Research

My current research activities involve the following fields in condensed matter physics: (1) Exotic states of matter in two-dimensional (2D) frustrated magnetic systems such as quantum spin liquids, valence-bond solid states, and some new magnetic ordered states; (2) Fractional Quantum Hall effect (FQHE) states in topological flat-band model and 2D electronic systems in magnetic field such as the double-layer FQHE systems; (3) Numerical characterizations of topological ordered states in exact diagonalization (ED) and density-matrix renormalization group (DMRG) simulations; (4) To develop computational condensed matter methods such as ED, DMRG, and variational quantum Monte Carlo (VMC).

(I) Exotic states of matter in 2D frustrated magnetic systems

Recently, we systematically studied a series of 2D frustrated magnetic systems using the unbiased DMRG and ED calculations. In a spin-1/2 kagome Heisenberg model with extended couplings, we fully established a chiral spin liquid (CSL) as the v=1/2 bosonic FQHE state, which is the first realistic Heisenberg model to host a CSL and may be realized in the magnetic materials and optical lattice systems (Nature Sci. Rep. 4, 6317 (2014)). By studing a global quantum phase diagram of this model, we found that the CSL emerges between an usual coplanar magnetic ordered state and an unusual non-coplanar magnetic ordered cuboc1 state that also breaks time-reversal symmetry (Phys. Rev. B 91, 075112 (2015)). To understand this CSL in theory, we constructed the parton wavefunction for this CSL and performed the VMC calculations. We discovered that this CSL state could be stabilized in the phase region consistent with the DMRG results, and we also obtained the topological properties in the VMC calculations, which are also consistent with the CSL found in DMRG (Phys. Rev. B 91, 041124(R) (2015)). This CSL we found is quite close to the previously identified gapped Z2 spin liquid. To understand the phase transition between two gapped topological spin liquid, we constructed a kagome model with the extended couplings only having the XY interactions, and studied the quantum phase transition between the CSL and the time-reveral invariant spin liquid. We found a critical spin liquid near the pure XY model. The quantum phase transition from the CSL to the critical SL is driven by the collapsing of singlet gap. Our results represent a significant progress in understanding the connection between different spin liquids by identifying the mechanism of the phase transitions and establishing the characteristic nature of the critical SL phase adjacent to the CSL (arXiv:1410.4883).

Another frustrated antiferromagnets with spin liquid state in experiment are triangular antiferromangets. We studied the spin-1/2 J1-J2 Heisenberg model on trianglar lattice using DMRG (arXiv:1504.00654). We found a non-magnetic phase between two magnetically order phases, which has neither magnetic nor dimer orders and was identified as a quantum spin liquid. By inserting flux, we found two competing ground states in two sectors in the non-magnetic phase. Interestingly, while one state has strong lattice nematic order, the other one has chiral order. It seems that there is a competing between the time-reversal symmetry breaking and preserving spin liquids in finite-site systems.

We have also studied the bipartite frustrated magnetic systems on the square (Phys. Rev. Lett. 113, 027201 (2014)) and honeycomb lattices (Phys. Rev. B 88, 165138 (2013)) Different from the non-bipartite triangular and kagome lattices, the non-magnetic phases in these two models were identified as the plaquette-valence-bond (PVB) state, which breaks lattice translational symmetry. The spin liquid behaviors found in the previous studies were found unstable with growing system width in our DMRG calculations.

(II) Numerical characterizations of topological ordered states in ED and DMRG simulations

Topological order is a new state of matter which cannot be described by the conventional Landau theory but originates from the long-range entanglement in the systems. Two typical topological ordered states are quantum spin liquid and FQHE states. How to describe topological orders is an important and challenge question in condensed matter field for several years. The topological ordered states have the topological degenerate ground states, quasiparticles with fractional statistics, and nontrivial topological entanglement entropy. However, these quantities sometimes cannot determine the topological order. Recently, it was found that the entanglement spectra of some topological ordered states have the chiral edge spectrum with the counting rule consistent with conformal-field theory. And the mininum entangled states can be used to construct the modular matrix, which includes all the information of the statistics of quasiparticles and could be used to identify the different topological orderes. By using ED and DMRG simulations, we obtained the modular matrix for Abelian (Phys. Rev. B 88, 035122 (2013)) and non-Abelian topological states (Phys. Rev. Lett. 112, 096803 (2014),arXiv:1502.05076,arXiv:1412.8115) in different systems. Also we can find the chiral edge mode of entanglement spectrum in DMRG calculations.