Quantum antiferromagnets with geometrical frustration exhibit rich many-body physics but are hard to simulate by means of classical computers. Although quantum-simulation studies for analyzing such systems are thus desirable, they are still limited to high-temperature regions, where interesting quantum effects are smeared out. Here we propose a feasible protocol to perform analog quantum simulation of frustrated antiferromagnetism with strong quantum fluctuations by using ultracold Bose gases in optical lattices at negative absolute temperatures. Specifically, we show from numerical simulations that the time evolution of a negative-temperature state subjected to a slow sweep of the hopping energy simulates quantum phase transitions of a frustrated Bose–Hubbard model with sign-inverted hoppings. Moreover, we quantitatively predict the phase boundary between the frustrated superfluid and Mott-insulator phases for triangular lattices with hopping anisotropy, which serves as a benchmark for quantum simulation. Classical computer simulations of quantum antiferromagnet exhibiting geometrical frustration are very demanding, and quantum simulation allows accessing high-temperature regimes where quantum effects are less relevant. By using a protocol for ultracold bosonic gases in optical lattices, the authors show that it is possible to achieve a regime of negative absolute temperature at which to study the physics of a frustrated Bose-Hubbard model.
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