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Register a new userAbelian flux induced magnetic frustrations of spinor boson superfluids on a square lattice
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Inspired by recent experimental advances to generate Abelian flux for neutral cold atoms and photons moving in a lattice, we investigate the possible effects of the $ pi $ flux through a unit cell in the pseudo-spin 1/2 spinor boson Hubbard model in a square lattice. We find that the $ pi $ flux induces a dramatic interplay between the charge and the spin which leads to a frustrated superfluid. We develop a new and systematic order from quantum disorder analysis to determine not only the true quantum ground state, but also the excitation spectrum. The superfluid ground state has a 4 sublattice $ 90^{circ} $ coplanar spin structure which supports 4 linear gapless modes with 3 different velocities. We speculate the transition from the weak coupling frustrated SF to the strong coupling Ferromagnetic Mott state to be in a new universality class of non-Ginsburg Landau type. These novel phenomena may be observed in these recent cold atom and photonic experiments.
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We study possible superfluid states of the Rashba spin-orbit coupled (SOC) spinor bosons with the spin anisotropic interaction $ lambda $ hopping in a square lattice. The frustrations from the non-abelian flux due to the SOC leads to novel spin-bond correlated superfluids. By using a recently developed systematic order from quantum disorder analysis, we not only determine the true quantum ground state, but also evaluate the mass gap in the spin sector at $ lambda < 1 $, especially compute the the excitation spectrum of the Goldstone mode in the spin sector at $ lambda=1 $ which would be quadratic without the analysis. The analysis also leads to different critical exponents on the two sides of the 2nd order transition driven by a roton touchdown at $ lambda=1 $. The intimate analogy at $ lambda=1 $ with the charge neutral Goldstone mode in the pseudo-spin sector in the Bilayer quantum Hall systems at the total filling factor $ u_T=1 $ are stressed. The experimental implications and detections of these novel phenomena in cold atoms loaded on a optical lattice are presented.
Two-component fermionic superfluids on a lattice with an external non-Abelian gauge field give access to a variety of topological phases in presence of a sufficiently large spin imbalance. We address here the important issue of superfluidity breakdown induced by spin imbalance by a self-consistent calculation of the pairing gap, showing which of the predicted phases will be experimentally accessible. We present the full topological phase diagram, and we analyze the connection between Chern numbers and the existence of topologically protected and non-protected edge modes. The Chern numbers are calculated via a very efficient and simple method.
We study possible many body phenomena in the Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice. There are various novel spin-bond correlated superfluids (SF) and quantum or topological phase transitions among these SF phases. One transition is a first order one driven by roton droppings ( but with non-zero gaps $ Delta_R $ ) tuned by the Zeeman field $ h $. Another is a second order bosonic Lifshitz transition with the dynamic exponents $ z_x=z_y=2 $ and an accompanying $ [C_4 times C_4]_D $ symmetry breaking. It is driven by the softening of the superfluid Goldstone mode tuned by the ratio of spin-orbit coupled (SOC) strength over the hopping strength. The two phase boundaries meet at a topological tri-critical (TT) point which separates the $ h=0 $ line into two SF phases with $ N=2 $ and $ N=4 $ condensation momenta respectively. At the $ h=0 $ line where the system has an anti-unitary $ Z_2 $ Reflection symmetry, there are infinite number of classically degenerate family of states on both sides. We perform a systematic order from quantum disorder analysis to find the quantum ground states, also calculate the roton gaps $ Delta_R $ generated by the order from disorder mechanism on both sides of the TT point. The $ N=2 $ and $ N=4 $ SF phases have the same spin-orbital XY-AFM spin structure, respect the anti-unitary symmetry and break the $ [C_4 times C_4]_D $ symmetry, so they be distinguished only by the different topology of the BEC condensation momenta instead of by any differences in the symmetry breaking patterns. All these novel quantum or topological phenomena can be probed in the recent experimentally realized weakly interacting Quantum Anomalous Hall (QAH) model of $ ^87 Rb $ by Wu, {sl et.al}, Science 354, 83-88 (2016).
We report that a possible Z2 quantum spin liquid (QSL) can be observed in a new class of frustrated system: spinor bosons subject to a pi flux in a square lattice. We construct a new class of Ginsburg-Landau (GL) type of effective action to classify possible quantum or topological phases at any coupling strengths. It can be used to reproduce the frustrated SF with the 4 sublattice $ 90^{circ} $ coplanar spin structure plus its excitations in the weak coupling limit and the FM Mott plus its excitations in the strong coupling limit achieved in our previous work. It also establishes deep and intrinsic connections between the GL effective action and the order from quantum disorder (OFQD) phenomena in the weak coupling limit. Most importantly, it predicts two possible new phases at intermediate couplings: a FM SF phase or a frustrated magnetic Mott phase. We argue that the latter one is more likely and melts into a $ Z_2 $ quantum spin liquid (QSL) phase. If the heating issue can be under a reasonable control at intermediate couplings $ U/t sim 1 $, the topological order of the $ Z_2 $ QSL maybe uniquely probed by the current cold atom or photonic experimental techniques.
We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general space-independent non-Abelian gauge potential. We first review and analyze the case of purely Abelian potentials, showing also that the so-called Hasegawa gauge yields a decomposition of the Hamiltonian into sub-matrices having minimal dimension. Explicit expressions for such matrices are derived, also for general anisotropic fluxes. Later on, we show that the introduction of a translational invariant non-Abelian coupling for multi-component spinors does not affect the dimension of the minimal Hamiltonian blocks, nor the dimension of the magnetic Brillouin zone. General formulas are presented for the U(2) case and explicit examples are investigated involving $pi$ and $2pi/3$ magnetic fluxes. Finally, we numerically study the effect of random flux perturbations.
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