Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session W36: Twenty years of the Quantum Cluster Theory: recent progressInvited

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Sponsoring Units: DCOMP Chair: Juana Moreno, Louisiana State University, Baton Rouge Room: 601/603 
Friday, March 6, 2020 8:00AM  8:36AM 
W36.00001: Impurity models and the development of quantum cluster approaches to lattice models of quantum condensed matter Invited Speaker: Hulikal Krishnamurthy My aim in this talk will be to provide a historical perspective of the evolution of computational quantum manybody ideas and methods connected with the first numerical solutions of quantum impurity problems leading on to the development of modern quantum cluster theories of strongly correlated and disordered condensed matter systems, the subject of this symposium. I will review the advances that took place, both in understanding and in the techniques of solution, of quantum impurity models in the 70s and 80s, the development of the dynamical meanfield theory in the late 80s and early 90s, and of its cluster extensions in the late 90s and early 2000s. 
Friday, March 6, 2020 8:36AM  9:12AM 
W36.00002: Quantum Cluster Theory of Unconventional Superconductivity Invited Speaker: Thomas Maier Quantum cluster theories provide an important framework to give insight into the complex behavior and different quantum states observed in correlated electron materials. In particular, they can provide an understanding of the mechanisms that give rise to superconductivity in unconventional superconductors, in which pairing is driven by electronelectron interactions. Here we discuss how dynamic cluster approximation quantum Monte Carlo calculations of Hubbard models have progressed in addressing this problem, and how this progress is linked to advances in algorithms and highend computing hardware. 
Friday, March 6, 2020 9:12AM  9:48AM 
W36.00003: Multiscale approaches to strongly correlated systems in and out of equilibrium Invited Speaker: Herbert Fotso The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, many of the mechanisms responsible for these technologically promising properties remain rather elusive. Computational approaches have played a major role in helping to fill this void. In particular, dynamical mean field theory (DMFT) and its cluster extension, the dynamical cluster approximation (DCA) have allowed significant progress. However, despite all the insightful results of the dynamical cluster approximation, computational constraints (sign problem, exponential growth of the Hilbert space) still limit the length scale within which correlations can be treated exactly in the formalism. A natural next step is the development of multiscale many body approaches whereby this challenge is addressed by introducing, between the short length scale where correlations are treated exactly using a cluster solver such Quantum Monte Carlo (QMC) or exact diagonalization, and the long length scale where correlations are treated in a mean field, an intermediate length scale within which correlations can be treated perturbatively. We will discuss implementations of this multiscale many body approach and the results they have yielded. In addition, we will discuss the framework for extension of quantum cluster approximations to the nonequilibrium problem. 
Friday, March 6, 2020 9:48AM  10:24AM 
W36.00004: Quantum cluster typical medium methods for the study of localization in strongly disordered electronic systems. Invited Speaker: Hanna Terletska Disorder is a common feature of many materials and often plays a key role in changing and controlling their mechanical, electronic and other functional properties. Anderson localization is one of the fascinating effects of disorder in materials, which is often hard to capture numerically. There has been great progress made in the last several years towards understanding the properties of disordered electronic systems and electron localization, in particular, based on the effective medium methods. We have recently developed the Typical Medium Dynamical Cluster Approximation (TMDCA) for disordered electronic systems [1, 2]. The TMDCA enables quantitative analysis of electron localized states in disordered electron systems. The method is an effective medium approach that maps a given disorder lattice problem onto a quantum cluster embedded in an effective typical medium, which is determined selfconsistently. Following the ideas of Dobrosavljevic et al. [3], the TMDCA employs the cluster typical (geometrically averaged) density of states as an order parameter to detect the localized electrons states. It has been shown that TMDCA not only correctly captures nonlocal effects but also recovers exact analytical results in simple disorder models [1]. In this talk, I will provide an overview of various recent applications of the TMDCA to a variety of models and systems, including application of the method to interacting disordered electrons as well as realistic systems in the framework of the abinitio methods. 
Friday, March 6, 2020 10:24AM  11:00AM 
W36.00005: Cluster dynamical mean field studies of twoparticle response functions in the Hubbard model Invited Speaker: Emanuel Gull Over the last twenty years, the cluster dynamical mean field theory has generated useful insight into the Hubbard model and its relation to the pseudogap and superconductivity in the twodimensional Hubbard model. While the behavior of singleparticle properties of the model is well understood, this was so far not the case for higher order correlation functions. This talk will introduce susceptibility calculations and show comparisons to a range of experimental twoparticle probes in the cuprates, including NMR, neutron spectroscopy, and MEELS. We will also show how twoparticle quantities can be used to identify the leading fluctuations. 
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