Abstract
The order from quantum disorders (OFQD) phenomenon is well-known and ubiquitous in particle physics and frustrated magnetic systems. Typically, OFQD transfers a spurious Goldstone mode into a pseudo-Goldstone mode with a tiny gap. Here, we report an opposite phenomenon: OFQD transfers a spurious quadratic mode into a true linear Goldstone mode with a very small velocity (named slow-Goldstone mode). This new phenomenon is demonstrated in an interacting bosonic system subjected to an Abelian flux. We develop a new and systematic OFQD analysis to determine the true quantum ground state and the whole excitation spectrum. In the weak-coupling limit, the superfluid ground state has a 4-sublattice 90° coplanar spin structure, which supports 4 linear Goldstone modes with 3 different velocities. One of which is generated by the OFQD is much softer than the other 3 Goldstone modes, so it can be easily detected in the cold atom or photonic experiments. In the strong-coupling limit, the ferromagnetic Mott ground state with a true quadratic Goldstone mode. We speculate that there could be some topological phases intervening between the two symmetry broken states. These novel phenomena may be observed in the current cold-atom or photonic experiments subjected to an Abelian flux at the weak coupling limit where the heatings may be well under control. Possible connections to Coleman-Weinberg potential in particle physics, 1/N expansion of Sachdev-Ye-Kitaev models and zero temperature quantum black hole entropy are outlined.
Highlights
On the other hand, the order from quantum disorder phenomena (OFQD) is quite common in particle physics [17,18,19] and frustrated magnetic systems [20,21,22,23,24,25,26]
We discover a completely opposite new phenomenon: the order from quantum disorders (OFQD) generates a true Goldstone mode with a very small velocity which can be observed in the current spinor cold atoms [27,28,29,30,31,32,33,34,35,36] or photonic experiments [37,38,39,40] subjected to an Abelian α flux in the weak coupling regime
Because the Goldstone mode generated by OFQD is much softer than the other three ones in the weak coupling, so it can be identified in the spinor cold atom or photonic experiments by various currently available detection methods
Summary
We consider a pseudo-spin-1/2 Boson-Hubbard model in a π-flux on the square lattice described by:. The 90◦ coplanar state in figure 2(a) breaks both the U(1)c and completely the spin SU(2) symmetry, so it should lead to 1+3 linear gapless modes instead of 3 linear and 1 quadratic mode. In the geometrically frustrated quantum spin systems, an “order from quantum disorder” analysis [21,22,23] was developed to calculate the gap at k = 0 When applying this analysis to eq (2.12), we find that due to the absence of the conjugate A term (as dictated by a U(1) subgroup of the spin SU(2) symmetry), there is still no gap at q = 0 generated to the quadratic ω3 mode. After including the order from quantum disorder effect, δφ acquires a small finite OfD generated potential, it modifies the quadratic dispersion to a true linear one ω ∼ q. Because the slow-Goldstone mode is much softer than the other three Goldstone modes, it can be identified in the spinor cold atom or photonic experiments
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