DMRG Studies of Frustrated and Doped Systems

University Of California-Irvine, Irvine CA

Investigators

Abstract

NONTECHNICAL SUMMARY The Division of Materials Research and the Chemistry Division jointly fund this award, which supports theoretical and computational research and education aimed at understanding condensed-matter and chemical systems that host strongly interacting electrons whose behavior is governed by quantum mechanics. Fundamental understanding of the quantum behaviors of these systems is crucial for developing novel materials and molecules with tailored properties and can also lead to the prediction of new states of matter. 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 is the inventor of 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 a new field of physics, tensor networks, with applications ranging from chemistry to the physics of black holes and to the quantum theory of gravity. The PI's current work is focused on quantum spin liquids and on high-temperature superconductivity. Spin liquids are a novel state of matter whose unusual properties could enable building a quantum computer, which can solve certain problems exponentially faster than any currently existing computer. 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 room-temperature superconductors. 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 a broad range of scientists that will not have to develop the software themselves. TECHNICAL SUMMARY The Division of Materials Research and the Chemistry Division jointly fund this award, which 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 frustrated spin systems and to doped fermion systems (such as the high-temperature superconductors), which suffer from the sign problem that makes quantum Monte Carlo methods ineffective. Of particular interest are spin liquid systems, a novel state of matter that can occur in frustrated spin systems. Spin liquids exhibit topological order, and their unusual properties could be used for eliminating decoherence, a requirement for creating a quantum computer. Experimental studies sometimes cannot distinguish between disordered spin systems and true quantum spin liquids; this project will clarify which systems are true quantum spin liquids. The project also involves studying 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. The PI is the inventor of the density matrix renormalization group (DMRG), one of the leading algorithms 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 science. The PI's work in algorithms now incorporates many of the ideas of tensor networks. The PI will further develop ITensor, a widely used software library for carrying out DMRG and tensor network calculations. 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 a broad range of scientists that will not have to develop the software themselves. 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.