arXiv subjects

Shu Chen

Publications and source records attributed to Shu Chen.

At least 181 records · Page 10Linked to original sources

arXiv2015

Fractional Topological States in Quantum Spin Chains with Periodical Modulation

We report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically nontrivial degenerate ground states at some specific magnetizations, which can be characterized by the nonzero-integer total Chern numbers of the degenerate ground states and the emergence of nontrivial edge states under open boundary conditions. We find that the low-energy excitations obey bosonic $ν=1/2$ fractional statistics for the spin-$1/2$ system and $ν=1$ non-Abelian statistics for the spin-$1$ system, respectively. The discovered fractional quantum states provide another route to the theoretical exploration of fractional quantum states in correlated spin systems.

cond-mat.str-el↗

arXiv2015

Phase diagram and topological superfluid state of spin-orbit coupled Fermi gas with attractive interactions in a one-dimensional optical lattice

Based on density matrix renormalization group method, we investigate the spin-orbit coupled Fermi gas with attractive interactions in one-dimensional optical lattice and present a complete phase diagram for a quarter-filling system with intermediate strong interactions. We unveil the exotic pairings induced by spin-orbit couplings and the phase transitions between different pairing states, and further demonstrate the existence of the long-sought topological superfluid state at moderate magnetic field and spin-orbit coupling strength. For the particle conserved system, this topological superfluid state can be fixed by its gapless single particle excitation, Luttinger parameter and non-trivial boundary effect. Our study removes out the widespread doubt on the existence of topological superfluid in one dimension and paves the way for simulating topological superfluid states in cold atom settings.

cond-mat.str-el↗

arXiv2015

$\mathcal{PT}$ symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

We study the $\mathcal{PT} $-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact $\mathcal{PT} $-symmetry phase to the phase with spontaneously breaking $\mathcal{PT} $-symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for the symmetry breaking. In the $\mathcal{PT} $-symmetry breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption Laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian $\mathcal{PT} $-symmetric potentials.

quant-ph↗

arXiv2015

Characterization of topological phase transitions via topological properties of transition points

We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of momentum and transition driving parameter. By applying our scheme to the Su-Schrieffer-Heeger model and Haldane model, we demonstrate that the topological phase transition can be well characterized by the defined topological invariant of the transition point, which reflects the change of topological invariants of topologically different phases across the phase transition point.

cond-mat.str-el↗

arXiv2015

Winding numbers of phase transition points for one-dimensional topological systems

We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.

cond-mat.str-el↗

arXiv2015

Many-body ground state localization and coexistence of localized and extended states in an interacting quasiperiodic system

We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a nonergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions of natural orbitals of the corresponding one-particle density matrix. This is very different from its noninterating limit, in which all eigenstaes undergo a delocaliztion-localization transtion when the strength of the incommensurate potential exceeds a critical value.

cond-mat.dis-nn↗

arXiv2015

Interplay between Fano resonance and $\mathcal{PT} $ symmetry in non-Hermitian discrete systems

We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for the absence or existence of the prefect reflection at one and two resonant frequencies. Our study can help us to understand the interplay between the Fano resonance and PT symmetry in non-Hermitian discrete systems, which may be realizable in optical waveguide experiments.

quant-ph↗

arXiv2015

Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices

The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase $π$ and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is qualitatively discussed and the ones with higher fillings can be understood as a $\frac{1}{3}$-filling topological phase on a background of trivial charge-density-wave or Mott insulators.

cond-mat.quant-gas↗

arXiv2015

Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars

By using Majorana's stellar representation, we give a clear geometrical interpretation of the topological phases of inversion-symmetric polymerized models by mapping the Bloch states of multi-band systems to Majorana stars on the Bloch sphere. While trajectories of Majorana stars of a filled Bloch band exhibit quite different geometrical structures for topologically trivial and nontrivial phases, we further demonstrate that these structures are uniquely determined by distributions of Majorana stars of two high-symmetrical momentum states, which have different parities for topologically different states.

cond-mat.other↗

arXiv2015

Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains

Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems has not been extensively explored due to the failure of direct explanation from the topological band insulator theory on such systems and the origin of the topological property is unclear. Here we report the theoretical discovery of strongly correlated topological states in quasi-periodic Heisenberg spin chain systems corresponding to a series of incommensurate magnetization plateaus under the presence of the magnetic field, which are uniquely determined by the quasi-periodic structure of exchange couplings. The topological features of plateau states are demonstrated by the existence of non-trivial spin-flip edge excitations, which can be well characterized by nonzero topological invariants defined in a two-dimensional parameter space. Furthermore, we demonstrate that the topological invariant of the plateau state can be read out from a generalized Streda formula and the spin-flip excitation spectrum exhibits a similar structure of the Hofstadter's butterfly spectrum for the two-dimensional quantum Hall system on a lattice.

cond-mat.str-el↗

arXiv2015

Hidden-symmetry-protected topological phases on a one-dimensional lattice

We demonstrate the existence of topologically nontrivial phase in a one-dimensional fermionic lattice system subjected to synthetic gauge fields, which is beyond the standard Altland-Zirnbauer classification of topological insulators. The topological phase can be characterized by the presence of degenerate zero-mode edge states or a quantized Berry phase of the occupied Bloch band. By analyzing symmetries of the system, we identify that the topological phase and zero-mode edge states are protected by two hidden symmetries. An extended model with hidden symmetry breaking is also studied in order to reveal the effect of hidden symmetries on the symmetry protected topological phase.

cond-mat.str-el↗

arXiv2014

Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices

We identify the existence of various symmetry-protected topological states in one-dimensional superlattices with periodically modulated hopping amplitudes or on-site potentials, which can be characterized by the quantized Berry phase $π$ or the emergence of a pair of degenerate boundary states. It is shown that there may exist three types of topological phases, which are protected by the inversion symmetry, the chiral symmetry, and both of them, respectively, depending on the modulations, the odd or even modulation period. The connection between the hopping and potential modulations is also discussed. Furthermore, we demonstrate that the topological phase protected by the inversion symmetry can be realized in the interacting boson systems trapped in the same superlattices. The results are very possibly studied experimentally in the superlattice systems engineered with state-of-art technologies.

cond-mat.mes-hall↗

arXiv2014

Topological nature of magnetization plateaus in periodically modulated quantum spin chains

We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.

cond-mat.str-el↗

arXiv2014

Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices

We study the dynamical localization transition in a one-dimensional periodically kicked incommensurate lattice, which is created by perturbing a primary optical lattice periodically with a pulsed weaker incommensurate lattice. The diffusion of wave packets in the pulsed optical lattice exhibits either extended or localized behaviors, which can be well characterized by the mean square displacement and the spatial correlation function. We show that the dynamical localization transition is relevant to both the strength of incommensurate potential and the kicked period, and the transition point can be revealed by the information entropy of eigenfunctions of the Floquet propagator.

cond-mat.quant-gas↗

arXiv2014

PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials

We study the parity- and time-reversal PT symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials $\pm iγ$ at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from unbroken PT-symmetry region to spontaneously broken $\mathcal{PT} $-symmetry region at a certain $γ_{c}$, and a second transition occurs at another transition point $γ_{c^{'}}$ when further increasing the strength of the imaginary potential $γ$. But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero $γ$ and the $\mathcal{PT}$-symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.

cond-mat.other↗

arXiv2014

Effect of incommensurate disorder on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev's chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of $e^2/h$, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate disorder suppresses the current at finite voltage bias, and then narrows the linear response regime of the $I-V$ curve which exhibits two plateaus corresponding to the superconducting gap and the band edge respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value $2+2Δ$ with $Δ$ the p-wave pairing amplitude, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage will also cause an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose $I-V$ curve exhibits an exponential shape.

cond-mat.mes-hall↗

arXiv2014

Topological phases of generalized Su-Schrieffer-Heeger models

We study the extended Su-Schrieffer-Heeger model with both the nearest-neighbor and next-nearest-neighbor hopping strengths being cyclically modulated and find the family of the model system exhibiting topologically nontrivial phases, which can be characterized by a nonzero Chern number defined in a two-dimensional space spanned by the momentum and modulation parameter. It is interesting that the model has a similar phase diagram as the well-known Haldane's model. We propose to use photonic crystal systems as the idea systems to fabricate our model systems and probe their topological properties. Some other models with modulated on-site potentials are also found to exhibit similar phase diagrams and their connection to the Haldane's model is revealed.

cond-mat.mes-hall↗

arXiv2013

Ferromagnetic to antiferromagnetic transition of one-dimensional spinor Bose gases with spin-orbit coupling

We have analytically solved one-dimensional interacting two-component bosonic gases with spin-orbit (SO) coupling by the Bethe-ansatz method. Through a gauge transformation, the effect of SO coupling is incorporated into a spin-dependent twisted boundary condition. Our result shows that the SO coupling can influence the eigenenergy in a periodical pattern. The interplay between interaction and SO coupling may induce the energy level crossing for the ground state, which leads to a transition from the ferromagnetic to antiferromagnetic state.

cond-mat.quant-gas↗