We study quantum fluctuation driven first-order phase transitions of a two-species bosonic system in a three-dimensional optical lattice. Using effective potential method we find that the superfluid-Mott insulator phase transition of one type of boso
ns can be changed from second-order to first-order by the quantum fluctuations of the other type of bosons. The study of the scaling behaviors near the quantum critical point shows that the first-order phase transition has a different universality from the second-order one. We also discuss the observation of this exotic phenomenon in the realistic cold-atom experiments.
A weakly interacting boson-fermion mixture model was investigated using Wisonian renormalization group analysis. This model includes one boson-boson interaction term and one boson-fermion interaction term. The scaling dimensions of the two interactio
n coupling constants were calculated as 2-D at tree level and the Gell-Mann-Low equations were derived at one-loop level. We find that in the Gell-Mann-Low equations the contributions from the fermion loops go to zero as the length scale approaches infinity. After ignoring the fermion loop contributions two fixed points were found in 3 dimensional case. One is the Gaussian fixed point and the other one is Wilson-Fisher fixed point. We find that the boson-fermion interaction decouples at the Wilson-Fisher fixed point. We also observe that under RG transformation the boson-fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson-fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.
Cuprates, ferropnictides and ferrochalcogenides are three classes of unconventional high-temperature superconductors, who share similar phase diagrams in which superconductivity develops after a magnetic order is suppressed, suggesting a strong inter
play between superconductivity and magnetism, although the exact picture of this interplay remains elusive. Here we show that there is a direct bridge connecting antiferromagnetic exchange interactions determined in the parent compounds of these materials to the superconducting gap functions observed in the corresponding superconducting materials. High superconducting transition temperature is achieved when the Fermi surface topology matches the form factor of the pairing symmetry favored by local magnetic exchange interactions. Our result offers a principle guide to search for new high temperature superconductors.
We develop a local spin model to explain the rich magnetic structures in the iron-based superconductors $Fe_{1+y}Te_{1-x}Se_x$. We show that our model exhibits both commensurate antiferromagnetic and incommensurate magnetic order along the crystal a-
axis. The transition from the commensurate to the incommensurate phase is induced when the concentration of excess $Fe$ atoms is larger than a critical value. Experimentally measurable spin-wave features are calculated, and the mean-field phase diagram of the model is obtained. Our model also suggests the existence of a large quantum critical region due to strong spin frustration upon increasing $Se$ concentration.
We investigate disordered graphene with strong long-range impurities. Contrary to the common belief that delocalization should persist in such a system against any disorder, as the system is ex-pected to be equivalent to a disordered two-dimensional
Dirac Fermionic system, we find that states near the Dirac points are localized for sufficiently strong disorder and the transition between the localized and delocalized states is of Kosterlitz-Thouless type. Our results show that the transition originates from bounding and unbounding of local current vortices.
By the first-principles electronic structure calculations, we find that the ground state of PbO-type tetragonal $alpha$-FeTe is in a bi-collinear antiferromagnetic state, in which the Fe local moments ($sim2.5mu_B$) are ordered ferromagnetically alon
g a diagonal direction and antiferromagnetically along the other diagonal direction on the Fe square lattice. This bi-collinear order results from the interplay among the nearest, next nearest, and next next nearest neighbor superexchange interactions $J_1$, $J_2$, and $J_3$, mediated by Te $5p$-band. In contrast, the ground state of $alpha$-FeSe is in the collinear antiferromagnetic order, similar as in LaFeAsO and BaFe$_2$As$_2$.
The experimental consequences of different order parameters in iron-based superconductors are theoretically analyzed. We consider both nodeless and nodal order parameters, with an emphasis on the $cos(k_x)cdot cos(k_y)$ nodeless order parameter recen
tly derived by two of us. We analyze the effect of this order parameter on the spectral function, density of states, tunneling differential conductance, penetration depth, and the NMR spin relaxation time. This extended s-wave symmetry has line-zeroes in between the electron and hole pockets, but they do not intersect the two Fermi surfaces for moderate doping, and the superconductor is fully gapped. However, this suggests several quantitative tests: the exponential decay of the penetration depth weakens and the density of states reveals a smaller gap upon electron or hole doping. Moreover, the $cos(k_x) cdot cos(k_y)$ superconducting gap is largest on the smallest (hole) Fermi surface. For the $1/T_1$ NMR spin relaxation rate, the inter-band contribution is consistent with the current experimental results, including a (non-universal) $T^{3}$ behavior and the absence of a coherence peak. However, the intra-band contribution is considerably larger than the inter-band contributions and still exhibits a small enhancement in the NMR spin relaxation rate right below $T_c$ in the clean limit.
The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that th
ere is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates. The presence of both DWCB and PDW orders with $4a times 4a$ periodicity can explain the checkerboard modulation observed in FT-STS from STM and the puzzling dichotomy between the nodal and antinodal regions as well as the characteristic features such as non-dispersive Fermi arc in the pseudogap state.
In this paper, we consider the coordination control of a group of autonomous mobile agents with multiple leaders. Different interconnection topologies are investigated. At first, a necessary and sufficient condition is proved in the case of fixed int
erconnection topology. Then a sufficient condition is proposed when the interconnection topology is switched. With a simple first-order dynamics model by using the neighborhood rule, both results show that the group behavior of the agents will converge to the polytope formed by the leaders.
