-function can also describe the *ground-state* of other model Hamiltonians, such as t-J ladders, and the Kondo lattice. This allows us to develop a unified formalism to describe SILL physics both at zero, and finite temperatures. [Preview Abstract] |
Wednesday, March 20, 2013 9:00AM - 9:12AM |
M22.00006: Duality of Weak and Strong Scatterer in Luttinger Liquid Coupled to Massless Bosons Alexey Galda, Igor Yurkevich, Oleg Yevtushenko, Igor Lerner We study electronic transport in a Luttinger liquid (LL) with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). The additional coupling competes with Coulomb interaction changing scaling exponents of various correlation functions. The impurity strength $\lambda$ and the tunneling amplitude $t$ in the WS and WL limits scale at low energies $\varepsilon$ as: $\lambda(\varepsilon) \sim \lambda_0\, \varepsilon^{\Delta_{\mathrm{ws}} - 1}$ and $t(\varepsilon) \sim t_0\, \varepsilon^{\Delta_{\mathrm{wl}} - 1}$, correspondingly. We find that the duality relation between the scaling dimensions established for the standard LL, $\Delta_{\mathrm{ws}}\Delta_{\mathrm{wl}} = 1 $, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. As a result, at low temperatures the system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. However, in the case when electron and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering. [Preview Abstract] |
Wednesday, March 20, 2013 9:12AM - 9:24AM |
M22.00007: Absence of Luttinger's Theorem Kiaran Dave, Philip phillips, Charles Kane We show exactly with an $SU(N)$ interacting model that even if the ambiguity associated with the placement of the chemical potential, $\mu$, for a $T=0$ gapped system is removed by using the unique value $\mu(T\rightarrow 0)$, Luttinger's sum rule is violated. The failure stems from the non-existence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter. [Preview Abstract] |
Wednesday, March 20, 2013 9:24AM - 9:36AM |
M22.00008: Non-Fermi Liquid behavior at the Orbital Ordering Quantum Critical Point in the Two-Orbital Model Ka Wai Lo, Wei-Cheng Lee, Philip Phillips The critical behavior of a two-orbital model with degenerate $d_{xz}$ and $d_{yz}$ orbitals is investigated by multidimensional bosonization. We find that the corresponding bosonic theory has an overdamped collective mode with dynamical exponent $z=3$, which appears to be a general feature of a two-orbital model and becomes the dominant fluctuation in the vicinity of the orbital-ordering quantum critical point. Since the very existence of this $z=3$ overdamped collective mode induces non-Fermi liquid behavior near the quantum critical point, we conclude that a two-orbital model generally has a sizable area in the phase diagram showing non-Fermi liquid behavior. Furthermore, we show that the bosonic theory resembles the continuous model near the $d$-wave Pomeranchuk instability, suggesting that orbital order in a two-orbital model is identical to nematic order in a continuous model. Our results can be applied to systems with degenerate $d_{xz}$ and $d_{yz}$ orbitals such as iron-based superconductors and bilayer strontium ruthenates Sr$_3$Ru$_2$O$_7$. [Preview Abstract] |
Wednesday, March 20, 2013 9:36AM - 9:48AM |
M22.00009: Time-reversal symmetry breaking Pomeranchuk instabilities in hexagonal systems: emergence of the $\beta$ phase Akash Maharaj, Ronny Thomale, Srinivas Raghu We show how nematic order that breaks time reversal symmetry can be stabilized by longer-range repulsive interactions in a variety of hexagonal systems. For the triangular, honeycomb and Kagome lattices at the van Hove filling, we show how spinful fermions can enter the so called $\beta$ phase, in analogy to the B phase in superfluid $^3$He. This Pomeranchuk instability in the spin channel involves a splitting of the Fermi surface into two parts, with the spin direction winding in momentum space. This is possible for angular momentum $l=2$ nematics, since these form a doubly degenerate irreducible representation of the $C_{6v}$ point group symmetry of the lattices in question. We demonstrate how our results are exact in the weak coupling limit, although separate numerical studies have shown that these phases can persist at stronger coupling. [Preview Abstract] |
Wednesday, March 20, 2013 9:48AM - 10:00AM |
M22.00010: Self consistent solution of the tJ model in the overdoped regime B. Sriram Shastry, Daniel Hansen Detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the t-J model in two dimensions, are presented. The theory is to second order in a parameter $\lambda$, and is valid in the overdoped regime of the tJ model. The solution reported here is from Ref [1], where relevant equations given in Ref [2] are self consistently solved for the square lattice. Thermodynamic variables and the resistivity are displayed at various densities and T for two sets of band parameters. The momentum distribution function and the renormalized electronic dispersion, its width and asymmetry are reported along principal directions of the zone. The optical conductivity is calculated. The electronic spectral function $A(k,\omega)$ probed in ARPES, is detailed with different elastic scattering parameters to account for the distinction between LASER and synchrotron ARPES. A high (binding) energy waterfall feature, sensitively dependent on the band hopping parameter $t'$ is noted.\\[4pt] [1] ``Extremely Correlated Fermi Liquids: Self consistent solution of the second order theory,'' D. Hansen and B. S. Shastry, arXiv:1211.0594 (2012). \\[0pt] [2] ``Extremely Correlated Fermi Liquids: The Formalism,'' B. S. Shastry, arXiv:1207.6826 (2012). [Preview Abstract] |
Wednesday, March 20, 2013 10:00AM - 10:12AM |
M22.00011: ECFL in the limit of infinite dimensions Edward Perepelitsky, Daniel Hansen, Antoine Georges, Sriram Shastry Novel techniques for strongly correlated matter are of great importance. Here we compare two recent and independent methods that show considerable promise, and have overlapping regimes of applicability. We evaluate in infinite dimensions the leading order (i.e. $O(\lambda^2)$) equations from the theory of Extremely Correlated Fermi Liquids of the tJ model and compare the resulting Greens functions with recent results from the dynamical mean field theory of the Hubbard model, valid at large U/t that are broadly in the same parameter range where the tJ model is valid. Using the Schwinger equations of motion of the tJ model, we also show exactly that in infinite dimensions a suitably defined Dysonian self energy for the tJ model is independent of the wave vector, while the two self energies of the ECFL theory $\Phi(\vec{k}, i \omega_n)$ and $\Psi(\vec{k}, i \omega_n)$ are respectively linear in $\varepsilon_{\vec{k}}$ and independent of $\vec{k}$ in a minimal description. In particular, we prove that in the minimal theory $\Psi(\vec{k},i\omega_n) = \Psi(i\omega_n)$ and $\Phi(\vec{k},i\omega_n)= \chi(i\omega_n)+ \varepsilon_{\vec{k}} \Psi(i\omega_n) $. [Preview Abstract] |
Wednesday, March 20, 2013 10:12AM - 10:24AM |
M22.00012: Chiral Non-Fermi Liquids Shouvik Sur, Sung-Sik Lee We propose a renormalization group scheme which is suitable for theories with Fermi surface. Low energy modes near the Fermi surface are viewed as a collection of one dimensional fermions with a continuous flavor labelling the momentum along the Fermi surface. Based on this approach, we study a class of chiral metals where one patch of Fermi surface is coupled with a gapless boson in two dimensions. Depending on the dispersion of the boson, one obtains either non-Fermi liquid or Fermi liquid state. We provide a non-perturbative argument for the stability of the states, and compute the exact critical exponents. Finally, we propose a possible experimental realization of a chiral non-Fermi liquid state. [Preview Abstract] |
Wednesday, March 20, 2013 10:24AM - 10:36AM |
M22.00013: Non-Fermi liquids in three dimensions Subhro Bhattacharjee, Sung-Sik Lee, Yong Baek Kim The shape of the fermi surface may have important effects in determining the relevance (in Renormalization group sense) of interactions for the underlying fermions. In our work, we show that for certain physically realizable fermi surfaces in three dimensions, the coupling of the fermions to critical bosons is relevant at the Gaussian fixed point. We find that such interactions may lead to a three dimensional non-Fermi liquid state. We calculate one-loop corrections to the electron self energy within a scheme of (3-$\epsilon$) perturbation in the spatial dimensions to understand the features of such a non-Fermi liquid state. [Preview Abstract] |
Wednesday, March 20, 2013 10:36AM - 10:48AM |
M22.00014: Broken time-reversal symmetry phase in a 2D electron fluid by using higher dimensional bosonization Wathid Assawasunthonnet, Eduardo Fradkin We explore a phase in two-dimensional electron fluids in which the time-reversal symmetry is broken spontaneously by using the method of higher dimensional bosonization. This phase breaks time-reversal and chiral symmetries but does not break space inversion and the combination of chiral and time-reversal symmetries. This phase exhibits non-quantized anomalous Hall effect in the absence of external magnetic fields which corresponds to the Berry curvature on the Fermi surface. In the mean-field limit we show that the fluid spontaneously transforms into the the time-reversal broken phase [1]. The properties deep within the phase is also studied by solving the semi-classical equation of the bosonized fields. [1] Kai Sun and Eduardo Fradkin, Phys. Rev. B {\bf 78}, 245122 (2008). [Preview Abstract] |
Wednesday, March 20, 2013 10:48AM - 11:00AM |
M22.00015: There is more to $d$-electrons than Hubbard $U$ and Hund's rule $J$ Hugo U. R. Strand, Nicola Lanat\`a, Mats Granath, Bo Hellsing Multi-band Hubbard models including all $d$-bands are central for the description of many interesting correlated materials, e.g., the Iron based High-T$_c$ materials. In this work we compare two prevailing spin and angular momentum rotationally invariant models for the local $dd$-interaction, the generalized Kanamori interaction, and the Slater-Condon atomic Coulomb interaction, and establish how the first can be mapped to a very special case of the former. Using the recently developed multi-band Gutzwiller approximation solver, we show that the partial localization of orbital moments in the intermediately correlated regime of the paramagnetic state, is poorly described by the Kanamori model containing only Hubbard and Hund's rule interactions. In fact, for some integer fillings it differs qualitatively compared to the Slater-Condon interaction. [Preview Abstract] |
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