This award supports theoretical and computational research and education to identify and understand properties of novel quantum phases of matter.
Strongly frustrated two-dimensional magnetic materials provide candidate systems for many novel phases. They can exhibit magnetically ordered phases, Valence Bond Crystal phases, Resonating Valence Bond phases as well as gapless or algebraic spin-liquid phases. Several of these phases and quantum phase transitions between them may lead to new types of particles with fractional quantum numbers, which cannot be understood from our standard models of condensed matter physics. A definitive demonstration of such phases in real materials remains a very active area of study and is the primary focus of this work.
The PI aims to model frustrated magnetic behavior of several quasi-two dimensional materials, such as Helium-3 layers absorbed on graphite, organic molecular crystals and recently discovered kagome-lattice based Herbertsmithites. Over the past decade the PI has developed Linked Cluster techniques that allow one to calculate thermodynamic and spectral properties of quantum lattice models with high accuracy. These calculations should help develop a comprehensive understanding of these systems.
The proposed activity would involve training the new generation of scientists from high school to graduate levels. In addition to working closely with graduate students, the PI will mentor undergraduate students, especially minority undergraduate students through the Minority Undergraduate Research Participation in the Physical Sciences program at UC Davis. In addition, the PI will remain engaged in training gifted high school students through the California State Summer School for Mathematics and Science program of University of California.
The PI will develop a web-accessible repository of spectral properties of quantum-lattice models for the broader community. An interdisciplinary workshop will be organized on Universal Themes in the Science of Molecular Frustration that will bring together scientists from diverse fields including magnetism, glasses and protein-folding.
NONTECHNICAL SUMMARY
This award supports research and education to identify and understand properties of novel quantum phases of matter.
The PI will use theoretical methods and computer simulation to see if the tiniest units of magnetism in a material can form a state of matter that is analogous to a peculiar kind of liquid, a quantum liquid. Most liquids, when cooled to sufficiently low temperatures, will freeze into a solid. A notable exception is the element Helium which under ordinary conditions remains a liquid down to the absolute zero of temperature. As a magnetic material is cooled, the north and south poles of the smallest units of magnetism at the atomic scale, often individual electrons, spontaneously align to form a magnet. But are there materials for which these tiny magnets exhibit some correlation in their fluctuations but never form a magnetic state even down to the absolute zero of temperature. What would be the properties of this spin-liquid as it is called? The PI seeks to answer this question.
It is believed that understanding the conditions under which spin-liquids might form and their properties may lead to the discovery of new sates of matter, for example a superconducting state, that is able to conduct electricity without loss, or exotic quantum mechanical states of matter that may be easily manipulated to form the basis of operation for a high performance supercomputer.
This research will provide educational experiences to help train students from graduate to high school levels. The PI has been involved over the last several years in developing and teaching a course for high school students in California dealing with random walks and their relation to essential properties of molecules in physics, chemistry and biology. The PI plans to incorporate advanced ideas of quantum physics in very simple terms in such courses. The PI also plans to organize interdisciplinary meetings to promote new ideas from the field of quantum magnetism to other fields where microscopic frustration or competing ordering tendencies play an important role such as the physics of glasses and protein-folding. The PI will develop a web-accessible repository of computational results of the research for the broader community.
Intellectual Merit: Condensed matter physics is a discipline at the interscetion of basic and applied sciences. On the one hand, it helps explore limits of and strengthen the foundations of quantum theory. On the other, it provides the scientific underpinning for much of the multi-faceted platforms of modern technology. Theoretical modeling constitutes the intellectual leadership of the field, developing bold new ideas and guiding it in novel directions. This project focused on one of the core themes of condensed matter physics: Understanding exotic quantum phases of matter, where standard paradigms of solid state physics break down. Frustrated and strongly correlated systems can have many competing phases. At the relevant time and length scales, the familiar microscopic degrees of freedom, such as electrons and their spins, can be replaced by emergent collective degrees of freedom. We made significant progress in understanding rare-earth Pyrochlore magnetic materials such as Yb2Ti2O7 and Er2Ti2O7. Anisotropic spin systems on the pyrchlore lattice, consisting of corner-sharing tetrahedron, are known as `spin-ice' materials, when their classical ground state manifold consists of two spins pointing in and two out of each tetrahedron. These can be mapped on to the `ice-rules' of ordinary water ice, with the associated residual ground-state entropy first calculated in the celebrated work of Linus Pauling. Our calculations provided a quantitatively accurate model for the heat capacity and entropy of the material Yb2Ti2O7, which can be viewed as a `quantum spin-ice', where Pauling's residual entropy is approximately realised over a brief temperature window, before quantum fluctuations lead to the selection of a magnetically ordered ground state. Our modeling of the XY pyrochlore system Er2Ti2O7 found that these materials show the remarkable phenomena of `order by disorder', where disorder in the form of quantum and thermal fluctuations, leads to the selection of an ordered state. This was a very subtle calculation requiring non-linear susceptibilities as the model remains degenerate in all orders of high temperature expansions when only linear susceptibilities are calculated. In a different direction, we made important progress in systematic computation of quantum entanglement in many-body systems. This remarkable subject connects the study of quantum phases and phase transitions in condensed matter physics with the disciplines of quantum information and quantum computing on one side and even quantum gravity and black-holes on the other. Entanglement entropy in the ground states of most many-body systems show an `area-law' analogous to the Bekenstein-Hawking entropy of a black-hole, where the entropy depends on the surface-area rather than the volume of the system. Our work showed that the study of entanglement entropy can be informative about a range of important condensed matter issues including quantum critical phenomena, thermalization, topological phases and fermi-surface geometry. Broader Impact: This project involved international collaboration with researchers in Canada, Argentina and Australia. It also involved training of students at all levels. The PI was involved in developing and teaching a course to high school students through the COSMOS program of the University of California. In addition several undergraduate and graduate students and postdocs were trained in methods of computational physics.
