119114164
A note on path integral formulism of Z2 slave-spin representation of Hubbard model
(4)where a ferromagnetic coupling J > 0 is assumed and Krepresents the the transverse external ﬁeld.At ﬁrst sight, one may directly use the coherent stateof spin operator in constructing the path integral rep-resentation, (One can ﬁnd a brief but useful introduc-tion to this issue in Ref. 9.) however, this will lead toan extra topological Berry phase term and is not easyto utilize practically. An alterative approach is to usethe eigenstates of spin operator τ
118708688
Extended dual description of Mott transition beyond two-dimensional space
Motivated by recent work of Mross and Senthil [Phys. Rev. B \textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees of freedom. For example, when the vortex lines condense in charge phase degrees of freedom, the resulting effective fermionic action is found to be equivalent to that obtained by well-studied slave-particle approaches for Hubbard and/or Anderson lattice models, which confirm the validity of the extended dual formalism in 3D. When the vortex lines condense in spin phase degrees of freedom, a doublon metal with a spin gap and an instability to the unconventional superconducting pairing can be obtained. In addition, when the vortex lines condense in both phase degrees, an exotic doubled U(1) gauge theory occurs which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D, the last one has not been reported in the previous works. The present work is expected to be useful in understanding the Mott transition happening beyond two space dimensions.
121072448
On the Nonautonomous Nonlinear Schrödinger Equations and Soliton Management
We present some novel results on the nonlinear Schrodinger equations with time‐ and space‐dependent dispersion, nonlinearity, dissipation/gain and external potentials which read i∂u(x,t)∂t+f(x,t)∂2u(x,t)∂x2+g(x,t)|u(x,t)|2u(x,t)+V(x,t)u(x,t)+iγ(x,t)u(x,t) = 0. Based on these results, we show some explicit ways to control the soliton dynamics in some physically interesting nonlinear systems like Bose‐Einstein condensates and optical soliton transmission.
54740420
Detection of Majorana bound states by thermodynamically stable $4\pi$-periodic D.C. Josephson current
We propose a scheme to detect the Majorana bound states (MBSs) by a thermodynamically stable D.C. Josephson current with $4\pi$-periodicity in the superconducting phase difference, which is distinct from the previous A.C. $4\pi$-periodicity found in topological superconducting Josephson junctions. The scheme, consisting of a quantum dot coupled to two s-wave superconducting leads and a floating topological superconductor supporting two MBSs at its ends, only exploits the interplay of a local Zeeman field and the exotic helical and self-Hermitian properties of MBSs, without requiring the conservation of fermion parity and not relying on the zero-energy property of MBSs. Our D.C. $4\pi$-periodicity is thus robust against the overlap between the two MBSs and various system parameters, including the local Coulomb interaction, the tunneling asymmetry, and the width of superconducting gap, which facilitates experimentally detection of the MBSs.
118605638
Subleading soft behavior of QCD amplitudes
We elaborate on the radiative behaviour of tree-level scattering amplitudes in the soft regime. We show that the sub-leading soft term in single-gluon emission of quark-gluon amplitudes in QCD is controlled by differential operators, whose universal form can be derived from both on-shell recursion relation and gauge invariance, as it was shown to hold for graviton- and gluon-scattering.