DMRG Studies of Frustrated and Doped Systems

University Of California-Irvine, Irvine CA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical and computational research, and education to advance understanding of quantum mechanical systems with many interacting particles, particularly electrons. The development of novel algorithms and software for solving the equations of quantum mechanics that describe systems of many interacting constituents remains one of the most important theoretical techniques. The PI invented one of the most prominent of these algorithms, the density matrix renormalization group (DMRG), and continues developing ITensor, a widely used software library for carrying out these calculations. Building on the PI's work, a large international group of scientists has extended DMRG to tensor networks, a new area with applications ranging from chemistry to the physics of black holes and to the quantum theory of gravity. A focus of the PI's current work is understanding high-temperature superconductivity and improving DMRG methods for quantum treatments of molecules and solids. At sufficiently low temperatures, some materials exhibit superconductivity, a cooperative quantum state of electrons with interesting and technologically useful properties, the ability to conduct electricity without loss among them. Most known superconductors exhibit superconductivity at temperatures near the absolute zero of temperature. High temperature superconductors exhibit superconductivity above the temperature at which Nitrogen becomes a liquid. High-temperature superconductivity is important for both fundamental reasons as well as for applications. Conceptually, understanding how high-temperature superconductivity works is considered one of the most important problems in condensed matter physics. High-temperature superconductors are already used in a number of important applications, such as wireless communications and power transmission. Unraveling how high-temperature superconductivity emerges in certain materials might enable the creation of long-sought materials that exhibit superconductivity at room-temperature and under ordinary conditions. Improved quantum treatments of molecules is one of the leading potential applications of quantum computers, potentially improving drug design and materials for energy applications. The current work focuses on the same developments but using current supercomputers rather than quantum computers. This research provides excellent opportunities for training the next generation of theoretical scientists. The further development of the ITensor software library is making DMRG and tensor-network methods available and useful for the scientific community to enable discoveries across many areas of science. TECHNICAL SUMMARY This project supports research and education aimed at understanding strongly interacting quantum systems in condensed matter, cold atoms, and chemical systems. The work consists primarily of simulating model systems and of developing new algorithms for enabling these simulations. The primary application of the work is to doped fermion systems (such as the high-temperature superconductors) and frustrated spin systems, which suffer from the sign problem that makes quantum Monte Carlo methods ineffective. The PI is the inventor of the density matrix renormalization group (DMRG), one of the leading algorithms for simulating 1D systems. Within the last two decades, DMRG has become part of a larger field, tensor networks, and has become closely associated with quantum information science. The PI's work in algorithms now incorporates many of the ideas of tensor networks. This group is also the creator of ITensor, a widely used software library for carrying out DMRG and tensor network calculations, and development of ITensor will continue in this project. These simulation techniques have improved rapidly, and are now enabling a much better and deeper understanding of the high-temperature superconductors, in particular the competition between stripes and other inhomogeneities with superconductivity, and the nature of the pseudogap phase. Of particular interest is studying the effect of long-range Coulomb interactions between electrons and their effect on the competition between stripes and superconductivity. Recent improvments include better dynamics and better finite temperature treatments, for example, using the minimally entangled typical thermal state algorithm. To improve DMRG methods on molecules and realistic treatments of solids, this project is continuing work on developing diagonal Hamiltonian representations stemming from highly local basis sets. These diagonal representations dramatically improve the efficiency of DMRG. This research provides excellent opportunities for training the next generation of theoretical scientists. The further development of the ITensor software library is making DMRG and tensor-network methods available and useful for the scientific community to enable discoveries across many areas of science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.