Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session M19: Strongly Correlated Electron Systems and Phase Transitions |
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Sponsoring Units: DCMP Chair: Andriy Nevidomskyy, Rice University Room: 321 |
Wednesday, March 20, 2013 8:00AM - 8:12AM |
M19.00001: Quantum criticality in the pseudogap two-channel Anderson and Kondo models Tathagata Chowdhury, Kevin Ingersent, Farzaneh Zamani, Pedro Ribeiro, Stefan Kirchner The two-channel Anderson and Kondo impurity models with a density of states $\rho(E) \propto |E|^r$ that vanishes at the Fermi energy ($E=0$) is of current interest in connection with impurities in graphene and in unconventional superconductors. The phase diagram of these models has been established previously [1,2]. We study the low-temperature static and dynamical properties of the models using the numerical renormalization-group method, and compare our results against exact and perturbative analytical theories [2], and against calculations performed within the non-crossing approximation. In the vicinity of the quantum critical points separating local-moment and non-Fermi liquid phases, the static local spin susceptibility is characterized by a set of critical exponents that satisfy the hyperscaling relations expected of an interacting system below its upper critical dimension. The dynamical local susceptibility and the impurity spectral function exhibit forms consistent with frequency-over-temperature scaling, another feature associated with interacting quantum critical points. [1] C. Gonzalez-Buxton and K. Ingersent, Phys. Rev. B 57, 14254 (1998). [2] I. Schneider et al., Phys. Rev. B, 84, 125139 (2011). [Preview Abstract] |
Wednesday, March 20, 2013 8:12AM - 8:24AM |
M19.00002: Phase Diagram of a Correlated Band Insulator George Batrouni, Axel Euverte, Richard Scalettar, Simone Chiesa The effect of on-site electron-electron repulsion U in a band insulator is explored for a bilayer Hubbard Hamiltonian with opposite sign hopping on the two sheets. Unlike the case of the ionic Hubbard model, which has a closely related noninteracting dispersion relation, no evidence is found for a metallic phase intervening between the Mott and band insulators: The gap in the spectral function monotonically increases with U from its initial band insulating value. The origin of such difference can be traced to the fact that the local interaction in a bilayer favors the formation of independent singlets whereas in the ionic model is responsible for a homogenization of the density and a consequent reduction of band structure effects. We found that the formation of singlets between the planes, and the resulting destruction of antiferromagnetic order occurs much more rapidly than in the case of a symmetric Hubbard bilayer, which has the same sign of hopping in the two sheets. [Preview Abstract] |
Wednesday, March 20, 2013 8:24AM - 8:36AM |
M19.00003: Quantum Griffiths singularities in ferromagnetic metals David Nozadze, Thomas Vojta We present a theory of the quantum Griffiths phases associated with the ferromagnetic quantum phase transition in disordered metals. For Ising spin symmetry, we study the dynamics of a single rare region within the variational instanton approach. For Heisenberg symmetry, the dynamics of the rare region is studied using a renormalization group approach. In both cases, the rare region dynamics is even slower than in the usual quantum Griffiths case because the order parameter conservation of an itinerant ferromagnet hampers the relaxation of large magnetic clusters. The resulting quantum Griffiths singularities in ferromagnetic metals are stronger than power laws. For example, the low-energy density of states $\rho(\epsilon)$ takes the asymptotic form $\exp[\{-\tilde{\lambda}\log (\epsilon_0/\epsilon)\}^{3/5}]/\epsilon$ with $\tilde{\lambda}$ being non-universal. We contrast these results with the antiferromagnetic case in which the systems show power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We also compare our result with existing experimental data of ferromagnetic alloy ${\rm{Ni}}_{x}{\rm{V}}_{1-x}$. [Preview Abstract] |
Wednesday, March 20, 2013 8:36AM - 8:48AM |
M19.00004: Quantum Criticality of Charged Particles in Polar Liquids Shahriar Shadkhoo, Robijn Bruinsma We propose a general theory for the interaction of electrons with polarizable media for which the dynamical structure factor for charge fluctuations is known. The theory is based on a generalization of Leggett's method for the construction of path integral functionals for electrons in dissipative media. We apply the method to the case of electrons in polar liquids using a dynamical structure factor obtained by numerical simulations. The functional integrals are approximated using Feynman's variational method. At low temperatures, a dynamical structure factor with local spatial structure along with a Debye-like decaying frequency dependence, as suggested by the simulations, produces a first-order transition at a critical coupling constant. This is in contrast with the Feynman polaron theory, which does not have local structure formation, where no transition takes place. We also find a line of continuous quantum criticality. [Preview Abstract] |
Wednesday, March 20, 2013 8:48AM - 9:00AM |
M19.00005: Unbinding of giant vortices in states of competing order Chris Hooley, Jon Fellows, Sam Carr, J\"org Schmalian We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O($M$), near a point in parameter space where they couple to become a single O($2+M$) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as $1/\sqrt{\Delta}$ and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as $1/\ln(1/\Delta)$, where $\Delta$ denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores. [Preview Abstract] |
Wednesday, March 20, 2013 9:00AM - 9:12AM |
M19.00006: Numerical study of a mobile magnetic impurity in a one-dimensional quantum liquid Julian Rincon, Daniel Garcia, Karen Hallberg, Matthias Vojta We study a mobile spin-1/2 impurity, coupled antiferromagnetically to a one-dimensional gas of fermions. Combining perturbative ideas and extensive density matrix renormalization group calculations, we study the interplay between the screening of the impurity by the electrons and the kinetic and magnetic properties of the impurity. We show that this problem displays a quantum phase transition between one- and two-channel Kondo physics. Using finite-size scaling, we construct a ground-state phase diagram and discuss various non-trivial regimes. [Preview Abstract] |
Wednesday, March 20, 2013 9:12AM - 9:24AM |
M19.00007: Critical fluctuations in $N$-component superconductor models Lorenz Bartosch Inspired by recent conflicting views on the order of the phase transition from an antiferromagnetic N\'eel state to a spin liquid or valence bond solid, we use the functional renormalization group to reconsider the $N$-component superconductor models, in which a dynamic gauge field is minimally coupled to $N$ bosonic complex fields. In contrast to previous work, we only expand in covariant derivatives and use a truncation in which the full field dependence of all wave-function renormalization functions is kept. As a consequence, we find non-trivial RG fixed points for all positive integer $N$. [Preview Abstract] |
Wednesday, March 20, 2013 9:24AM - 9:36AM |
M19.00008: Zigzag Quantum Phase Transition in Quantum Wires Abhijit C. Mehta, Cyrus J. Umrigar, Harold U. Baranger We use Quantum Monte Carlo (QMC) techniques to study the quantum phase transition of interacting electrons in a quantum wire to a quasi-one-dimensional zigzag phase. Interacting electrons confined to a wire by a transverse harmonic potential form a linear Wigner crystal at low densities; as density increases, symmetry about the axis of the wire is broken and the electrons undergo a transition to a quasi-one-dimensional zigzag phase. The phase diagram of particles with Coulomb interaction that undergo a linear to zigzag transition is relevant to electrons in quantum wires and ions in linear traps. We characterize this phase transition by using QMC to study the order parameter, correlation functions, pair density, power spectrum, and addition energies. [Preview Abstract] |
Wednesday, March 20, 2013 9:36AM - 9:48AM |
M19.00009: Construction of local order parameters from non-vanishing mutual information Wing Chi Yu, Shi-Jian Gu, Hai-Qing Lin In the recent decades, raising attention has been paid in the study of quantum phase transitions (QPTs) from quantum information perspectives. In this talk, we will present a scheme in constructing the local order parameters by investigating the spectra of the reduced density matrices that are used to calculate the mutual information. We will briefly review the relation between non-vanishing mutual information and the presence of long-range correlation in a system. In particular, we will illustrate our scheme using the numerical exact diagonalization result of the one-dimensional Hubbard model. [Preview Abstract] |
Wednesday, March 20, 2013 9:48AM - 10:00AM |
M19.00010: Columnar and superfluid order in an extended Shastry-Sutherland model Keola Wierschem, Pinaki Sengupta The low temperature magnetic properties of several rare-earth tetraborides have been shown to be well-characterized by an extension of the Shastry-Sutherland model (SSM). This extension includes additional next-nearest-neighbor bonds, and the exchange interaction along all bonds is anisotropic with strictly ferromagnetic transverse exchange. The extended SSM is thus equivalent to a system of hard-core bosons and is free of the quantum Monte Carlo (QMC) sign problem. Using large scale QMC simulations, we study the phase diagram of the extended SSM in a new parameter regime that stabilizes a zero-field columnar antiferromagnetic state. We show how application of an external magnetic field can induce a phase transition to a spin supersolid phase. We compare the overall magnetization process to experimental observations of ErB$_4$, a rare-earth tetraboride with ground state columnar antiferromagnetic ordering. Finally, we speculate that if the zero-field columnar order present in ErB$_4$ is driven by similar interactions it may also possess a field-induced supersolid phase. [Preview Abstract] |
Wednesday, March 20, 2013 10:00AM - 10:12AM |
M19.00011: Resummation of divergent fluctuations near to metallic ferromagnetic quantum criticality Chris Pedder, Andrew Green Fluctuations near to the metallic ferromagnetic quantum critical point can have profound effects. They lead to new quantum critical scaling at high temperatures, which gives way to reconstruction of the phase diagram at lower temperatures. In the vicinity of the quantum critical point, new spatially modulated magnetic or spin nematic phases appear. These new phases may be revealed by means of non-analytic corrections to Hertz-Millis theory [1], or in the recently-developed quantum order-by-disorder approach [2]. Here we demonstrate a re-summation of all the leading divergences in the latter approach to extend the analysis from the finite-temperature tricritical point down to zero temperature.\\[4pt] [1] D. Belitz, T.R. Kirkpatrick and T. Vojta, Rev. Mod. Phys. 77, 579 (2005); D. V. Efremov, J.J. Betouras, A.V. Chubukov Phys. Rev. B 77, 220401(R), (2008)\\[0pt] [2] G.J. Conduit, A.G. Green \& B.D. Simons Phys. Rev. Lett. 103, 207201 (2009) [Preview Abstract] |
Wednesday, March 20, 2013 10:12AM - 10:24AM |
M19.00012: ABSTRACT WITHDRAWN |
Wednesday, March 20, 2013 10:24AM - 10:36AM |
M19.00013: Tractable Crossing-symmteric Equations Formalism and Applications in Two Dimensions Kelly Reidy, Khandker Quader, Kevin Bedell The tractable crossing symmetric formalism is developed for the 2D case. We first consider circular Fermi surfaces and then extend this to 2D square lattice systems. Limiting cases, such as small $(q,\omega)$, vanishing momentum-energy transfer $(q\rightarrow0, \omega\rightarrow0)$, vanishing q but non-zero $\omega$ are considered. This is applied to the study of various properties of 2D Fermi systems. Of particular interest is the physics near Pomeranchuk instabilities: in Fermi systems, interactions can cause symmetry-breaking deformations of the Fermi surface, called Pomeranchuk instabilities. In Fermi liquid theory language, this occurs when one of the Landau harmonics $F_{\ell}^{s,a}\rightarrow -(2\ell+1)$; e.g. $F_{0}^{s,a}\rightarrow-1$ are related to ferromagnetic transition (a), and density instabilities(s). The corresponding points in parameter space may be viewed as quantum critical points. Using graphical and numerical methods to solve coupled non-linear integral equations that arise in the crossing symmetric equation scheme, we obtain results in the 2D case close to Pomeranchuk instabilities. We compare our 2D results for various response functions and instabilities with the results of recent calculations in the 3D case, which will also be discussed. [Preview Abstract] |
Wednesday, March 20, 2013 10:36AM - 10:48AM |
M19.00014: Strongly-correlated phases in a flatband with incommensurate filling Evelyn Tang, Xiao-Gang Wen We explore strongly-correlated electronic phases in flatband systems (such as on the kagome lattice) with incommensurate filling, in the presence of spin-orbit interactions and ferromagnetism. The competition between Fermi-liquid, charge-density wave and superconducting phases in this system is examined. [Preview Abstract] |
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