  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.

Quantum Gases;Strongly Correlated Electrons