Emergence: from nanomagnets to quantum spin liquids

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A collection of entities, at a certain scale and complexity, can acquire a new 'emergent' identity. A classic example is the raindrop, a collection of 1020 water molecules at room temperature and pressure. The raindrop is completely unlike a water molecule. It even obeys a different set of physical laws, e.g., its shape is determined by surface tension, a concept that has no meaning at the molecular level. We say that the raindrop has 'emerged' as an independent object. As emergence is highly nonlinear, it cannot usually be calculated from first principles. For example, starting with knowledge of water molecules, it is impossible to predict the shape of a raindrop. However, recent work from my group shows that such predictions can be made in a large class of quantum magnets. They follow an 'emergence principle': at low energies, the quantum magnet resembles a single particle that moves according to the laws of quantum mechanics. The particle moves on an abstract space that can often be determined from simple geometric arguments. For example, an XY dimer (a simple magnet with two spins) emerges as a particle that moves on a circle. The energy levels of the magnet are indistinguishable from that of the particle. I propose to build on this idea to understand the mechanisms that underlie emergence and to engineer desirable emergent properties. My first objective is to find novel emergent properties in nanomagnets. At low temperatures, these small magnets resemble simple single-particle problems. The particle's motion can be affected by quantum effects such as Berry phase and interference. I hope to establish nanomagnets as a platform to study quantum dynamics, exploring ideas such as ergodicity, thermalization and quantum chaos. My second objective is to study localization. Recent studies from my group have demonstrated 'quantum indecision' where a low-energy particle freezes at a crossroads, unable to pick a direction. This is seen in the emergent physics of certain quantum magnets with the magnet effectively freezing into an ordered configuration. This idea has only been demonstrated in small model systems. I propose to extend it to larger systems that are experimentally realizable, e.g., in metals where electrons can be thought to move along Fermi surfaces. The third goal of my research programme is to study quantum spin liquids, emergent states of magnets where spins do not order. They have been described using gauge theory, a concept that originates from electromagnetism. I seek to address two broad open questions - how do spins settle into an unordered state? What gives rise to gauge structure? I propose to study candidate spin liquids that are built from triangular and tetrahedral motifs. Using the emergence principle at the level of each motif, I propose to construct field theory descriptions. This can reveal the approach to emergence, tracking the physics of the magnet as its energy is lowered.