Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session J41: Hubbard Model |
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Sponsoring Units: DCMP Chair: Philip Phillips, University of Illinois at Urbana-Champaign Room: 413 |
Tuesday, March 17, 2009 11:15AM - 11:27AM |
J41.00001: Origin of the Mott Gap Philip Phillips, Robert G. Leigh We show exactly that the only charged excitations that exist in the strong-coupling limit of the half-filled Hubbard model are gapped composite excitations generated by the dynamics of the charge $2e$ boson that appears upon explicit integration of the high-energy scale. At every momentum, such excitations have non-zero spectral weight at two distinct energy scales separated by the on-site repulsion $U$. The result is a gap in the spectrum for the composite excitations when $U$ exceeds the bandwidth. Consequently, we resolve the long-standing problem of the cause of the charge gap in a half-filled band in the absence of symmetry breaking. [Preview Abstract] |
Tuesday, March 17, 2009 11:27AM - 11:39AM |
J41.00002: Diagrammatic Monte Carlo Kris Van Houcke, Felix Werner, Evgeny Kozik, Lode Pollet, Nikolay Prokof'ev, Boris Svistunov Diagrammatic Monte Carlo (DiagMC) is an exact technique that allows one to simulate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem, that is typically fatal to Monte Carlo approaches, appears to be manageable with DiagMC. We introduce a general DiagMC scheme for strongly interacting fermions. As an illustrative example, we discuss the application of DiagMC to the Fermi-Hubbard model, and benchmark the technique against state-of-the-art numerical tools for strongly correlated fermions. In addition, we discuss the thermodynamic properties of a Fermi gas at unitarity, obtained through DiagMC simulation. [Preview Abstract] |
Tuesday, March 17, 2009 11:39AM - 11:51AM |
J41.00003: Unconventional soft gaps in strongly-correlated systems with coexisting short-range interaction and disorder Hiroshi Shinaoka, Masatoshi Imada We report a theoretical study of the Anderson-Hubbard model under coexisting short-range interaction and disorder, which is one of the minimum models of real strongly-correlated materials. We determined the ground-state phase diagram in three dimensions within the unrestricted Hartree-Fock approximation. Although only short-range interaction is present, we found a soft gap in the single-particle density of states of the insulating phases [1]. This unconventional soft gap (soft Hubbard gap) cannot be explained within the conventional theory [2] which ascribes the formation of soft gaps to the long-range part of the Coulomb interaction. We present a phenomenology to clarify the origin of the soft Hubbard gap. We propose a multi-valley energy landscape as their origin. Further support by the exact diagonalization in one dimension beyond the mean-field level is given. Possible experiments to verify the present theory are also proposed. [1] H. Shinaoka and M. Imada, arXiv:0811.2492v1. [2] A. L. Efros and B. I. Shklovskii, J. Phys. C 8, L49 (1975). [Preview Abstract] |
Tuesday, March 17, 2009 11:51AM - 12:03PM |
J41.00004: Determinant Quantum Monte Carlo method applied to the t-J model Aleksander Zujev, Richard Fye, Richard Scalettar The usual approach to simulating the t-J model with the Determinant Quantum Monte Carlo (DQMC) method starts with the Hubbard model with a finite on-site interaction U which is then increased to ``almost'' infinity. This approach, however, has considerable difficulties with large round-off errors (stability) and variances, and also a very bad fermion sign problem. In this talk, I will describe a different approach which starts with (almost) infinite U by means of a projector operator and further prohibiting double occupancy by using a modified creation operator. The new technique will be shown to solve some of these difficulties. Unfortunately, the sign problem remains significant. I will discuss the different attempts we have made to reduce it. [Preview Abstract] |
Tuesday, March 17, 2009 12:03PM - 12:15PM |
J41.00005: Ordering and Frustration in a Strongly Correlated Chain system Siddhartha Lal, Mukul Laad We present recent results of our study on the one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. With the complex phase diagram of the TMTSF and TMTTF organic charge transfer salts as motivation, we explore the possible charge and spin ordered states that arise from frustrating interactions. We find a quantum critical point in the phase diagram of the single chain and present results for some response functions in the quantum critical regime. RPA studies of coupled chains reveal a phase diagram with the ordered phase extended to finite temperatures and a phase boundary again ending at a quantum critical point. Critical quantum fluctuations at the QCP enhance the transverse dispersion, leading to a dimensional crossover and a low temperature transition from insulating chains to anistropic metallic bulk behaviour. These results have been reported in arxiv:0708.2156 and are in press at Int. J. Mod. Phys. B. [Preview Abstract] |
Tuesday, March 17, 2009 12:15PM - 12:27PM |
J41.00006: Mott and Wigner-Mott transition away from half-filling Chunhua Li, Ziqiang Wang We study the Mott transition in strongly correlated electron systems away from half-filling in the presence of finite-range Coulomb interaction and/or a superstructure associated with an inhomogeneous electronic state. Using a cluster Gutzwiller approach, we map a minimal single band $t$-$U$-$V$-$\Delta$ model with nearest neighbor Coulomb repulsion $V$ and superlattice potential $\Delta_i$ to a two-orbital Hubbard model with intra and interorbital Coulomb repulsion $U$ and $U^\prime$ and a crystal field splitting $\Delta$. We obtain the Mott transition at quarter-filling from both uniform and $\sqrt{2}\times\sqrt{2}$ charge density wave metals and discuss the physics of the Mott and Wigner-Mott metal-insulator transition. [Preview Abstract] |
Tuesday, March 17, 2009 12:27PM - 12:39PM |
J41.00007: Effect of Interchain Hopping on Nonequivalent Hubbard Chains Takami Tohyama, Hiroyuki Yoshizumi, Takao Morinari Motivated by recent report on the presence of different orders in each CuO$_2$ plane and their coexistence in multi-layered high-temperature superconductors, we examine a simple model with two nonequivalent Hubbard chains coupled by interchain hopping, employing the density-matrix renormalization group (DMRG) and a mean-field calculation. We consider a coupled non-interacting and spin-density-wave (SDW) chains as an example. We find that the interchain hopping induces a short-rang SDW order from adjacent SDW chain and the induced order decreases with increasing the original SDW order of the adjacent chain. We discuss the finding in connection with the multi-layered cuprates. [Preview Abstract] |
Tuesday, March 17, 2009 12:39PM - 12:51PM |
J41.00008: High Precision QMC Study of the 2D Hubbard Model Christopher Varney, Simone Chiesa, Richard Scalettar The Hubbard model has provided insight into a wide variety of strongly correlated systems, including the cuprates and manganites. Recent advances in the generation of optical lattices allow for the possibility of experimentally studying the 2D Hubbard model in a new context. To enhance our understanding of the model, we examine the magnetic correlations on a rectangular lattice using Determinant Quantum Monte Carlo. In this talk, we discuss high precision calculations of the anti-ferromagnetic order parameter as a function of interaction strength and the effect of the aspect ratio on finite size scaling. [Preview Abstract] |
Tuesday, March 17, 2009 12:51PM - 1:03PM |
J41.00009: Quantum phase transition in the one-dimensional half-filled asymmetric Hubbard model Yang Liu, Wen-Ling Chan, Shi-Jian Gu, Hai-Qing Lin We study the quantum phase transition in the one-dimensional asymmetric Hubbard chain at half-filling in terms of spin stiffness by the exact diagonalization method. Since the phase transition is believed to be of Kosterlitz-Thouless type, no local order parameter can describe such a transition. We find instead that spin stiffness might be able to describe the quantum phase transition since the spin degree of freedom is gapless in the Hubbard region. while gapful in the Falicov-Kimball region. [Preview Abstract] |
Tuesday, March 17, 2009 1:03PM - 1:15PM |
J41.00010: Effect of nonlocal interactions on the disorder-induced zero-bias anomaly in the extended Anderson-Hubbard model Rachel Wortis, Hongyi Chen, W.A. Atkinson Adding disorder to a system of correlated electrons moves single-particle states away from the Fermi surface. In the weakly correlated regime, consensus exists on the evolution of the resulting density of states anomaly between the limits of weak and strong disorder. Recently a number of groups have made progress in understanding the strongly correlated regime, mostly in the context of purely local interactions. We study the extended Anderson-Hubbard model using exact diagonalization on two-dimensional 12-site clusters, exploring the evolution of the zero-bias anomaly with the strength of the nonlocal interaction and with doping. At half filling, an exchange-driven Altshuler-Aronov-like anomaly develops Efros-Shklovskii-like atomic character and moves to a regime of strong charge-density correlations, whereas at quarter filling both the Efros-Shklovskii-like behavior and the charge density correlations are much weaker. [Preview Abstract] |
Tuesday, March 17, 2009 1:15PM - 1:27PM |
J41.00011: Local Order and the gapped phase of the Hubbard model: a plaquette dynamical mean field investigation Emanuel Gull, Philipp Werner, Xin Wang, Matthias Troyer, Andrew Millis The four-site DCA method of including intersite correlations in the dynamical mean field theory is used to investigate the metal-insulator transition in the Hubbard model. At half filling a gap-opening transition is found to occur as the interaction strength is increased beyond a critical value. The gapped behavior found in the 4-site DCA approximation is shown to be associated with the onset of strong antiferromagnetic and singlet correlations and the transition is found to be potential energy driven. It is thus more accurately described as a Slater phenomenon (induced by strong short ranged order) than as a Mott phenomenon. Doping the gapped phase leads to a non-Fermi-liquid state with a Fermi surface only in the nodal regions and a pseudogap in the antinodal regions at lower dopings $x \alt 0.15$ and to a Fermi liquid phase at higher dopings. [Preview Abstract] |
Tuesday, March 17, 2009 1:27PM - 1:39PM |
J41.00012: Delocalization effect of the Hubbard repulsion in two dimensions and exact terms Zsolt Gulacsi The physical reasons explaining the delocalization effect of the Hubbard repulsion U leading in 2D to an insulator to metal transition are analyzed. The study is made in exact terms by deducing exact ground states and ground state expectation values of interest based on a positive semidefinite operator technique [1]. First it is shown that always when this effect is observed, U acts on the background of a macroscopic degeneracy present in a multiband type of system. After this step I demonstrate that acting in such conditions, by strongly diminishing the double occupancy, U spreads out the contributions in the ground state wave function, hence strongly increases the one-particle localization length, and consequently extends the one-particle behavior producing conditions for a delocalization effect [2]. \\[3pt] References: [1] Z. Gulacsi, D. Vollhardt, Phys. Rev. Lett. 91,186401(2003); Z. Gulacsi, A. Kampf, D. Vollhardt, Phys. Rev. Lett. 99,026404(2007). [2] Z. Gulacsi, Phys. Rev. B77,245113(2008). [Preview Abstract] |
Tuesday, March 17, 2009 1:39PM - 1:51PM |
J41.00013: One-dimensional periodic Anderson model at partial band filling Miklos Gulacsi, Ian McCulloch An effective hamiltonian is derived for the one-dimensional periodic Anderson model via bosonization. The effective hamiltonian is shown to reproduce all the features of the model as identified by DMRG and provides new information on the ferromagnetic to paramagnetic phase transitions and the paramagnetic phase. We are using a non-Abelian DMRG to determine numerically the phase diagram of the one-dimensional periodic Anderson model. We found very good agreement between the bosonization approach and the DMRG results. [Preview Abstract] |
Tuesday, March 17, 2009 1:51PM - 2:03PM |
J41.00014: The Marginal Fermi Liquid-A Derivation Based on Dirac's Constraints D. Schmeltzer Dirac's method for constraints is used for enforcing the exclusion of double occupancy for Correlated Electrons. The constraintt is given by the pair $Q(\vec{x})=\psi_{\downarrow}(\vec{x})\psi_{\uparrow}(\vec{x})$ which annihilates the ground state $|\Psi>$. Away from half fillings $Q(\vec{x})$ is replaced by a set of $first$ $class$ class Non-Abelian constraints $Q^{(-)}_{\alpha}(\vec{x})$ which are restricted to negative energies. The propagator for the single hole is determined by a measure which is a function of time duration for the hole propagator. a)-The imaginary part of the self energy - is linear in the frequency. b)-In the Superconducting phase the tunneling density of states is asymmetric. [Preview Abstract] |
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