Condensed Matter

We present a paradigm for effective descriptions of quantum magnets. Typically, a magnet has many classical ground states — configurations of spins (as classical vectors) that have the least energy. The set of all such ground states forms an abstract space. Remarkably, the low energy physics of the quantum magnet maps to that of a single particle moving in this space.

This presents an elegant route to simulate simple quantum mechanical models using molecular magnets. For instance, a dimer coupled by an XY bond maps to a particle moving on a ring. An XY triangular magnet maps to a particle moving on two disjoint rings. We can even simulate Berry phases; when the spin has half-integer values, the particle sees a pi-flux  threaded through the rings.

A particularly interesting example is the XY tetrahedral magnet. Here, the ground state space is a 'non-manifold' due to singularities. These singularities behave like strong impurities to create bound states. The entire low energy physics of the magnet is dominated by these bound states. We call this phenomenon 'order by singularity’. This leads to a preference for certain classical ground states purely due to topology, rather than due to thermal or quantum fluctuations. Unlike order-by-disorder, this effect persists even in the classical limit.

The Wilson formulation of lattice gauge theories provides a first-principles study of many properties of strongly interacting theories, such as quantum chromodynamics (QCD). Certain other properties, such as real-time dynamics, pose insurmountable challenges in this paradigm. Quantum Link Models are generalized lattice gauge theories, which not only offer novel approaches to study dynamics of gauge theories with quantum simulators, but also connect to
gauge theory descriptions of certain condensed matter systems (such as frustrated magnetism). In this talk, we explore some novel properties of gauge theories using quantum link models on classical computers, and explain how to realize them on quantum simulators.