This award supports research and related educational activities in computational quantum many-body physics, with a focus on collective quantum phenomena in spin systems. Quantum spin systems are important models for describing the magnetic properties of Mott insulators. In addition to their important role in direct modeling of experimentally studied materials, quantum spin models can also be used as simplified prototypical models capturing essential physics of various many-body phenomena that are currently subjects of ongoing theoretical and computational investigations. The main objective of this award is to gain new generic insights into the physics of collective quantum many-body states through unbiased computer simulations, primarily using quantum Monte Carlo methods. Of particular interest are quantum phase transitions, phase transitions that take place at zero temperature with associated scaling behavior also at finite temperature, as a function of some model parameter that regulates the strength of the quantum fluctuations in the system. The PI has devised a class of spin-one-half lattice systems in which the standard antiferromagnetic Heisenberg exchange interaction is supplemented by multi-spin interactions engineered to destroy the antiferromagnetic order. This transition in two dimensions may be associated with fractionalization of elementary excitations. Normally, the excitations of the Neel state are spin waves carrying spin one, and in the valence-bond-solid state there are gapped spin-one "triplon" excitations. However, close to the phase transition, previous analytical and numerical studies indicate that these excitations may fractionalize into spinons carrying spin-one-half. This deconfinement of spinons has far reaching consequences both for the theoretical description of the phase transition and for experimental signatures of it. Spinons may play an important role in many strongly-correlated electron systems, for example in the "strange metal" state of underdoped high-Tc superconductors. The PI is carrying out quantum Monte Carlo studies in order to characterize the nature of the spinons and their manifestations in physical observables. Both pristine and disordered systems are considered. Work on novel and improved simulation methods will be carried out as an integral part of the award. The methods to be developed through this award are contributing to the emerging "toolbox" of software enabling simulations of magnetic properties of Mott insulators. These methods have broader applicability, beyond the main scientific questions addressed, and are of interest in other fields, for example studies of ultracold atoms in optical lattices and in quantum information theory. Graduate students supported by this award will receive training in these advanced methods and their applications. The PI is also actively teaching graduate students and postdoctoral researchers at summer schools, and is also developing on-line instructional material for learning quantum Monte Carlo simulations and other numerical many-body techniques.
NON-TECHNICAL SUMMARY
This award supports research and related educational activities in computer simulation studies of quantum spin models. These systems of interacting microscopic magnetic moments represent electrons localized at individual atoms or molecules in certain electrically insulating materials. Various magnetic properties can be achieved, depending on the crystal structure and the chemical composition of the material. The objective of the award is to carry out computer simulation studies to aid experimental investigations carried out by other researchers, as well as to study fundamental aspects of the model systems to gain further insights into what kind of properties are possible to achieve in principle. These simulations relate to existing analytical theories and influence developing theoretical concepts. In analogy with the three common phases of matter encountered in daily life - liquid, solid, and gas - a system of a large number of electronic spins can also from different phases. The possibilities are very rich, with many different phases analogous to the three common ones. Spins can "solidify" into states in which the individual electronic magnetic moments or pairs of moments form various regular patterns. These patterns can "melt" at phase transitions where new liquid-like spin states appear. Understanding these quantum phases and quantum phase transitions is very challenging and important, both from a fundamental scientific perspective and for ultimate technological applications involving the special properties of electronic spins. The PI has previously developed computational methods and devised a class of spin models in which certain magnetic quantum phase transitions can be studied in unprecedented detail. The PI will study the nature of the elementary excitations of spin systems close to quantum phase transitions. An excitation can be thought of as a defect propagating as a wave through the system. These waves carry certain amounts of magnetic moment and normally there is a smallest unit of it. An exciting possibility with both experimental and theoretical consequences, is that this smallest unit can split up into two independently propagating waves. The PI is investigating these spinons in model systems. Information gained from computer simulations will give unique insights into the properties of these intriguing quantum entities and the role they play in various circumstances. New and improved computational methods will be developed to this research. These computational tools will contribute to the software infrastructure of computational quantum physics. Graduate students supported by the award are developing expertise in advanced simulation methods and many-body quantum physics. The PI is also actively involved in various other educational activities, including lecturing at international summer schools and developing pedagogical on-line material for learning the advanced computational techniques related to the award.
In this project, models of interacting electrons are studied under conditions pertaining, e.g., in certain materials formed by copper-oxide layers separated from each other by other atoms. These materials exhibit the still unexplained phenomenon of superconductivity (loss of electrical resistance) at (relatively) high temperature ("high-Tc"), and, depending on external and internal conditions, also show other ill-understood intriguing behaviors. Here the focus is on the behavior of the electronic spin (magnetic) degrees of freedom, and to understand generic physics associated with quantum magnets and how their magnetic properties can be tuned, even leading to loss of magnetism due to quantum-mechanical fluctuations (as happens in the high-Tc materials and many other materials of great experimental and technological interest). At the heart of the project is to understand they way an insulating antiferromagnetic state (in which electronic magnetic moments at copper atoms anti-align with their neighbors to form a checker-board pattern) can be destroyed when a model parameter is changed, and how additional electrons injected into this state behave. Understanding this model system may be key to solving the high-Tc puzzle, which has challenged physicists for more than two decades. Progress is also important for further fundamental general advances and applications of "strong-correlation" physics. Microscopic models have been developed and studied using computer simulation methods (which are developed and improved as an integral part of the project). Many results of computer simulations have been analyzed within the mathematical framework of quantum field theory – an analytic approach which can capture universal (generic) large-scale behaviors but which needs input from microscopic model calculations. The results have helped to establish the range of validity of the quantum field theories in describing physical phenoma occurring when an antiferromagnetic system undergoes a phase transition into a non-magnetic state where the electronic spins pair up and crystallize (in analogue with a solid). Quantitatively studying the "melting" of this kind of quantum solid has been one of the main focus areas of the project. One of the key outcomes has been to quantify the way in which the frozen spin pairs "deconfine", i.e., become separated from each other when the solid melts. These objects are called spinons and are examples of quantum objects which cannot easily be described within the traditional simplified "mean field" description iof quantum physics. In addition to its scientific significance, the project has trained several graduate students in state-of-the-art physical modeling and computer simulations. Three of them have graduated with their PhD degrees and work in the commercial sector as data scientists and in academia.
