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تسجيل مستخدم جديدSimulating frustrated magnetism with spinor Bose gases
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Although there is a broad consensus on the fact that critical behavior in stacked triangular Heisenberg antiferromagnets --an example of frustrated magnets with competing interactions-- is described by a Landau-Ginzburg-Wilson Hamiltonian with O(3)$times$O(2) symmetry, the nature of the phase transition in three dimensions is still debated. We show that spin-one Bose gases provide us with a simulator of the O(3)$times$O(2) model. Using a renormalization-group approach, we argue that the transition is weakly first order and shows pseudoscaling behavior, and give estimates of the pseudocritical exponent $ u$ in $^{87}$Rb, $^{41}$K and $^7$Li atom gases which can be tested experimentally.
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We show that phase transitions in spin-one Bose gases and stacked triangular Heisenberg antiferromagnets -- an example of frustrated magnets with competing interactions -- are described by the same Landau-Ginzburg-Wilson Hamiltonian with O(3)$times$O
(2) symmetry. In agreement with previous nonperturbative-renormalization-group studies of the three-dimensional O(3)$times$O(2) model, we find that the transition from the normal phase to the superfluid ferromagnetic phase in a spin-one Bose gas is weakly first order and shows pseudoscaling behavior. The (nonuniversal) pseudoscaling exponent $ u$ is fully determined by the scattering lengths $a_0$ and $a_2$. We provide estimates of $ u$ in $^{87}$Rb, $^{41}$K and $^7$Li atom gases which can be tested experimentally. We argue that pseudoscaling comes from either a crossover phenomena due to proximity of the O(6) Wilson-Fisher fixed point ($^{87}$Rb and $^{41}$K) or the existence of two unphysical fixed points (with complex coordinates) which slow down the RG flow ($^7$Li). These unphysical fixed points are a remnant of the chiral and antichiral fixed points that exist in the O($N$)$times$O(2) model when $N$ is larger than $N_csimeq 5.3$ (the transition being then second order and controlled by the chiral fixed point). Finally, we discuss a O(2)$times$O(2) lattice model and show that our results, even though we find the transition to be first order, are compatible with Monte Carlo simulations yielding an apparent second-order transition.
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 t
o 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.
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