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Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields


Magnetism plays a key role in modern science and technology, but still many open questions arise from the interplay of magnetic many-body interactions. Deeper insight into complex magnetic behaviour and the nature of magnetic phase transitions can be obtained from, for example, model systems of coupled XY and Ising spins. Here, we report on the experimental realization of such a coupled system with ultracold atoms in triangular optical lattices. This is accomplished by imposing an artificial gauge field on the neutral atoms, which acts on them as a magnetic field does on charged particles. As a result, the atoms show persistent circular currents, the direction of which provides an Ising variable. On this, the tunable staggered gauge field, generated by a periodic driving of the lattice, acts as a longitudinal field. Further, the superfluid ground state presents strong analogies with the paradigm example of the fully frustrated XY model on a triangular lattice.

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Figure 1: Illustration of the triangular optical lattice, the artificial gauge fluxes, the phase distribution and the mass currents.
Figure 2: Effect of staggered gauge fluxes in momentum space.
Figure 3: Measurement of the statistical distribution of the Ising magnetization.
Figure 4: Magnetization curves obtained via a classical Monte Carlo simulation.
Figure 5: Experimental and theoretical evaluations, related to the U(1) order parameter.


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We acknowledge support from the Deutsche Forschungsgemeinschaft (GRK1355, SFB925) and the Landesexzellenzinitiative Hamburg (supported by the Joachim Herz Stiftung), ERC AdG QUAGATUA, AAII-Hubbard, Spanish MICINN (FIS2008-00784), Catalunya-Caixa, EU Projects AQUTE and NAMEQUAM, the Spanish foundation, the Austrian Science Fund (SFB F40 FOQUS), the DARPA OLE program and the John von Neumann Institute for Computing (NIC) for providing us with computing time on the supercomputers of the Juelich Supercomputing Centre (JSC).

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J. Struck, M.W., C.Ö., P.W., J. Simonet and K.S. proposed the study and performed the experimental work. R.H., P.H., A.E, M.L. and L.M. performed the theoretical work.

All authors discussed the experimental as well as the theoretical results and contributed to writing the manuscript.

Corresponding author

Correspondence to K. Sengstock.

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The authors declare no competing financial interests.

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Struck, J., Weinberg, M., Ölschläger, C. et al. Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields. Nature Phys 9, 738–743 (2013).

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