This award supports theoretical and computational work using the density matrix renormalization group for two dimensional frustrated magnetic systems and strongly correlated doped electron systems. An exciting area in materials research is the study of strong correlation effects in low dimensional systems. These systems exhibit a wide range of behavior, such as high temperature superconductivity, antiferromagnetism, striped, and spin liquid phases. Numerical simulation techniques have become increasingly necessary to understand these systems, as the systems have strong coupling terms and competition between different types of order. The density matrix renormalization group is one of the most effective numerical techniques for studying strongly correlated systems. The PI and his group will apply density matrix renormalization group to a variety of these systems, including spin chains, ladders, and two-dimensional clusters, both for spin systems and with doping. The focus during this period will be increasingly to large enough clusters that results can be extrapolated to the limit of infinite size.
A substantial effort will be made on understanding quantum spin liquids, continuing work of the previous period in which the kagome Heisenberg model was demonstrated to have a spin liquid ground state. The kagome model will be studied further, particularly in a generalized form with next nearest neighbor interactions. In addition to mapping out the phase diagram in the larger parameter space, the nature of the elementary excitations and topological order will be studied. In addition, other frustrated spin systems, such as the Heisenberg model on the honeycomb lattice with frustrated next nearest neighbor interactions, and exchange anisotropies, will be studied.
The PI will extend and further develop a publicly available software library appropriate for many different types of density matrix renormalization group related algorithms. The library is called ITensor, for Intelligent Tensor. The initial work for this library was begun with previous NSF support and substantial progress has been made. The work under this award will focus on making the library easy to use for the non-expert, while simultaneously increasing its capabilities with a new parallel algorithm.
NONTECHNICAL SUMMARY
This award supports theoretical and computational research and education aimed at understanding exotic quantum states of matter. One might think that everything freezes well before absolute zero in temperature. However, liquid helium remains a liquid even at absolute zero at atmospheric pressure, but it is the only substance which does so. Liquid helium does not solidify because unceasing quantum mechanical fluctuations of the atoms overcome their very weak attraction. Freezing into a solid is one kind of order. What about magnetism? Do the all the microscopic magnets in a magnetic material have to align to become a magnet at absolute zero?
A hypothetical magnetic system which fails to become a magnet at absolute zero is called a "spin liquid". Spin liquids have been sought, experimentally and theoretically for some time. A recent excitement shows that an unusual mineral with the name HerbertSmithite seems to be a spin liquid. The PI has recently provided evidence for a spin liquid in the theoretical model most appropriate for HerbertSmithite. The PI aims to continue to explore this model and also look for other models for materials which might be spin liquids. In addition to studying spin liquids, the PI will use his numerical techniques to study high temperature superconductivity and one dimensional magnetic systems.
Spin liquids may hold the key toward understanding frustrated magnetic materials and the discovery of new electronic states of matter that may lead to new technologies. Spin liquids may also illuminate the mechanisms for superconductivity, a state of electronic matter that can carry electric current without loss, enabling superconductivity at higher temperatures with potential applications to power transmission.
