Developing and improving numerical algorithms to study intrinsically correlated electron systems

Steven R. White

Over the last two years, we have used several different numerical techniques to study a variety of intrinsically correlated electron systems. The three main types of numerical techniques we have used are: (1) finite- temperature quantum Monte Carlo (QMC); (2) exact diagonalization; and (3) numerical renormalization groups. We have made substantial progress both on developing and improving the numerical algorithms and in using these methods to study interesting systems. We have developed techniques for analytically continuing imaginary-time QMC data to obtain dynamical properties, and have used these techniques to study pseudogap and gap formation in the repulsive and attractive Hubbard models. We have developed a program to calculate two particle interaction vertices with full frequency and momentum dependence using QMC, and have studied possible magnetic and superconducting instabilities in the Hubbard model.

Yukinori Ota, 太田 幸則

S. G. Kuzmin, T. M. O'Neil

In recent experiments, ultracold plasmas were produced by photoionizing small clouds of laser-cooled atoms. It has been suggested that the low initial temperature of these novel plasmas leads directly to strong correlation and order. In contrast, we argue that rapid intrinsic heating raises the electron temperature to the point where strong correlation cannot develop. The argument is corroborated by a molecular-dynamics simulation of the early-time plasma evolution.

Anna Brünisholz, Markus Reiher

Future fault-tolerant quantum computers will allow us to calculate electronic structures of atomistic systems. However, these systems will be intrinsically limited in size, requiring embedding theories for many systems because of the unfavorable scaling of the number of terms describing the electron-electron interaction in the second-quantized electronic Hamiltonian. Quantum embedding theories address this challenge by partitioning a quantum system into a region of interest, the impurity, and its (larger) complement, the environment. However, currently available quantum embedding methods place restrictive demands on near-future quantum computers, such as the need to measure reduced density matrices or the need for repeated evaluations. Here, we introduce the new orbital embedding method eCAS that steers clear of these pitfalls by constructing a multi-CAS problem, the active spaces of which are localized and can be solved independently of each other with any quantum algorithm. This also allows for the development of comparatively simple gradient expressions. eCAS leverages the Schmidt decomposition to construct initial impurity and bath orbitals and augments them with localized environment orbitals, based on a mutual correlation criterion. The mutual correlation criterion makes eCAS systematically improvable without the need for any iteratively determined quantities.

Shan-Wen Tsai

Tôru Sakai