## General information

**Description:**Quantum physics requires the solution of PDEs in high dimensional spaces, but this is hard. Various numerical schemes have been developed to solve these PDEs approximately in the past decades. Understandably, some high fidelity models can only be applied to systems of very small sizes, while relatively low fidelity models can be applied to much larger systems. The theory (or sometimes more accurately, "recipe") of embedding allows one to marry different approximations together to handle large systems with relatively high fidelity. These theories are widely used in quantum physics and chemistry, but there is little mathematical understanding available. We plan to investigate some of the work in the literature from a mathematical perspective.

This student seminar aims at understanding one paper or so on a focused topic per week.

**When:**Thursday 2PM-3:30PM

**Where:**Evans 891

## Schedule

Date | Content |
---|---|

8/31 | Introduction (Lin Lin) |

9/7 | Green's function embedding: mean field (Lin Lin) |

9/14 | Density functional embedding (Joonho Lee) |

9/21 | Density functional embedding (Joonho Lee) |

9/28 | Density matrix embedding (Michael Lindsey) |

10/5 | Density matrix embedding (Michael Lindsey) |

10/12 | No meeting |

10/19 | [CRS16] (Ze Xu) |

10/26 | [ZC11] (Leonardo Zepeda) |

11/2 | [LZ17] (Jeffmin Lin) |

11/9 | [WJS16] (Dong An) |

11/16 | [EBC10] (Jiefu Zhang) |

11/30 | [H16] (Yu Tong) |

## Reading materials

Overview

- [KSH06] Kotliar et al. - 2006 - Electronic structure calculations with dynamical mean-field theory
- [SC16] Sun, Chan - 2016 - Quantum Embedding Theories
- [CSR15] Chung et al. - 2015 - The ONIOM Method and Its Applications
- [TLK17] Ayral, Lee, Kotliar, G - 2017 - Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective

- [LLL17] Li, Lin, Lu - 2017 - PEXSI-Sigma: A Green's function embedding method for Kohn-Sham density functional theory
- [P06] Potthoff - 2006 - Non-perturbative construction of the Luttinger-Ward functional
- [ZC11] Zgid, Chan - 2011 - Dynamical mean-field theory from a quantum chemical perspective
- [LMM11] Lin et al. - 2011 - Dynamical mean-field theory for quantum chemistry
- [I01] Ishida - 2001 - Surface-embedded Green-function method A formulation using a linearized-augmented-plane-wave basis set
- [LZ17] Lan, Zgid - 2017 - Generalized Self-Energy Embedding Theory
- [CRS16] Chibani et al. - 2016 - Self-consistent Green's function embedding for advanced electronic structure methods based on a dynamical mean-f

- [MGS12] Manby et al. - 2012 - A Simple, Exact Density-Functional-Theory Embedding Scheme
- [HC11] Huang, Carter - 2011 - Potential-functional embedding theory for molecules and materials
- [H16] Huang - 2016 - Extending the density functional embedding theory to finite temperature
- [FLM15] Fornace et al. - 2015 - Embedded Mean-Field Theory
- [EBC10] Elliott et al. - 2010 - Partition density-functional theory