arXiv subjects

Fuxiang Li

Publications and source records attributed to Fuxiang Li.

At least 37 records · Page 2Linked to original sources

arXiv2023

Dynamical characterization of topological phases beyond the minimal models

Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have been focused on systems of which the Hamiltonian consists of matrices that commute with each other and satisfy Clifford algebra. In this work, we consider the characterization of topological phases with Hamiltonians that are beyond the minimal model. Specifically, the quantum quench dynamics of two types of layered systems is studied, of which the consisting matrices of Hamiltonians do not all satisfy Clifford algebra. We find that the terms which anti-commute with others can hold common band-inversion surfaces, which controls the topology of all the bands, but for other terms, there is no universal behavior and need to be treated case by case.

quant-ph↗

arXiv2023

Full investigation of nonadiabatic dynamical characterization in arbitrary quenching process

Recently, dynamical characterization of bulk topology has been experimentally realized under nonadiabatic sudden quench dynamics. However, it has been shown that only the topology of final phase can be characterized when the system is quenched from initial topologically trivial phase. In this paper, taking the two-dimensional Chern insulator as an example, we make a thorough investigation of different types of quenching processes under nonadiabatic slow quench dynamics, and study not only the processes between nontrivial phase and trivial phase, but also between the phases with different topological invariants. We find that, under slow quench dynamics, both the initial and final topological phase can be characterized and the topological invariant can be captured by time-averaged spin polarization. Moreover, different types of processes can be distinguished from the special regions where the time-averaged spin polarization vanishes. All the dynamical characterization schemes are entirely based on the experimentally measurable quantity time-averaged spin polarization, and thus one can expect our findings may provide reference for future experiments.

quant-ph↗

arXiv2022

Many-body slow quench dynamics and nonadiabatic characterization of topological phases

Previous studies have shown that the bulk topology of single-particle systems can be captured by the band inversion surface or by the spin inversion surface emerged on the time-averaged spin polarization. Most of the studies, however, are based on the single-particle picture even though the systems are fermionic and of multi-bands. Here, we study the many-body quench dynamics of topological systems with all the valence bands fully occupied, and show that the concepts of band inversion surface and spin inversion surface are still valid. More importantly, the many-body quench dynamics is shown to be reduced to a nontrivial three-level Landau-Zener model, which can be solved exactly. Based on the analytical results, the topological spin texture revealed by the time-averaged spin polarization can be applied to characterize the bulk topology and thus provides a direct comparison for future experiments.

cond-mat.str-el↗

arXiv2022

Unconventional optical selection rules in ZrTe5 under an in-plane magnetic field

The optical selection rules of an electron system under a magnetic field play key roles in determining its optical properties, from which the band structures and underlying symmetries can be derived. In this Letter, based on a three-dimensional strong topological insulator model describing ZrTe5,we study the Landau levels (LLs) and magneto-optical conductivity under an in-plane magnetic field. We reveal that in the transverse conductivity Re(σ_{zz}), the unconventional optical selection rules n\righatarrow n\pm 2 dominate, with n being the LL index. We attribute the unconventional selection rules to the peculiar distribution of parity carried by the LLs, resulting from the chiral symmetry of the sub-Hamiltonians. Moreover, we predict that, if the strong anisotropic system is tuned to be nearly isotropic, the LLs would redistribute and the conventional selection rules n\rightarrow n\pm 1 can be recovered.

cond-mat.mes-hall↗

arXiv2022

High Chern number phase in topological insulator multilayer structures: a Dirac cone model study

We use the Dirac cone model to explore the high Chern number (C) phases that are realized in the magnetic-doped topological insulator (TI) multilayer structures by Zhao et al. [Nature 588, 419 (2020)]. The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters and then the Chern number phase diagrams of the TI multilayer structures are obtained. The high-C behavior is attributed to the band inversion of the renormalized Dirac cones, along with which the spin polarization at the Γpoint will get increased. Moreover, another two TI multilayer structures as well as the TI superlattice structures are also studied.

cond-mat.mes-hall↗

arXiv2022

A density peaks clustering algorithm with sparse search and K-d tree

Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks clustering algorithm with sparse search and K-d tree is developed to solve this problem. Firstly, a sparse distance matrix is calculated by using K-d tree to replace the original full rank distance matrix, so as to accelerate the calculation of local density. Secondly, a sparse search strategy is proposed to accelerate the computation of relative-separation with the intersection between the set of $k$ nearest neighbors and the set consisting of the data points with larger local density for any data point. Furthermore, a second-order difference method for decision values is adopted to determine the cluster centers adaptively. Finally, experiments are carried out on datasets with different distribution characteristics, by comparing with other six state-of-the-art clustering algorithms. It is proved that the algorithm can effectively reduce the computational complexity of the original DPC from $O(n^2K)$ to $O(n(n^{1-1/K}+k))$. Especially for larger datasets, the efficiency is elevated more remarkably. Moreover, the clustering accuracy is also improved to a certain extent. Therefore, it can be concluded that the overall performance of the newly proposed algorithm is excellent.

stat.ML↗

arXiv2022

Generic theory of characterizing topological phases under quantum slow dynamics

Dynamical characterization of equilibrium topological phases has attracted considerable attention in recent years. In this paper, we make a thorough exploration of the non-adiabatic characterization of topological phases under slow quench protocol. We first propose an exactly solvable multi-state Landau-Zener model that can be directly applied to the non-adiabatic slow quench dynamics of topological systems. Then we present two different schemes to characterize the bulk topology of the system based on the so called spin inversion surface. The first one needs least number of quenching processes, but requires to measure the gradients of time-averaged spin-polarization on the SIS. The second one only needs to measure the value of time-averaged spin-polarization on the SIS, thus makes it possible to directly characterize the topological phases by introducing an extra quenching process. Moreover, high-order SIS or band inversion surface (BIS) relying on the dimension reduction approach, is also generalized to the above two different characterization schemes. One can extract the topological invariant from pairs of points with opposite signs both on the 0D highest order BIS and on the 0D highest order SIS, which greatly simplifies the measurement strategy and characterization process. In a word, superior to the sudden quench protocol, we demonstrate that the topological invariant can be captured not only by the topological information on BIS, but also on the SIS. In particular, direct characterization of topological phases based on BIS and SIS can be realized.

quant-ph↗

arXiv2022

Field-driven side-by-side magnetic domain wall dynamics in ferromagnetic nanostrips

There has been a plethora of studies on domain wall dynamics in magnetic nanostrips, mainly because of its versatile non-linear physics and potential applications in data storage devices. However, most of the studies focus on out-of-plane domain walls or in-plane head-to-head (tail-to-tail) domain walls. Here, we numerically study the field-driven dynamics of in-plane side-by-side domain walls in ferromagnetic strips, which can be stable in the presence of an in-plane easy-axis anisotropy transverse to the strip. The domain walls move in a rigid-body manner at low field, and show complex Walker breakdown behavior at high field. We observe a multi-step Walker breakdown through vortex nucleation in wide strips. In the presence of Dzyaloshinskii-Moriya interaction (DMI), the first Walker breakdown field first decreases then increases with interfacial DMI, while keeps increasing with bulk DMI. These findings complement the current understanding on domain wall dynamics.

cond-mat.mes-hall↗

arXiv2021

Gapped Dirac semimetal with mixed linear and parabolic dispersions

In this paper, we make a comprehensive study of the properties of a gapped Dirac semimetal model, which was originally proposed in the magnetoinfrared spectroscopy measurement of ZeTe$_5$, and includes both the linear and parabolic dispersions in all three directions. We find that, depending on the band inversion parameters, $ζ'$ and $ζ_z'$, the model can support three different phases: the single Dirac point (DP) phase, the double DPs phase and the Dirac ring phase. The three different phases can be distinguished by their low-energy features in the density of states (DOS) and optical conductivity. At high energy, both the DOS and optical conductivity exhibit power-law like behaviors, with the asymptotic exponents depending heavily on the signs of $ζ'$ and $ζ_z'$. Moreover, the thumb-of-rule formula between the DOS and optical conductivity is satisfied only when $(ζ',ζ_z')>0$. The implications of our results for experiments are discussed.

cond-mat.mes-hall↗

arXiv2021

High-Chern number phase in the topological insulator multilayer structures

The high-Chern number phases with a Chern number C>1 have been observed in a recent experiment that performed on the topological insulator (TI) multilayer structures, consisting of the alternating magnetic-doped and undoped TI layers. In this paper, we develop an effective method to determine the Chern numbers in the TI multilayer structures and then make a systematic study on the Chern number phase diagrams that are modulated by the magnetic doping and the middle layer thickness. We point out that in the multilayer structure, the high-C behavior can be attributed to the band inversion mechanisms. Moreover, we find that the lowest bands may be multifold degenerate around the Gamma point, and when they are inverted, the Chern number change will be larger than one. Besides the TI multilayer structures implemented in the experiment, we also explore the high-C phase realizations in two other kinds of the TI multilayer structures. The implications of our results for experiments are discussed.

cond-mat.mes-hall↗

arXiv2021

Phase diagram and orbital Chern insulator in twisted double bilayer graphene

Compared with twisted bilayer graphene, twisted double bilayer graphene (TDBG) provides another important platform to realize the moiré flat bands. In this paper, we first calculate the valley Chern number phase diagram of TDBG in the parameter space spanned by the twist angle and the interlayer electric potential. To include the effects of interactions, we then phenomenologically introduce the spin-splitting and valley-splitting. We find that when the valley splitting is larger than the bandwidth of the first conduction band so that a gap is opened and the spin splitting is relatively weak, the orbital Chern insulator emerges at half-filling, associated with a large orbital magnetization (OM). Further calculations suggest that there is no sign reversal of the OM when the Fermi energy goes from the bottom to the top of the half-filling gap, as the OM remains negative in both AB-AB stacking and AB-BA stacking. The implications of our results for the ongoing experiments are also discussed.

cond-mat.mes-hall↗

arXiv2020

Emergent topology under slow non-adiabatic quantum dynamics

Characterization of equilibrium topological quantum phases by non-equilibrium quench dynamics provides a novel and efficient scheme in detecting topological invariants defined in equilibrium. Nevertheless, most of the previous studies have focused on the ideal sudden quench regime. Here we provide a generic non-adiabatic protocol of slowly quenching the system Hamiltonian, and investigate the non-adiabatic dynamical characterization scheme of topological phase. The {\it slow} quench protocol is realized by introducing a Coulomb-like Landau-Zener problem, and it can describe, in a unified way, the crossover from sudden quench regime (deep non-adiabatic limit) to adiabatic regime. By analytically obtaining the final state vector after non-adiabatic evolution, we can calculate the time-averaged spin polarization and the corresponding topological spin texture. We find that the topological invariants of the post-quench Hamiltonian are characterized directly by the values of spin texture on the band inversion surfaces. Compared to the sudden quench regime, where one has to take an additional step to calculate the {\it gradients} of spin polarization, this non-adiabatic characterization provides a {\it minimal} scheme in detecting the topological invariants. Our findings are not restricted to 1D and 2D topological phases under Coulomb-like quench protocol, but are also valid for higher dimensional system or different quench protocol.

quant-ph↗

arXiv2020

Integrable multistate Landau-Zener models with parallel energy levels

We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/τ$-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ models from this class must contain bands of parallel diabatic energy levels. The structure of the scattering matrix and other properties are found to be the same as in the previously discussed completely solvable MLZ Hamiltonians.

math-ph↗

arXiv2020

Examining the validity of the two-dimensional conical model to describe the three-dimensional ZrTe5

Understanding the low-energy excitation state in three-dimensional layered compound ZrTe5 remains a challenging problem in the study of novel topological materials. Recently, a two-dimensional conical model was proposed to explain the experimental optical spectroscopy in the 3D ZrTe5, Martino et al. [Phys. Rev. Lett. 122, 217402 (2019)]. Motivated by this work, in this paper, we perform a systematic theoretical study on the optical conductivity of this model in both cases without and with an external magnetic field to further demonstrate the validity of this model and to recover new physics.We find that there exist completely different characteristics for optical conductivity along different directions, due to anisotropic low-energy excitations in this two-dimensional conical model. Specifically, for the interband optical conductivity, we find asymptotic dependence on the optical frequency as Re(σ_x)\simω^{1/2} and Re(σ_z)\simω^{3/2}, which are universal both in the gapped insulator phase and Weyl semimetal phase. For the magneto-optical conductivity, on the contrary, Re(σ^B_{x/z}) shows distinct signatures in the gapped insulator phase and Weyl semimetal phase, which can help distinguish the two phases. Our results, to be verified in future experiments, could provide more insights into the understanding of the topological nature of ZrTe5.

cond-mat.mes-hall↗

arXiv2020

Phase Diagram of the Dynamics of a Precessing Qubit under Quantum Measurement

We study the phase transitions induced by sequentially measuring a single qubit precessing under an external transverse magnetic field. Under projective quantum measurement, the probability distribution of the measurement outcomes can be mapped exactly to the thermodynamic probability distribution of a one-dimensional Ising model, whose coupling can be varied by the magnetic field from ferromagnetic to anti-ferromagnetic. For the general case of sequential quantum measurement,we develop a fast and exact algorithm to calculate the probability distribution function of the ferromagnetic order and anti-ferromagnetic order, and a phase diagram is obtained in the parameter space spanned by the measurement strength and magnetic field strength. The mapping to a long-range interacting Ising model is obtained in the limit of small measurement strength. Full counting statistical approach is applied to understand the phase diagram, and to make connections with the topological phase transition that is characterized by the braid group. This work deepens the understanding of phase transitions induced by quantum measurement, and may provide a new method to characterize and steer the quantum evolution.

quant-ph↗

arXiv2020

Disorder and magnetic transport in tilted Weyl semimetals

We investigate the effect of disorder on the Landau levels (LLs) in tilted three dimensional Weyl semimetals (WSMs) when a magnetic field is present. Based on the minimum lattice model and by using the exact diagonalization and Kubo's formula, we numerically calculate the Hall conductivity and the density of states (DOS), from which several striking signatures are found to distinguish type-I WSMs from type-II WSMs: the first is the response of the Hall conductivity to the Fermi energy around the band center in clean limit, the second is the performance of the Hall conductivity to disorder, where in type-I WSMs, the robustness of the low-energy LLs is broken successively from the higher LLs to the lower ones and can be understood with the sink down picture, and the third is the behavior of the DOS at zero energy to disorder. The implications of our results are discussed.

cond-mat.dis-nn↗

arXiv2020

Interaction-induced phase transitions of type-II Weyl semimetals

The study of Weyl semimetals (WSMs) lies at the forefront of the nontrivial topological phenomena in condensed-matter physics. In this work, we study the effect of on-site repulsive Hubbard interaction on the WSM system with a nonzero tilt at half filling. Within the Hartree-Fock mean-field approximation, we treat the Hubbard interaction self-consistently and find that the Fock exchange field vanishes, while the Hartree field can renormalize the topological mass, the tilt, and the Fermi velocity of the Weyl cones. When the renormalized tilt is larger than the renormalized Fermi velocity, the Hubbard interaction will induce the quantum phase transition from a type-I WSM to a type-II WSM. We then provide the interaction-induced phase diagrams of WSMs in different parametric spaces, in which the antiferromagnetic order at strong interaction is also considered. In addition, we analyze another model hosting two pairs of Weyl nodes, and similar results are obtained. The implications of these results are discussed.

cond-mat.str-el↗

arXiv2020

Emergence of asymmetric fermionic order in interacting birefringent fermions

The birefringent fermions possess a spectrum with two distinct Fermi velocities. Here based on the lattice model, we use the mean-field method to investigate the interaction-induced phase transitions of the birefringent fermions. We consider both the short-range nearest-neighbor (NN) and next-nearest-neighbor (NNN) repulsive interactions and calculate the phase diagrams under different conditions. We find that the NN interactions can induce the asymmetric charge density wave order, while the NNN interactions can drive the asymmetric quantum anomalous Hall order (AQAH) in the large limit of anisotropy in the hopping integrals, β\rightarrow 1. The AQAH order is characterized by the unequal loop currents connecting the NNN sites and by the appearance of a gap between the two conduction (valence) bands. Such asymmetric fermionic orders can be attributed to the specific lattice geometry of the birefringent fermions. The implications of our results for experiments are also discussed.

cond-mat.str-el↗