Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session Y14: Progress Towards a Solution of the Hubbard ModelInvited

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Sponsoring Units: DCOMP Chair: Emanuel Gull, University of Michigan Room: 310 
Friday, March 18, 2016 11:15AM  11:51AM 
Y14.00001: Tensor network studies of the twodimensional tJ and Hubbard models Invited Speaker: Philippe Corboz Tensor networks are a class of variational wave functions enabling an efficient representation of quantum manybody states, where the accuracy can be systematically controlled by the bond dimension of the tensors. A wellknown example are matrix product states, the underlying ansatz of the density matrix renormalization group (DMRG) method, which has become the stateoftheart tool to study (quasi) 1D systems. Progress in quantum information theory, in particular a better understanding of entanglement in quantum manybody systems, has led to the development of 2D tensor networks, including projected entangledpair states (PEPS) or the 2D multiscale entanglement renormalization ansatz (MERA). These methods provide one of the most promising routes for the simulation of strongly correlated systems in 2D, in particular models where Quantum Monte Carlo fails due to the negative sign problem. In this talk I report on recent progress in simulating the 2D tJ and Hubbard models with infinite PEPS (iPEPS) which is a tensor network ansatz for a 2D wave function in the thermodynamic limit. Our results reveal an extremely close competition between a uniform dwave superconducting state and different types of stripe states, where iPEPS yields better variational energies than other stateoftheart variational methods for large 2D systems.\footnote{P. Corboz, T. M. Rice, and M. Troyer, Phys. Rev. Lett. 113, 046402 (2014); P. Corboz, arXiv:1508.04003.} The stripes are sitecentered with coexisting charge, spin, and superconducting order, where stripes with inphase dwave order have an equal or only slightly lower energy than stripes with antiphase dwave order. Finally, a nematic anisotropy reduces the pairing amplitude and the energies of stripe states are lowered relative to the uniform state with increasing nematicity. [Preview Abstract] 
Friday, March 18, 2016 11:51AM  12:27PM 
Y14.00002: Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms Invited Speaker: James LeBlanc In this talk we present numerical results for ground state and excited state properties (energies, double occupancies, and Matsubaraaxis self energies) of the singleorbital Hubbard model on a twodimensional square lattice. In order to provide an assessment of our ability to compute accurate results in the thermodynamic limit we employ numerous methods including auxiliary field quantum Monte Carlo, bare and boldline diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multireference projected HartreeFock. We illustrate cases where agreement between different methods is obtained in order to establish benchmark results that should be useful in the validation of future results. [Preview Abstract] 
Friday, March 18, 2016 12:27PM  1:03PM 
Y14.00003: Mott physics and spin fluctuations: A unified framework Invited Speaker: Olivier Parcollet I will present the "TRILEX" formalism for strongly correlated electron systems and its application to the Hubbard model. TRILEX is designed to unify Dynamical Mean Field Theory (DMFT) and spin fluctuation approaches close to the Mott transition in a minimal way. It is based on a local approximation of the dynamical threeleg interaction vertex and solved using a selfconsistent local quantum impurity model. It allows to address simultaneously the Mott physics \`a la DMFT and the effect of long range antiferromagnetic fluctuations. While its computational cost is comparable to a single site ExtendedDMFT computation, the selfenergy is momentumdependent. Moreover TRILEX is the starting point of a systematic and controlled method based on clusters. I will discuss the application of TRILEX to the Hubbard model on a twodimensional square lattice. As interactions are increased towards the Mott insulating state, the local vertex acquires a strong frequency dependence, driving the system to a Mott transition, while at low enough temperatures the momentum dependence of the selfenergy is enhanced due to large spin fluctuations. Upon doping, a Fermi arc is found in the oneparticle spectral function, which is one signature of the pseudogap state. [Preview Abstract] 
Friday, March 18, 2016 1:03PM  1:39PM 
Y14.00004: Dynamical Vertex Approximation for the Hubbard Model Invited Speaker: Alessandro Toschi A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum manybody algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation [1], which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss [2] the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of nonlocal fluctuations beyond DMFT grow enormously, determining the appearance of a lowtemperature insulating behavior for all values of the interaction in the unfrustrated model [3]: Here the prototypical features of the MottHubbard metalinsulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the MerminWagner theorem. Eventually, by a fluctuation diagnostics [4] analysis of cluster DMFT selfenergies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holeddoped frustrated case, with important implications for the theoretical modeling of the cuprate physics. \\ \\ $[1]$ A. Toschi, A.A. Katanin, and K. Held, {\sl "Dynamical vertex approximation: A step beyond dynamical meanfield theory"}, Phys.\ Rev.\ B {\bf 75}, 045118 (2007).\\ $[2]$ G. Rohringer, A. Toschi, A. Katanin, and K. Held, {\sl "Critical Properties of the HalfFilled Hubbard Model in Three Dimensions"}, Phys.\ Rev.\ Lett.\ {\bf 107}, 256402 (2011).\\ $[3]$ T. Sch\"afer, F. Geles, D. Rost, G. Rohringer, E. Arrigoni, K. Held, N. Bl\"umer, M. Aichhorn, and A. Toschi, {\sl "Fate of the false MottHubbard transition in two dimensions"}, Phys.\ Rev.\ B {\bf 91}, 125109 (2015).\\ $[4]$ O. Gunnarsson, T. Sch\"afer, J.P.F. LeBlanc, E. Gull, J. Merino, G. Sangiovanni, G. Rohringer, and A. Toschi, {\sl "Fluctuation Diagnostics of the Electron SelfEnergy: Origin of the Pseudogap Physics"}, Phys.\ Rev.\ Lett.\ {\bf 114}, 236402 (2015).\\ [Preview Abstract] 
Friday, March 18, 2016 1:39PM  2:15PM 
Y14.00005: Density matrix embedding theory studies of the twodimensional Hubbard model Invited Speaker: BoXiao Zheng Density matrix embedding theory (DMET) provides a quantum embedding framework to compute the electronic structure in strongly correlated lattice systems. It has been applied to various model Hamiltonians and \textit{ab initio} systems. In this talk, I will review the results obtained in the twodimensional oneband Hubbard model using DMET. Over the last years, we mapped a calibrated groundstate phase diagram of the twodimensional Hubbard model, concerning magnetic, superconducting and various inhomogeneous phases. Based on the results from this work, as well as the consistent data from other numerical methods, we are able to conclude that many parts of the Hubbard phase diagram is already settled up to an accurate energy scale of 0.001t. Recently, by using largescale auxiliaryfield quantum Monte Carlo (AFQMC) in the impurity problem, we are able to treat much larger embedded clusters at halffilling (and with the constrained path approximation at nonhalffilling), which provides a deeper understanding on the finitesize effects of energy and observables in both quantum embedding and finite cluster numerical methods. Finally, we systematically investigated the putative inhomogeneous phases in the underdoped, strong coupling Hubbard model, proposing new inhomogeneous patterns as strong candidates for the ground state. Reference: [1] BoXiao Zheng, Garnet K.L. Chan, arXiv:1504.01784 [2] J.P.F. Leblanc, Andrey E. Antipov, et al., arXiv:1505.02290 [Preview Abstract] 
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