DMRG Studies of Frustrated and Doped Systems

University Of California-Irvine, Irvine CA

Investigators

Abstract

NON-TECHNICAL SUMMARY This award supports theoretical and computational research, and education aimed at understanding condensed matter and chemical systems involving many strongly interacting electrons which can be described by quantum mechanics. Understanding these systems is key to developing novel materials and molecules that can lead to the prediction of new states of matter, and to designing new materials with useful properties. One of the most important techniques for making theoretical progress is the development of novel computer algorithms and software for solving the equations of quantum mechanics that describe systems of many interacting particles. The PI has invented an important algorithm, the density matrix renormalization group (DMRG), and is the developer of a software library for carrying out the calculations, ITensor. Building on this work, an international group of scientists has extended DMRG to a new field of physics, Tensor Networks, with applications ranging from chemistry to black holes and quantum gravity. This award supports research focused on novel states of matter, quantum spin liquids and high temperature superconductivity. Quantum spin liquids result when quantum mechanical fluctuations due to Heisenberg's uncertainty principle melt away any trace of magnetism in a material down to the absolute zero of temperature, leaving a liquid with unusual properties that could provide the foundation for building a quantum computer. A quantum computer is predicted to be able to solve certain problems exponentially faster than any currently existing computer. High temperature superconductors can transport electric current without loss at higher temperatures than other known superconductors, but still almost at temperatures where nitrogen is a liquid. Current applications include wireless communications and power transmission. Understanding how electrons self-organize into the high temperature superconducting state is an important problem that may lead to superconductors at room temperature. This research provides opportunities for training the next generation of theoretical and computational scientists. The ITensor software library provides a scientists from different research areas access to DMRG techniques and tensor networks and forms part of the cyberinfrastructure of the materials research and chemistry communities. TECHNICAL SUMMARY This award supports theoretical and computational research, and education aimed at understanding strongly interacting quantum condensed matter, cold atom, and chemical systems. The research involves simulating model systems and developing new algorithms for these simulations, and is focused primarily on frustrated spin systems and doped fermion systems like high temperature superconductors. To avoid the sign problem of quantum Monte Carlo methods, the PI plans to utilize density matrix renormalization group methods. Of particular interest are spin liquid systems, a novel state of matter that can occur in spin systems that exhibit frustration. Spin liquids have topological order, and their unusual properties could be used for eliminating the barrier of decoherence in building a quantum computer. This project also involves studying the high temperature superconductors, with a focus on the competition among inhomogeneous phases including stripes with superconductivity, and on the nature of the pseudogap phase. The PI invented the density matrix renormalization group (DMRG), a leading algorithm for simulating 1D systems. Within the last decade, DMRG has become part of a larger field, tensor networks, and has become closely associated with quantum information. The PI's work in algorithms now incorporates many of the ideas of tensor networks. Most of the application work uses DMRG rather than some of the newer tensor network methods, as DMRG continues to be very effective. The PI is the developer of a leading software library for carrying out DMRG and tensor network calculations, ITensor. This research provides opportunities for training the next generation of theoretical and computational scientists. The ITensor software library provides a scientists from different research areas access to DMRG techniques and tensor networks and forms part of the cyberinfrastructure of the materials research and chemistry communities.