Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session P41: Models of Strongly Correlated Electrons |
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Sponsoring Units: DCMP DMP Chair: Paul Fendley, University of Virginia Room: 413 |
Wednesday, March 18, 2009 8:00AM - 8:12AM |
P41.00001: Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids Kai Sun, Eduardo Fradkin We study the spontaneous non-magnetic time-reversal symmetry breaking in a 2D Fermi liquid without breaking either the translational symmetry or the $U(1)$ charge symmetry. Using a Berry phase approach, we found that for a large class of models, including all one- and two-band models, the time-reversal symmetry breaking states can be classified into two classes, dubbed type I and II, depending on the accompanying spatial symmetry breaking patterns. The properties of each class are studied. In particularly, we show that the states breaking both time-reversal and chiral symmetries (type II) are described by spontaneously generated Berry phases and exhibit anomalous Hall effect in the absence of magnetic fields and magnetic impurities. We also show examples of the time-reversal symmetry breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. In particularly, we found a simple lattice structure in which the time-reversal symmetry breaking phases is stabilized by infinitesimal interactions. [Preview Abstract] |
Wednesday, March 18, 2009 8:12AM - 8:24AM |
P41.00002: String-nets, quantum loop gases and the sign problem for non-abelian anyons Andrea Velenich, Claudio Chamon, Xiao-Gang Wen Hamiltonians giving rise to topological ground states can be constructed explicitly as sums of local operators acting on Hilbert spaces where distinct classical string-net configurations are orthogonal. We show explicitly the connection beteewn string-nets and quantum loop gas models with their non-orthogonal inner product. Also we emphasize the role of the ``sign problem'' for a Hamiltonian in enforcing the topological character of its ground state. [Preview Abstract] |
Wednesday, March 18, 2009 8:24AM - 8:36AM |
P41.00003: Hydrodynamic description of spin Calogero-Sutherland model Alexander Abanov, Manas Kulkarni, Fabio Franchini We study a non-linear collective field theory for an integrable spin-Calogero-Sutherland model. The hydrodynamic description of this $SU(2)$ model in terms of charge density, charge velocity and spin currents is used to study non-perturbative solutions (solitons) and examine their correspondence with known quantum numbers of elementary excitations [1]. A conventional linear bosonization or harmonic approximation is not sufficient to describe, for example, the physics of spin-charge (non)separation. Therefore, we need this new collective bosonic field description that captures the effects of the band curvature. In the strong coupling limit [2] this model reduces to integrable $SU(2)$ Haldane-Shastry model. We study a non-linear coupling of left and right spin currents which form a Kac-Moody algebra. Our quantum hydrodynamic description for the spin case is an extension for the one found in the spinless version in [3].\\[3pt] [1] Y. Kato,T. Yamamoto, and M. Arikawa, J. Phys. Soc. Jpn. 66, 1954-1961 (1997).\\[0pt] [2] A. Polychronakos, Phys Rev Lett. 70,2329-2331(1993).\\[0pt] [3] A.G.Abanov and P.B. Wiegmann, Phys Rev Lett 95, 076402(2005) [Preview Abstract] |
Wednesday, March 18, 2009 8:36AM - 8:48AM |
P41.00004: Supersymmetry in strongly correlated fermion models Dimitris Galanakis, Stefanos Papanicolaou, Chris Henley We investigate the Fendley and Schoutens~\footnote{ P. Fendley and K. Schoutens, Phys. Rev. Lett. 90, 120402 (2003).} model of hard core fermions on lattice which have hopping elements $t$, and potential terms $V$ which include a second-neighbor repulsion with some multi-particle terms. At the special point $t=V$, they showed that the Hamiltonian is $H = \{Q^\dagger(r), Q\}$ with $Q = \sum_r q(r)= \sum_r c(r)P(r)$, where $c(r)$ is an annihilation operator and $P(r)$ enforces the hardcore. That means the system acquires an exact non-relativistic supersymmetry, and for a range of fillings has a large number of zero-energy ground states~$^1$. To obtain insights on the nature of the zero-energy states and excitations, we perform exact diagonalization studies on finite clusters for various interaction strengths, fillings and lattice geometries. We note that for fillings beyond $n\approx 0.3$, we find coexisting domains of the inert crystal at $n=1/2$, in contrast to a related non-supersymmetric model~\footnote{ N.G. Zhang and C.L. Henley, Phys. Rev. B 68, 014506 (2003).} Moreover, using both numerical and analytical tools, we investigate perturbative limits where $q(r)$ is changed so as to preserve supersymmetry but a particular class of ground-states becomes trivial. [Preview Abstract] |
Wednesday, March 18, 2009 8:48AM - 9:00AM |
P41.00005: Hexatic and Microemulsion Phases in the 2d Quantum Plasma Bryan Clark, Michele Casula, David Ceperley It has been long known that the two-dimensional one component plasma supports both a Wigner-crystal and liquid phase. Classically [1,2], it is known that a hexatic phase exists but it is not known how this hexatic phase extends into the quantum regime. Moreover, at low temperature, phenomenological arguments [3] from Jamei, et. al. suggest the existence of microemulsion phases including stripes and bubbles. We use diffusion and path integral Monte Carlo to map out this phase diagram. We are able to extend the hexatic phase into the quantum regime as well as quantify the nature of the defects and exponents in the long range quantum system. We also specify the the nature, extent and existence (or lack thereof) of the expected low-T microemulsion phases. \\[0pt] [1] Muto, S. \& Aoki, H. Crystallization of a classical two-dimensional electron system: Positional and orientational orders. Phys. Rev. B 59, 14911(1999).\\[0pt] [2] He, W.J. et al. Phase transition in a classical two-dimensional electron system. Phys. Rev. B 68, 195104(2003).\\[0pt] [3] Jamei, R., Kivelson, S. \& Spivak, B. Universal Aspects of Coulomb-Frustrated Phase Separation. Phys. Rev. Lett. 94, 056805-4(2005). [Preview Abstract] |
Wednesday, March 18, 2009 9:00AM - 9:12AM |
P41.00006: Quantum phase transition in a staggered flux phase Christoph Puetter, Hae-Young Kee We study the quantum critical point inside the staggered flux phase. We present the dynamics of the fermions at the critical point and discuss their relevance for the phenomena observed in high-Tc cuprates. [Preview Abstract] |
Wednesday, March 18, 2009 9:12AM - 9:24AM |
P41.00007: Quantum correlated percolation Liang Cao, M. Jeng, J. M. Schwarz Abstract: Quantum percolation is the study of hopping transport of a quantum particle on randomly diluted percolation clusters. Inspired by correlated percolation models of geometrical jamming, we extend quantum percolation to investigate hopping transport on percolation clusters with geometric constraints on the occupation of bonds/sites. An example of a geometric constraint is each occupied site must have at least $k$ occupied neighboring sites to remain occupied ($k$-core percolation). Another example is particular sets of neighboring sites containing at least one occupied site for an occupied site to remain occupied (spiral model). Both models exhibit long-range geometrical correlations differing from ordinary percolation and give rise to a discontinuous phase transition (in high dimensions for $k$-core percolation). To investigate how these atypical long-range geometrical correlations affect the hopping transport of a quantum particle, we numerically study the level statistics of quantum $k$-core percolation on the Bethe lattice and the two-dimensional quantum spiral model. While the quantum $k$-core model exhibits an insulator-to-metal transition as the occupation probability is increased, preliminary results indicate that there is no insulator-to-metal transition in the two-dimensional quantum spiral model. Studies of a three- dimensional quantum spiral model will also be addressed as will possible physical applications of quantum jamming. [Preview Abstract] |
Wednesday, March 18, 2009 9:24AM - 9:36AM |
P41.00008: Frustration of dissipation in a spin-boson model Kevin Ingersent, Alper Duru The spin-boson model (SBM), in which a quantum two-level system couples via one component of its effective spin to a dissipative bosonic bath, has many realizations. There has been much recent interest in the SBM with a sub-Ohmic bath characterized by a power-law spectral exponent $0 < s < 1$, where at zero temperature a quantum critical point separates delocalized and localized phases. Numerical renormalization group calculations have called into question [1] the validity of the long-assumed mapping between the SBM and the classical Ising chain with interactions decaying with distance $|i-j|$ as $1/|i-j|^{1+s}$. Attention has also fallen on a variant of the SBM in which two components of the impurity spin couple to different bosonic baths. For Ohmic case ($s = 1$), competition between the baths has been shown to frustrate the dissipation and reduce the coupling of the impurity to the environment [2]. The present study addresses the SBM with two sub-Ohmic baths, where dissipative effects are intrinsically stronger than for $s=1$. Numerical renormalization group methods are used to identify a continuous quantum phase transition in this model and to evaluate critical exponents characterizing the quantum-critical behavior in the vicinity of the transition. [1] M. Vojta et al., Phys. Rev. Lett. 94, 070604 (2005). [2] E. Novais et al., Phys. Rev. B 72, 014417 (2005). Supported by NSF Grant DMR-0710540. [Preview Abstract] |
Wednesday, March 18, 2009 9:36AM - 9:48AM |
P41.00009: Fidelity susceptibility and quantum phase transitions Shi-Jian Gu In this talk, I will introduce the quantum fidelity approach to quantum phase transitions based on its leading term, i.e. the fidelity susceptibility. The fidelity susceptibility denotes the adiabatic leading response of the ground state to the driving parameter. Differ from traditionally approach based on the ground-state energy, the fidelity susceptibility shows distinct scaling and singular behaviours around the critical point. I will present also the ground-state fidelity approach to both Landau's phase transition and topological phase transition, as illustrated by the Lipkin-Meshkov-Glick model and the Kitaev honeycomb model, respectively. [Preview Abstract] |
Wednesday, March 18, 2009 9:48AM - 10:00AM |
P41.00010: Scaling of logarithmic quantum fidelity in the Lipkin-Meshkov-Glick model Ching Yee Leung, Ho-Man Kwok, Shi-Jian Gu, Hai-Qing Lin The quantum fidelity is used to describe quantum phase transitions in many works. As the classical expression of logarithmic fidelity is shown to be an extensive value, it was suggested that the logarithmic fidelity can be averaged over the system size and named as fidelity per site. However, illustrated by the anisotropic Lipkin-Meshkov-Glick model, which exhibits different scaling behaviour in different phases, we show that the logarithmic fidelity in the ground state of the model scales like $N$ in the symmetry-broken phase and $N^0$ in the polarizing phase. It is suggested to be a pure quantum effect and generalization of fidelity per site is proposed. [Preview Abstract] |
Wednesday, March 18, 2009 10:00AM - 10:12AM |
P41.00011: Multicanonical Monte Carlo simulations of anisotropic SU(3) and SU(4) Heisenberg models Kenji Harada, Naoki Kawashima, Matthias Troyer We present the results of multicanonical Monte Carlo simulations on two-dimensional anisotropic SU(3) and SU(4) Heisenberg models. In our previous study [K.~Harada, et al., J.~Phys.~Soc.~Jpn. \textbf{76}, 013703 (2007)], we found evidence for a direct quantum phase transition from the valence-bond-solid(VBS) phase to the SU(3) symmetry breaking phase on the SU(3) model and we proposed the possibility of deconfined critical phenomena (DCP) [T.~Senthil, et al., Science \textbf{303}, 1490 (2004); T.~Grover and T.~Senthil, Phys. Rev. Lett. \textbf{98}, 247202 (2007)]. Here we will present new results with an improved algorithm, using a multicanonical Monte Carlo algorithm. Using a flow method-like technique [A.B.~Kuklov, et al., Annals of Physics \textbf{321}, 1602 (2006)], we discuss the possibility of DCP in both models. [Preview Abstract] |
Wednesday, March 18, 2009 10:12AM - 10:24AM |
P41.00012: Topological stability of q-deformed quantum spin chains Charlotte Gils, Eddy Ardonne, Simon Trebst, Andreas Ludwig, Matthias Troyer, Zhenghan Wang Quantum mechanical systems, whose degrees of freedom are so-called $su(2)_k$ anyons, form a bridge between ordinary spin systems and systems of interacting non-Abelian anyons. Such a connection can be made for arbitrary spin-S systems, and we explicitly discuss spin-$1/2$ and spin-$1$ systems. Anyonic spin-$1/2$ chains exhibit a topological protection mechanism that stabilizes their gapless ground states and which vanishes only in the limit ($k \to \infty$) where the system turns into the ordinary spin-$1/2$ Heisenberg chain. For anyonic spin-$1$ chains we show that their phase diagrams closely mirror the one of the biquadratic spin-$1$ chain. This includes generalizations of the Haldane phase, of the AKLT point, and the appearance of several stable critical phases described by (super)conformal field theories. [Preview Abstract] |
Wednesday, March 18, 2009 10:24AM - 10:36AM |
P41.00013: Momentum distribution of the one-dimensional hard-core boson Hubbard model Min-Chul Cha, Jong-Geun Shin, Ji-Woo Lee We investigate the momentum distributions, $n_k$, of the one- dimensional hard-core boson Hubbard model as a function of the nearest-neighbor interaction strength by exact diagonalizations for lattices up to 30 sites. It is well known that the ground state of this model shows a quantum phase transition between the Ising-ordered insulating phase and the XY-ordered superfluid phase at $V=2t$. Predetermination of the critical point helps us to investigate various critical behaviors. At the critical point, the momentum distribution shows a linear dependence ($n_k \sim |k-\pi|$). $n_k (k=\pi)$ shows different critical behaviors upon appoaching the critical point in the Ising or XY regions. Some other properties of the momentum distributions and the crtical behaviors are discussed. [Preview Abstract] |
Wednesday, March 18, 2009 10:36AM - 10:48AM |
P41.00014: Ring-exchange interaction in doubly degenerate orbital system with strong electron correlation Joji Nasu Orbital degree of freedom is one of the attractive themes in transition-metal oxides. Since the inter-site orbital interaction depends explicitly on the bond direction, one orbital configuration which minimizes the bond energy in one direction does not minimize in other directions. This is a kind of frustration. We study the e$_{g}$ orbital model (EOM) where the e$_{g}$ orbital is represented by the pseudo-spin (PS) with nearest neighbor (NN) interaction in a cubic lattice. Due to this frustration, this model shows a macroscopic number of degenerate states in the classical ground states. It is known that these states are lifted by thermal and quantum fluctuations. We examine the long-range interaction effect in the EOM. This interaction is derived by the higher-order perturbational processes of the electron transfer under strong on-site Coulomb repulsion in the two orbital Hubbard model. In particular, roles of the orbital ring-exchange interaction are focused on. This includes the magnetic octupole operator which does not appear in the previous EOM with NN interaction. We analyzed this model by the mean field approximation and the classical Monte-Carlo method. We found that PS canted state is stabilized rather than PS collinear state which is realized in the previous EOM due to thermal and quantum fluctuations. It is also shown that the magnetic octupole polarization appears in a wide parameter region. [Preview Abstract] |
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