Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session X18: Twenty Years of Quantum Cluster Theory: Recent ProgressInvited Live
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Sponsoring Units: DCOMP Chair: Juana Moreno, Louisiana State University |
Friday, March 19, 2021 8:00AM - 8:36AM Live |
X18.00001: 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 on the evolution of computational quantum many-body ideas and methods, starting from the first numerical solutions of quantum impurity problems leading on to the development of modern quantum cluster theories of strongly correlated and disordered systems, which is the subject of this symposium. I will review some of the advances that took place in the solution of quantum impurity models in the 70s and 80s, the development of the dynamical mean-field theory in the late 80s and early 90s, and of its cluster extensions in the late 90s and the early 2000s, both in terms of the techniques that were involved and the understanding they led to. |
Friday, March 19, 2021 8:36AM - 9:12AM Live |
X18.00002: 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 electron-electron 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 high-end computing hardware. |
Friday, March 19, 2021 9:12AM - 9:48AM Live |
X18.00003: Quantum cluster theories for disordered electron systems. Invited Speaker: Hanna Terletska Recently, quantum cluster theories have been developed to understand the properties of disordered electronic systems. The disorder is a common and often unavoidable feature of many materials. It plays a critical role in determining and controlling the properties of many functional quantum systems. Anderson localization is one of such fascinating effects of disorder and is often challenging to capture numerically. In this talk, I will discuss the recently developed Typical Medium Dynamical Cluster Approximation (TMDCA) [1], an effective medium quantum cluster approach for disordered systems. The TMDCA enables quantitative analysis of electron localized states in disordered electron systems. Following the ideas of Dobrosavljevic et al. [2], 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 non-local effects but also recovers exact analytical results in simple disorder models [1]. I will also provide an overview of various recent applications of the TMDCA to a variety of models and systems, including the application of the method to interacting disordered electrons as well as realistic systems in the framework of the ab-initio methods. |
Friday, March 19, 2021 9:48AM - 10:24AM Live |
X18.00004: Cluster dynamical mean field studies of two-particle 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 two-dimensional Hubbard model. While the behavior of single-particle 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 two-particle probes in the cuprates, including NMR, neutron spectroscopy, and M-EELS. We will also show how two-particle quantities can be used to identify the leading fluctuations. |
Friday, March 19, 2021 10:24AM - 11:00AM Live |
X18.00005: 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 correlation 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, the results they have yielded and some challenges that persist. In addition, we will discuss the framework for extension of the quantum cluster approximations to the nonequilibrium problem. |
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