This award supports theoretical research and education in computer simulation studies of ground state phases and criticality in correlated quantum matter. Large-scale computer simulations of lattice quantum many-body systems are carried out in this work. These studies are inspired by the phenomenology of strongly-correlated electron systems?their complex phase diagrams and quantum phase transitions in particular?but are not complete descriptions of specific materials (because of the computational complexity). Instead, simplified quantum spin models are used to capture physical phenomena of interest and gain generically valid insights through unbiased simulations.
Complex ground states and phase transitions induced by competing interactions are studied, focusing in particular on the transition between an antiferromagnetic (AF) and a valence-bond-solid in two-dimensional quantum spin systems. The transition and the VBS phase are investigated using sophisticated numerical methods. Research into novel computational algorithms based on states defined by tensor-networks and related objects are also carried out. Such methods have the potential to enable studies of ground states of previously intractable frustrated quantum spin systems.
The effort undertaken has broader impacts with both scientific and educational consequences. The work on numerical simulation techniques produces new algorithms that have broad applications in condensed matter physics and atomic and molecular physics (ultra-cold condensates). The work on tensor-network and related states for describing correlated quantum states is also of interest in quantum information theory. An educational aspect of this proposal, beyond the important training of students in physics and advanced scientific computing, is a web-site in which a variety of computational methods developed by the PI are presented in a pedagogical manner, along with example programs for a variety of models.
NONTECHNICAL SUMMARY: This award supports theoretical research and education in the use of state-of-the-art computer simulation studies of novel electronic structures that have been discovered in exotic materials like the two-dimensional carbon sheets called graphene. Large-scale computer simulations of quantum physics that describes these systems are carried out in this work. These studies are inspired by experiments and discovery of these novel materials, but are not aimed at complete descriptions of specific materials because such detailed numerical studies are not yet possible because of the computational complexity. Instead, simplified quantum spin models are used in order to capture physical phenomena of interest, with the objective of gaining new generically valid insights through unbiased computer simulations.
The effort undertaken has broader impacts with both scientific and educational consequences. The work on computer simulations produces new algorithms that have broad applications in condensed matter physics and atomic and molecular physics (ultra-cold condensates). The work on novel computational algorithms is also important in quantum information theory. An educational aspect of this proposal, beyond the important training of students in physics and advanced scientific computing, is a web-site in which a variety of computational methods developed by the PI are presented in a pedagogical manner, along with easy-to-use example programs for a variety of models.
This project has addressed various magnetic and non-magnetic states emerging in systems of interacting microscopic magnetic moments (quantum spins). Computer simulation techniques have been developed and used to study the nature of these states and the ways in which one can tune systems between different kinds of states (phase transitions). The concept of different states (or phases) of matter is familiar in everyday life, e.g., water can existin the forms of gas (steam), liquid, and ice (solid). The different states can be understood from the molecular perspective. The degree of motion of the molecules is related to the temperature. At high temperature, in the gas state, the molecules move around rapidly and cannot stick to each other. At lower temperatures the motion is reduced and the tendency of the molecules to stick to each other can overcome the kinetic (motional) energy, leading to the much denser liquid state. At still lower temperatures, the motion is further impeded and the molecules lock to each other to form a solid crystalline pattern. The concept of states applies more generally to systems formed by a large number of particles, e.g., the electrons in a solid. An isolated atom has a certain number of electrons bound to it, but in a solid some fraction of these electrons can become mobile and move through the crystal lattice of atoms. One can think ofthese electrons as forming a kind of liquid. This electronic liquid conducts electricity - it is the metallic electronic state. In some cases the repulsive Coulomb interactions between the electrons can inpede their motion, leading to an insulating state (which can be viewed as a kind of solid of electrons inside the crystal). There are many other phases of electrons as well, e.g., superconductors, in which the electrons can flow without resistance (in contrast to the metallic state, in which collisions of electrons with each other lead to electric resistivity - manifested, e.g., in heating of current-carrying wires), and ferromagnets, in which the small magnetic moments associated with each electron line up to some degree to form a collective magnetic moment (as in magnetized iron). This project has focused on states formed by the electronic magnetic moments (called spins) in insulators. Although the electronic motion in this case is impeded, the interactions among the spins can lead to several states with different magnetic properties. The interactions are similar to what one can see in common bar magnets - placing two magnets next to each other they will tend to align in such a way that the north pole of one of them is close to the south pole of the other one. In the mathematical model systems studied here, thousand of spins are arranged in a crystal structure and each of them interacts with its neighbors, and possibly also with other spins further away. Depending on the exact nature of the crystal and the interactions, one can obtain various collective phases of the spin system. Since the magnetic moments are very small, they obey the laws of quantum mechanics. Large-scale computer simulations were used to elucidate the properties of the models. Better simulation method have been developed as an integral part of the project. The results obtained have led to a better understanding of the states formed in spin systems. In particular, a phase called the valence-bond-solid has been studied in detail. In this phase there is no net magnetic moment. Instead, the spins fluctuate in a certain columnar pattern which resembles a crystal. The nature of thefluctuations and the phase transition to a magnetic state have been characterized. The knowledge gained through these and other studies within the project is useful for understanding magnetic properties of various insulating compounds studied experimentally. In the long run, understanding these properties is a prerequisite for controlling them and exploiting them in new technologies. The graduate students trained within this project have gained valuable skills in physics and computational science, preparing them for future careers in a key area of science. The PI has also trained junior physicists more broadly, giving numerous lectures on topics related to the project at various summer and winter schools.
