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In recent years, arrays of atomic ions in a linear RF trap have proven to bea particularly successful platform for quantum simulation. However, a widerange of quantum models and phenomena have, so far, remained beyond the reachof such simulators. In this work we introduce a technique that cansubstantially extend this reach using an external field gradient along the ionchain and a global, uniform driving field. The technique can be used togenerate both static and time-varying synthetic gauge fields in a linear chainof trapped ions, and enables continuous simulation of a variety of couplinggeometries and topologies, including periodic boundary conditions and highdimensional Hamiltonians. We describe the technique, derive the correspondingeffective Hamiltonian, propose a number of variations, and discuss thepossibility of scaling to quantum-advantage sized simulators. Additionally, wesuggest several possible implementations and briefly examine two: theAharonov-Bohm ring and the frustrated triangular ladder.

Quantum simulations with complex geometries and synthetic gauge fields in a trapped ion chain