arXiv subjects

Shu Chen

Publications and source records attributed to Shu Chen.

At least 145 records · Page 8Linked to original sources

arXiv2018

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems being integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number $ν$ of a non-Hermitian system is equal to half of the summation of two winding numbers $ν_1$ and $ν_2$ associated with two exceptional points respectively. The winding numbers $ν_1$ and $ν_2$ represent the times of real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of $ν_1$ and $ν_2$ is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number $ν_1$ and $ν_2$.

cond-mat.mes-hall↗

arXiv2018

Dynamical evolutions in non-Hermitian triple-well system with complex potential

We investigate the dynamical properties for non-Hermitian triple-well system with a loss in the middle well. When chemical potentials in two end wells are uniform and nonlinear interactions are neglected, there always exists a dark state, whose eigenenergy becomes zero, and the projections onto which do not change over time and the loss factor. The increasing of loss factor only makes the damping form from the oscillating decay to over-damping decay. However, when the nonlinear interaction is introduced, even interactions in the two end wells are also uniform, the projection of the dark state will be obviously diminished. Simultaneously the increasing of loss factor will also aggravate the loss. In this process the interaction in the middle well plays no role. When two chemical potentials or interactions in two end wells are not uniform all disappear with time. In addition, when we extend the triple-well system to a general (2n + 1)-well, the loss is reduced greatly by the factor 1=2n in the absence of the nonlinear interaction.

cond-mat.quant-gas↗

arXiv2017

Topological Mott Insulator with Bosonic Edge Modes in 1D Fermionic Superlattices

We investigate topological phase transitions driven by interaction and identify a novel topological Mott insulator state in one-dimensional fermionic optical superlattices through numerical density matrix renormalization group (DMRG) method. Remarkably, the low-energy edge excitations change from spin-1/2 fermionic single-particle modes to spin-1 bosonic collective modes across the phase transition. Due to spin-charge separation, the low-energy theory is governed by an effective spin superexchange model, whereas the charge degree of freedom is fully gapped out. Such topological Mott state can be characterized by a spin Chern number and gapless magnon modes protected by a finite spin gap. The proposed experimental setup is simple and may pave the way for the experimental observation of exotic topological Mott states.

cond-mat.quant-gas↗

arXiv2017

Quench dynamics in the Aubry-André-Harper model with \textit{p}-wave superconductivity

The Anderson localization phase transition in the Aubry-André-Harper (AAH) model with \textit{p}-wave superconducting (SC) pairing is numerically investigated by suddenly changing the on-site potential from zero to various finite values which fall into the extended, critical and localized phase regimes shown in this model. The time evolutions of entanglement entropy (EE), mean width of wave packets and Loschmidt echo of the system exhibit distinct but consistent dynamical signatures in those three phases. Specifically, the EE grows as a power function of time with the exponent of which varies in the extended phase but keeps almost unchanged in the critical phase for different quench parameters. However, if the system is in the localized phase after a quench, the EE grows much slower and will soon get saturated. The time-dependent width of wave packets in the system shows similar behaviors as the EE. In addition, from the perspective of dynamical phase transition, we find that the Loschmidt echo oscillates and always keeps finite when the system is quenched in the extended phase. In contrast, in the critical or localized phase, the echo will reach to zero at some time intervals or will decay almost to zero after a long-time evolution. The universal features of these quantities in the critical phase of the system with various SC pairing amplitudes are also observed.

cond-mat.dis-nn↗

arXiv2017

Topological edge states and pumping in a chain of coupled superconducting qubits

Topological insulators have inspired the study with various quantum simulators. Exploiting the tunability of the qubit frequency and qubit-qubit coupling, we show that a superconducting qubit chain can simulate various topological band models. When the system is restricted to the single-spin excitation subspace, the Su-Schrieffer-Heeger (SSH) model can be equivalently simulated by alternating the coupling strength between neighboring qubits. The existence of topological edge states in this qubit chain is demonstrated in the quench dynamics after the first qubit is excited. This excitation propagates along the chain where the qubit-qubit coupling is homogeneous. In contrast, in our qubit chain, the spin-up state localizes at the first qubit and the rest qubits remain in the spin-down state. We further show that the spin-up state can be transported along the chain by modulating the coupling strengths and the qubit frequencies. This demonstrates adiabatic pumping based on the Rice-Mele model. Moreover, we also discuss possible ways to construct other topological models with different topological phenomena within the current technology of superconducting qubits.

quant-ph↗

arXiv2017

Characterization of Lifshitz transitions in topological nodal line semimetals

We introduce a two-band model of three-dimensional nodal line semimetals, the Fermi surface of which at half-filling may form various one-dimensional configurations of different topology. We study the symmetries and "drumhead" surface states of the model, and find that the transitions between different configurations, namely, the Lifshitz transitions, can be identified solely by the number of gap-closing points on some high-symmetry planes in the Brillouin zone. A global phase diagram of this model is also obtained accordingly. We then investigate the effect of some extra terms analogous to a two-dimensional Rashba-type spin-orbit coupling. The introduced extra terms open a gap for the nodal line semimetals and can be useful in engineering different topological insulating phases. We demonstrate that the behavior of surface Dirac cones in the resulting insulating system has a clear correspondence with the different configurations of the original nodal lines in the absence of the gap terms.

cond-mat.mes-hall↗

arXiv2017

Zeros of Loschmidt echo in the presence of Anderson localization

We study the Loschmidt echo and the dynamical free energy of the Anderson model after a quench of the disorder strength. If the initial state is extended and the eigenstates of the post-quench Hamiltonian are strongly localized, we argue that the Loschmidt echo exhibits zeros periodically with the period $2π/D$ where $D$ is the width of spectra. At these zeros, the dynamical free energy diverges in a logarithmic way. We present numerical evidence of our argument in one- and three-dimensional Anderson models. Our findings connect the dynamical quantum phase transitions to the localization-delocalization phase transitions.

cond-mat.quant-gas↗

arXiv2017

Dynamical topological invariant after a quantum quench

We show how to define a dynamical topological invariant for general one-dimensional topological systems after a quantum quench. Focusing on two-band topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifold $S^2$, and thus we are able to define a dynamical topological invariant on each of the sphere. We also unveil the intrinsic relation between the dynamical topological invariant and the difference of topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.

cond-mat.str-el↗

arXiv2017

Real-Time Illegal Parking Detection System Based on Deep Learning

The increasing illegal parking has become more and more serious. Nowadays the methods of detecting illegally parked vehicles are based on background segmentation. However, this method is weakly robust and sensitive to environment. Benefitting from deep learning, this paper proposes a novel illegal vehicle parking detection system. Illegal vehicles captured by camera are firstly located and classified by the famous Single Shot MultiBox Detector (SSD) algorithm. To improve the performance, we propose to optimize SSD by adjusting the aspect ratio of default box to accommodate with our dataset better. After that, a tracking and analysis of movement is adopted to judge the illegal vehicles in the region of interest (ROI). Experiments show that the system can achieve a 99% accuracy and real-time (25FPS) detection with strong robustness in complex environments.

cs.CV↗

arXiv2017

Transition from nodal loop to nodal chain phase in a periodically modulated optical lattice

We propose to study the transition from a nodal loop to nodal chain phase in a tunable two-dimensional $π$-flux lattice with periodical modulation potential. The Hamiltonian describes a periodically modulated optical lattice system under artificial magnetic fluxes and the tunable modulation phase factor provides additionally an artificial dimension of external parameter space. We demonstrate that this lattice system is able to describe a semimetal with either nodal loop or nodal chain Fermi surface in the extended three-dimensional Brillouin zone. By changing the strength of modulation potential $V$, we realize the transformation between the nodal-loop and nodal-chain semimetal.

cond-mat.other↗

arXiv2017

Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry

Based on the exact solution of one-dimensional Fermi gas systems with $SU(n)$ symmetry in a hard wall, we demonstrate that we are able to sort the ordering of the lowest energy eigenvalues of states with all allowed permutation symmetries, which can be solely marked by certain quantum numbers in the Bethe ansatz equations. Our results give examples beyond the scope of the generalized Lieb-Mattis theorem, which can only compare the ordering of energy levels of states belonging to different symmetry classes if they are comparable according to the pouring principle. In the strongly interacting regime, we show that the ordering of energy levels can be determined by an effective spin-exchange model and extend our results to the non-uniform system trapped in the harmonic potential.

cond-mat.quant-gas↗

arXiv2017

Exact solution to an interacting dimerized Kitaev model at symmetric point

We study the interacting dimerized Kitaev chain at the symmetry point $Δ=t$ and the chemical potential $μ=0$ under open boundary conditions, which can be exactly solved by applying two Jordan-Wigner transformations and a spin rotation. By using exact analytic methods, we calculate two edge correlation functions of Majorana fermions and demonstrate that they can be used to distinguish different topological phases and characterize the topological phase transitions of the interacting system. According to the thermodynamic limit values of these two edge correlation functions, we give the phase diagram of the interacting system which includes three different topological phases: the trivial, the topological superconductor and the Su-Schrieffer-Heeger-like topological phase and we further distinguish the trivial phase by obtaining the local density distribution numerically.

cond-mat.str-el↗

arXiv2017

Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices

Continuous symmetries are believed to emerge at many quantum critical points in frustrated magnets. In this work, we study two candidates of this paradigm: the transverse-field frustrated Ising model (TFFIM) on the triangle and the honeycomb lattices. The former is the prototypical example of this paradigm, and the latter has recently been proposed as another realization. Our large-scale Monte Carlo simulation confirms that the quantum phase transition (QPT) in the triangle lattice TFFIM indeed hosts an emergent O(2) symmetry, but that in the honeycomb lattice TFFIM is a first-order QPT and does not have an emergent continuous symmetry. Furthermore, our analysis of the order parameter histogram reveals that such different behavior originates from the irrelevance and relevance of anisotropic terms near the QPT in the low-energy effective theory of the two models. The comparison between theoretical analysis and numerical simulation in this work paves the way for scrutinizing investigation of emergent continuous symmetry at classical and quantum phase transitions.

cond-mat.str-el↗

arXiv2017

Topological Phase Transition and Charge Pumping in a One-Dimensional Periodically Driven Optical Lattice

Experimental realizations of topological quantum systems and detections of topological invariants in ultracold atomic systems have been a greatly attractive topic. In this work, we propose a scheme to realize topologically different phases in a bichromatic optical lattice subjected to a periodically driven tilt harmonic oscillation, which can be effectively described by a superlattice model with tunable long-range hopping processes. By tuning the ratio of nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes, the system undergoes a topological phase transition accompanied by the change of topological numbers of the lowest band from -1 to 2. Using a slowly time-periodic modulation, the system emerges distinct quantized topological pumped charges (TPCs) of atoms in the filled band for different topological phases. Our scheme is realizable in current cold atomic technique.

cond-mat.quant-gas↗

arXiv2017

Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss

We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

cond-mat.dis-nn↗

arXiv2017

Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing

Off-diagonal Aubry-André (AA) model has recently attracted a great deal of attention as they provide condensed matter realization of topological phases. We numerically study a generalized off-diagonal AA model with p-wave superfluid pairing in the presence of both commensurate and incommensurate hopping modulations. The phase diagram as functions of the modulation strength of incommensurate hopping and the strength of the p-wave pairing is obtained by using the multifractal analysis. We show that with the appearance of the p-wave pairing, the system exhibits mobility-edge phases and critical phases with various number of topologically protected zero-energy modes. Predicted topological nature of these exotic phases can be realized in a cold atomic system of incommensurate bichromatic optical lattice with induced p-wave superfluid pairing by using a Raman laser in proximity to a molecular Bose-Einstein condensation.

cond-mat.quant-gas↗

arXiv2017

$2π$-flux loop semimetals

We introduce a model of $2π$-flux loop semimetals which holds nodal loops described by a winding number $ν=2$. By adding some extra terms, this model can be transformed into a recently discovered Hopf-link semimetal, and the symmetries distinguishing these two phases are studied. We also propose a simpler physical implementation of $2π$-flux loops and of the Hopf-link semimetals which only involves nearest-neighbor hoppings, although in the presence of spin-orbit interaction. Finally, we investigate the Floquet properties of the $2π$-flux loop, and find that such a loop may be driven into two separated $π$-flux loops or four Weyl points by light with circular polarization in certain directions.

cond-mat.str-el↗

arXiv2017

Numerical Electromagnetic Frequency Domain Analysis with Discrete Exterior Calculus

In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations in terms of DEC for 3D and 2D inhomogeneous structures, and also show that the charge continuity relation is naturally satisfied. Then we introduce effective signed dual volume to incorporate material information into Hodge star operators and take into account the case when circumcenters fall outside triangles or tetrahedrons, which may lead to negative dual volume without Delaunay triangulation. Then we demonstrate the implementation of various boundary conditions, including perfect magnetic conductor (PMC), perfect electric conductor (PEC), Dirichlet, periodic, and absorbing boundary conditions (ABC) within this method. An excellent agreement is achieved through the numerical calculation of several problems, including homogeneous waveguides, microstructured fibers, photonic crystals, scattering by a 2-D PEC, and resonant cavities.

physics.comp-ph↗