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.
118391466
Topological quantum phase transition in Kane-Mele-Kondo lattice model
We systematically explore the ground-state phase diagram of the Kane-Mele-Kondo lattice model on the honeycomb lattice; particularly, we focus on its magnetic properties, which are ubiquitous and important in many realistic heavy-fermion materials but have not been clearly studied in the previous publication [X. Y. Feng, J. Dai, C. H. Chung, and Q. Si, Phys. Rev. Lett. 111, 016402 (2013)]. Besides the Kondo insulator found in that paper, two kinds of antiferromagnetic spin-density-wave phases are discovered. One is the normal antiferromagnetic spin-density-wave state and the other is a nontrivial topological antiferromagnetic spin-density-wave state, which shows the unexpected Z(2) topological order with a quantized spin Hall conductance and a helical edge state similar to the hotly studied topological insulators. The quantum spin Hall insulator in the work of Feng et al. is found to be absent since it is always unstable to antiferromagnetic spin-density-wave states at least at the mean-field level in our model. Interestingly, the transition between the two spin-density-wave phases is an exotic topological quantum phase transition, whose critical behavior is described by an emergent three-dimensional quantum electrodynamics, in which conduction electrons contribute to the low-energy Dirac fermions while the spin-wave fluctuation of local spins gives rise to an effective dynamic U(1) gauge field. Such nontrivial transition shows radical critical thermodynamic, transport, and single-particle behaviors, which provide a fingerprint for this transition. Additionally, the transition of antiferromagnetic spin-density-wave states to the Kondo insulator is found to be first order. The introduction of two novel magnetic phases and their topological quantum phase transition show rich and intrinsic physics involved in the Kane-Mele-Kondo lattice model.
119262048
Z2fractionalized Chern/topological insulators in an exactly soluble correlated model
In this paper we propose an exactly soluble model in two-dimensional honeycomb lattice, from which two phases are found. One is the usual Chern/topological insulating state and the other is an interesting $Z_2$ fractionalized Chern/topological insulator. While their bulk properties are similar, the edge-states of physical electrons are quite different. The single electron excitation of the former shows a free particle-like behavior while the latter one is gapped, which provides a definite signature to identify the fractionalized states. The transition between these two phases is found to fall into the 3D Ising universal class. Significantly, near the quantum transition point the physical electron in the edge-states shows strong Luttinger liquid behavior. An extension to the interesting case of the square lattice is also made. In addition, we also discuss some relationship between our exactly soluble model and various Hubbard-like models existing in the literature. The essential difference between the proposed $Z_{2}$ fractionalized Chern insulator and the hotly pursued fractional Chern insulator is also pointed out. The present work may be helpful for further study on the fractionalized insulating phase and related novel correlated quantum phases.
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.
111372582
Generating many Majorana modes via periodic driving: A superconductor model
Realizing Majorana modes (MMs) in condensed-matter systems is of vast experimental and theoretical interests, and some signatures of MMs have been measured already. To facilitate future experimental observations and to explore further applications of MMs, generating many MMs at ease in an experimentally accessible manner has become one important issue. This task is achieved here in a one-dimensional $p$-wave superconductor system with the nearest- and next-nearest-neighbor interactions. In particular, a periodic modulation of some system parameters can induce an effective long-range interaction (as suggested by the Baker-Campbell-Hausdorff formula) and may recover time-reversal symmetry already broken in undriven cases. By exploiting these two independent mechanisms at once we have established a general method in generating many Floquet MMs via periodic driving.
118453102
On general BCJ relation at one-loop level in Yang-Mills theory
A bstractThe tree-level BCJ relations reveal a duality between color and kinematic structure, this can be used to reduce the number of independent color-ordered amplitudes. At one-loop level in Yang-Mills theory, we investigate a similar BCJ relation in this paper. The four-point one-loop example in $\mathcal{N}=4$ SYM gives hints about the relations between integrands. The five-point example suggests that the general formula can be proven by the unitary-cut method. We will then prove a ‘general’ BCJ relation for one-loop integrands by D-dimension unitary cut, which can be regarded as a non-trivial generalization of the (fundamental)BCJ relation given by Boels and Isermann in [17, 18].
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.
11584906
Geometrical hierarchies in classical supergravity.
We introduce a N=1 supergravity model with a very simple hidden sector coupled to the electroweak gauge and Higgs sectors of the minimal supersymmetric standard model. At the classical level, supersymmetry and SU(2)×U(1) are both spontaneously broken, with vanishing vacuum energy. Two real flat directions control the two symmetry-breaking scales m(3/2) and m(Z). The two massless scalars are a gauge singlet and the standard Higgs boson. All other unobserved particles have masses of order m(3/2). This may be a new starting point for studying the compatibility of naturalness with the observed mass hierarchies.