Synthetic tensor gauge fields

Abstract

Synthetic gauge fields have provided physicists with a unique tool to explore a wide range of fundamentally important phenomena in physics. However, only synthetic vector gauge fields are currently available in experiments. The study of tensor gauge fields, which play a vital role in fracton phase of matter, remains purely theoretical. Here, we propose schemes to realize synthetic tensor gauge fields using techniques readily available in laboratories. A lattice tilted by a strong linear potential and a weak quadratic potential naturally yields a rank-2 electric field for a lineon formed by a particle-hole pair. Such a rank-2 electric field leads to a new type of Bloch oscillations, where neither a single particle nor a single hole responds but a lineon vibrates. A synthetic vector gauge field carrying a position-dependent phase could also be implemented to produce the same synthetic tensor gauge field for a lineon. In higher dimensions, the interplay between interactions and vector gauge potentials imprints a phase to the ring-exchange interaction and thus generates synthetic tensor gauge fields for planons. Such tensor gauge fields make it possible to realize a dipolar Harper-Hofstadter model in laboratories.Comment: 6+3 pages, 4+3 figure