Topological Structures and Topological Excitations: We analytically derived the effective magnetic field and eddy currents induced by spin-dependent inter-particle interactions in spinor Bose-Einstein condensates (BEC) [PRA.92.013604(2015)]. Through classical Monte Carlo, we uncovered diverse magnetic textures arising from the interplay between spin-orbit coupling and inter-particle interactions [PRA.94.063611(2016), PRA.99.043628(2020)]. Furthermore, we numerically demonstrated the topological phase transitions from domain walls to vortex-antivortex pairs under applied magnetic fields [Chaos, Solitons & Fractals.174.113918(2023)]. We extended the concept of topology to open systems, investigating anomalous topological phenomena induced by interlayer coupling. Additionally, formal theories on the topological properties based on the single-particle density matrice were developed [PRB.97.195434(2018), PRB.102.075403(2020)], alongside the proposal of a cold-atom experimental setup for measuring single-particle density matrices [PRA.101.013631(2020)]. We also explored the formation, excitation spectrum, and dynamical stability of lattice droplets in condensates after considering the Lee-Huang-Yang correction [PRA.108.053310(2023)].

Interaction-Induced Topological Phase Transitions: Extensive investigations utilizing the dynamical mean-field approximation were conducted. We studied the interaction-induced topological Mott phase transition in topological semimetals [PRB.103.125132(2021)]. We also explored the combined effects of strong interactions between particles and disorders, by numerically developing the dynamical mean-field approximation within disordered systems [PRB.99.125138(2019)]. Additionally, a dynamical mean-field approximation was developed for high-spin systems [PRB.101.245159 (2020)]. Furthermore, we developed local markers to characterize the local topological properties of topological insulators in real space [PRR.2.013299(2020)] and proposed a method to observe interaction-induced topological phase transitions in cold atomic systems experiments [PRL.122.010406(2019)].

Dynamics of Bose-Einstein condensates (BEC): We investigated the tunneling phenomenon among multiple channels within a spin-orbit-coupled BEC system, uncovering the associated non-adiabatic effects [PRA.91.063602(2015)].  We studied the quench dynamics after suddenly changing the atom-atom interaction in BEC, revealing how the dark solitons decay into vortex-antivortex pairs and searching for the possible stable vortex pattern [CPL.39.070304(2022)]. We explored the collisions of quantum droplets with or without a vortex, analyzing how the velocities and sizes of droplets affect their stability, fusion, and fragmentation [AIP Adv.13.055130(2023)]. We also explored the immiscible two-component BEC and searched for methods for creating stable vortices in BEC [Front.Phys.18(6).62302(2023)].

Quantum transport: We revealed the impact of magnetic impurities on topological transport by employing the bosonization theory [PRB.97.235402 (2018)]. We explored the magnetoresistance of antiferromagnetic metals with domain walls and found the anomalous negative domain-wall magnetoresistance [PRB.102.184413(2020)]. We also studied the transport properties of Majorana particles in quantum spin liquids with Z2 flux backgrounds [PRB.104.064437 (2021)].