Quantum-disordered slave-boson theory of underdoped cuprates

We study the stability of the spin gap phase in the U(1) slave-boson theory of the t-J model in connection to the underdoped cuprates. We approach the spin gap phase from the superconducting state and consider the quantum phase transition of the slave-bosons at zero temperature by introducing vortices in the boson superfluid. At finite temperatures, the properties of the bosons are different from those of the strange metal phase and lead to modified gauge field fluctuations. As a result, the spin gap phase can be stabilized in the quantum critical and quantum disordered regime of the boson system. We also show that the regime of quantum disordered bosons with the paired fermions can be regarded as the strong coupling version of the recently proposed nodal liquid theory.Comment: 5 pages, Replaced by the published versio

Lagrangian approach to local symmetries and self-dual model in gauge invariant formulation

Taking the St\"uckelberg Lagrangian associated with the abelian self-dual model of P.K. Townsend et al as a starting point, we embed this mixed first- and second-class system into a pure first-class system by following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin. The resulting Lagrangian possesses an extended gauge invariance and provides a non-trivial example for a general Lagrangian approach to unravelling the full set of local symmetries of a Lagrangian.Comment: LaTeX, 15 page

Cluster aggregation model for discontinuous percolation transition

The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel $K_{ij}\sim ij$, where $ij$ is the product of the sizes of two merging clusters. Here, we study more general cases in which $K_{ij}$ is sub-linear as $K_{ij}\sim (ij)^{\omega}$ with $0 \le \omega < 1/2$; we find that the percolation transition (PT) is discontinuous. Moreover, PT is also discontinuous when the ER dynamics evolves from proper initial conditions. The rate equation approach for such discontinuous PTs enables us to uncover the mechanism underlying the explosive PT under the Achlioptas process.Comment: 5 pages, 5 figure

Symmetries of coupled harmonic oscillators

It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2)