Some Recent Research Themes

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 novel phases using exact diagonalization (ED) and density-matrix renormalization group (DMRG) simulations, and applying new concepts, algorithms and codes that will significantly advance our understanding of the behavior of materials.

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 (Phys. Rev. B 92, 014424 (2015)).

Another frustrated antiferromagnets with candidate spin liquid state are square spin=½ J1-J2 Heisenberg model. By means of density-matrix renormalization group calculation, the intermediate non-magnetic phases in this model was identified as the plaquette-valence-bond state, which breaks lattice translational symmetry. The spin liquid behaviors found in the previous studies were found unstable with growing system width in our density-matrix renormalization group calculations [S. S. Gong, W. Zhu, D. N. Sheng, Olexei I. Motrunich, and Matthew P. A. Fisher, “Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-12 J1−J2 Square Heisenberg Model”, Phys. Rev. Lett. 113, 027201 (2014).].

Non-Abelian states in Fractional Quantum Hall Effect

The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. Despite the great potential applications, many of the basic and practical questions remain open. They must be resolved in order for these ideas to become a reality, and they touch upon fundamental issues in physics. The first question is whether the non-Abelian topological phases actually exist in nature and specifically, in quantum hall systems.

One promising candidate for finding non-Abelian statistics seems to be the fractional quantum Hall state observed at the ν=12/5 plateau. In a recent paper [W. Zhu, S. S. Gong, F. D. M Haldane, D. N. Sheng, “Fractional Quantum Hall States at ν = 13/5 and 12/5 and their Non-Abelian Nature”, Phys. Rev. Lett. 115, 126805 (2015)], we presented what we believe to be compelling evidence that the essence of the Coulomb-interaction ground states at ν = 13/5 and 12/5 is indeed captured by the parafermion k = 3 Read-Rezayi state, in which quasiparticles obey non-Abelian “Fibonacci-anyon” statistics.

Another quasi-realistic microscopic model hosting non-Abelian topological orders is the topological flat-band lattice model or fractional Chern insulator. By utilizing the entanglement-based diagnosis, we provided a complete characterization of the universal properties of bosonic Moore-Read state in Haldane honeycomb lattice model, including both the edge spectrum and the bulk anyonic quasiparticle statistics (such as braiding statistics, topological spin) [W. Zhu, S. S. Gong, F. D. M. Haldane, D. N. Sheng, “Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group”, Phys. Rev. B 92 165106 (2015). ]. We also investigate the possibility of realizing non-Abelian states in double-layer systems by coupling two Abelian fractional quantum Hall states together. We find partial evidences of non-Abelian Moore-Read state by tuning the tunneling strength between two layers, for example [W. Zhu, S. S. Gong, D. N. Sheng, L. Sheng, “Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system”, Phys. Rev. B 91, 245126 (2015) ], and [W. Zhu, Zhao Liu, F. D. M. Haldane, and D. N. Sheng, “Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase”, Phys. Rev. B 94, 245147 (2016) ].

Novel Phases Driven By Electron-Electron Interactions

Non-interacting topological states of matter can be realized in band insulators with intrinsic spin-orbital couplings or external magnetic field as a result of the nontrivial band topology. In recent years, the possibility of realizing novel interaction-driven topological phase has attracted a lot of research activities, which can significantly enrich the classes of topological materials and is thus of great importance.

In our recent work [W. Zhu, S.S. Gong, T. S. Zeng, L. Fu, D. N. Sheng, “Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice”, Phys. Rev. Lett. 117, 096402 (2016)], we propose an extended fermionic Hubbard model on kagome lattice, and unveil the nature of ground state is equivalent to the quantum anomalous Hall state. This serves as the first solid evidence of topological Mott insulator from a microscopic view of point. Significantly, this work provides a “proof-of-the-principle” demonstration of interaction-driven topological phase in a “gauge-field-free” non-interacting band, without the requirement of external magnetic field or other mechanism of time-reversal symmetry explicit breaking.