Abstract
Gauge field theories play a central role in modern physics and are at the heart of the Standard Model of elementary particles and interactions. Despite significant progress in applying classical computational techniques to simulate gauge theories, it has remained a challenging task to compute the real-time dynamics of systems described by gauge theories. An exciting possibility that has been explored in recent years is the use of highly-controlled quantum systems to simulate, in an analog fashion, properties of a target system whose dynamics are difficult to compute. Engineered atom-laser interactions in a linear crystal of trapped ions offer a wide range of possibilities for quantum simulations of complex physical systems. Here, we devise practical proposals for analog simulation of simple lattice gauge theories whose dynamics can be mapped onto spin-spin interactions in any dimension. These include 1+1D quantum electrodynamics, 2+1D Abelian Chern-Simons theory coupled to fermions, and 2+1D pure Z2 gauge theory. The scheme proposed, along with the optimization protocol applied, will have applications beyond the examples presented in this work, and will enable scalable analog quantum simulation of Heisenberg spin models in any number of dimensions and with arbitrary interaction strengths.
Highlights
The invariance of physical systems under local transformations of fields leads to fundamental constraints on how matter fields interact, and introduces new bosonic degrees of freedom, the gauge fields
To establish a duality relation with the 2D Ising model, the gauge invariance can be taken into account to (1) fix the gauge conveniently such that σz on all links along one of the spatial directions is set to unity and (2) use the operator identity G(n) = 1 in the physical Hilbert space of the theory to replace σx along the same space direction as in (1) with those along the other direction
We took on the question of how to best leverage the current technologies in ion-trap analog quantum simulators to engineer the Hamiltonian of gauge field theories
Summary
The invariance of physical systems under local transformations of fields leads to fundamental constraints on how matter fields interact, and introduces new bosonic degrees of freedom, the gauge fields. Given the current size of controlled quantum systems, only a small number of degrees of freedom can be studied, leading to unavoidable truncations in the Hilbert space of a gauge theory that lives in a continuous infinite-volume spacetime Such a limitation is present in other digital and analog quantum platforms as well. The former case is implemented with a single detuning for each set of the lasers used, while the latter takes advantage of a multifrequency, multiamplitude scheme, requiring a thorough optimization of interaction couplings. For clarity in the presentation, further details of the proposed scheme and a number of involved analytical forms will be provided in the appendices
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