It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically non-trivial flat-band model on a checkerboard lattice. In the presence of nearest-neighbouring repulsion, we find that at 1/3 filling, the Fermi-liquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram.

We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering multi-layer Chern number C = 1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a twoband model on a triangular lattice with a Chern number C = 3 and an N -band square lattice model with C = N for an arbitrary integer N . In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate inter-particle interactions, these models are likely to lead to the formation of novel Abelian and Non-Abelian fractional Chern insulators. As a simple example, we test the C = 2 model with hardcore bosons at 1/3 filling and an intriguing fractional quantum Hall (FQH) state is observed. Introduction -The experimental fractional quantum Hall effect (FQHE) arises from the highly degenerate Landau levels of continuum 2D electron systems, and is described by variational wave functions, first proposed by Laughlin for the primary FQHE states [1] and later generalized by Jain for composite fermion states [2], which are analytic functions of the 2D spatial coordinates. Many important properties of the FQHE, e.g., the hierarchy structures and fractionalized excitations [3,4], can be understood within this framework. It even leads to the predictions of intriguing non-Abelian FQH states at certain filling fractions [5][6][7][8]. Moreover, based on a classification of the pattern of zeros of symmetric (analytic) polynomials, a systematic way to classify FQH states [9,10] has been proposed. Thus, our current theoretical knowledge of FQHE is based on the analytic structure the 2D Landau level (LL) Hilbert space.

We classify and construct models for two-dimensional (2D) interacting fermionic symmetryprotected topological (FSPT) phases with general finite Abelian unitary symmetry G f . To obtain the classification, we couple the FSPT system to a dynamical discrete gauge field with gauge group G f and study braiding statistics in the resulting gauge theory. Under reasonable assumptions, the braiding statistics data allows us to infer a potentially complete classification of 2D FSPT phases with Abelian symmetry. The FSPT models that we construct are simple stacks of the following two kinds of existing models: (i) free-fermion models and (ii) models obtained through embedding of bosonic symmetry-protected topological (BSPT) phases. Interestingly, using these two kinds of models, we are able to realize almost all FSPT phases in our classification, except for one class. We argue that this exceptional class of FSPT phases can never be realized through models (i) and (ii), and therefore can be thought of as intrinsically interacting and intrinsically fermionic. The simplest example of this class is associated with Z f 4 × Z4 × Z4 symmetry. We show that all 2D FSPT phases with a finite Abelian symmetry of the form Z f 2 × G can be realized through the above models (i), or (ii), or a simple stack of them. Finally, we study the stability of BSPT phases when they are embedded into fermionic systems.

Recently it has been established that two-dimensional bosonic symmetry-protected topological(SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H 3 (G, U(1)). Later, group super-cohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group super-cohomology, and we also show that with an additional H 1 (G, Z2) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G × Z f 2 is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time reversal symmetry.

We study a generalized Kane-Mele-Hubbard model with third-neighbor hopping, an interacting two-dimensional model with a topological phase transition as a function of third-neighbor hopping, by means of the determinant projector Quantum Monte Carlo (QMC) method. This technique is essentially numerically exact on models without a fermion sign problem, such as the one we consider. We determine the interaction-dependence of the Z2 topological insulator/trivial insulator phase boundary by calculating the Z2 invariants directly from the single-particle Green's function. The interactions push the phase boundary to larger values of third-neighbor hopping, thus stabilizing the topological phase. The observation of boundary shifting entirely stems from quantum fluctuations. We also identify qualitative features of the single-particle Green's function which are computationally useful in numerical searches for topological phase transitions without the need to compute the full topological invariant.

According to the principle of electromagnetic wave propagation and the model of radar multipath propagation, this paper established radar detection power model in natural space under the impact of sea clutter, and on condition that conducting simulations to study detection power of shore-based radars on different altitudes and different operating frequencies. Simulation results indicate that when the radar operating frequency is constant, with the erection height increases, the detection range will increase at the same time, while significantly reduced about blind region. When the radar erection height is constant, blind region is filled with radars working at C, S and X operating frequencies. The effect of blind filling is of great importance for adjacent bands. This paper provides theoretical reference analysis for radar detection power assessing and overall with a strong engineering application value.