Person:

Vishwanath, Ashvin

Lattice gauge theories are ubiquitous in physics, describing a wide range of phenomena from quark confinement to quantum materials. At finite fermion density, gauge theories are notoriously hard to analyze due to the fermion sign problem. Here, we investigate the Ising gauge theory in 2+1 dimensions, a problem of great interest in condensed matter, and show that it is free of the sign problem at arbitrary fermion density. At generic filling, we find that gauge fluctuations mediate pairing leading to a transition between a deconfined BCS state to a confined BEC. At half-filling, a π-flux phase is generated spontaneously with emergent Dirac fermions. The deconfined Dirac phase, with a vanishing Fermi surface volume is a non-trivial example of violation of Luttinger’s theorem due to fractionalization. At strong coupling, we find a single continuous transition between the deconfined Dirac phase and the confined BEC, in contrast to the expected split transition.

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter1. A prime example is the breaking of spatial translation symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a “time crystal” was recently proposed2,3, but later shown to be forbidden in thermal equilibrium4–6. However, nonequilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency7–10. This new phase of matter has been dubbed a “discrete time crystal” (DTC)10 (This phase is also referred to as a π-spin glass7 or a Floquet time crystal8). Here, we present the first experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization (MBL) conditions, and observe a sub-harmonic temporal response that is robust to external perturbations. Such a time crystal opens the door for studying systems with long-range spatial-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions7.

Topological materials have attracted much attention in the past decade. While several theoret- ically proposed topological materials have been experimentally confirmed, extensive experimental exploration of topological properties as well as applications in realistic devices have been held back due to the lack of excellent topological materials in which interference from trivial Fermi surface states are minimized. Here we tackle this problem by applying our recently developed method of symmetry indicators to all non-magnetic compounds in the 230 space groups. An exhaustive database search reveals thousands of topological materials candidates. Of these, we highlight the excellent candidates, the 241 topological insulators and 142 topological crystalline insulators which have either noticeable full band gap or a considerable direct gap together with small trivial Fermi pockets. We also give a list of 692 topological semimetals with the band crossing points located near the Fermi level. All predictions obtained through standard generalized gradient approximation calculations were cross-checked with the modified Becke-Johnson potential calculations, appropriate for narrow gap materials. These newly found topological materials candidates open wide possibilities for realizing the promise of topological materials in next-generation electronic devices.