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A Thouless pump can be regarded as a dynamical version of the integer quantum Hall effect. In a finite-size configuration, such topological pump displays edge modes that emerge dynamically from one bulk-band and dive into the opposite…

We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the…

Supersymmetric quantum Hall liquids are constructed on a supersphere in a supermonopole background. We derive a supersymmetric generalization of the Laughlin wavefunction, which is a ground state of a hard-core $OSp(1|2)$ invariant…

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be…

Motivated by the experiments on double monolayer graphene that observe a variety of fractional quantum Hall states [Liu et al., Nat. Phys. 15, 893 (2019); Li et al., Nat. Phys. 15, 898 (2019)], we study the special setting in which two…

Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a…

Variational wave function is proposed to describe electronic properties of an array of one-dimensional conductors coupled by transverse hopping and interaction. For weak or intermediate in-chain interaction the wave function has the…

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a…

We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors $\nu=1/q$) on torus geometry. Surprisingly, the exactly…

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an…

Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…

Recent discoveries in topological physics hold a promise for disorder-robust quantum systems and technologies. Topological states provide the crucial ingredient of such systems featuring increased robustness to disorder and imperfections.…

Ultra-thin 3D topological insulators provide a stage to study the surface physics of such materials by minimizing the bulk contribution. Further, the experimentally verified snowflake like structure of the Fermi surface leads to a hexagonal…

It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…

Wave-function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the…

We study the topological properties of quantum states for the spinless particle hopping in a Mobius ladder. This system can be regarded as a molecular device possibly engineered from the aromatic Mobius annulenes, which enjoys a pseudo-spin…

We propose an ansatz for the wave function of a non-interacting quantum particle in a deterministic quasicrystalline potential. It is applicable to both continuous and discrete models and includes Sutherland's hierarchical wave function as…

Topologically ordered states are characterized by topological quantities like the Hall conductance, topological entanglement entropy, and chiral central charge. Techniques based on the modular Hamiltonian have recently been developed to…

Hall tube with a tunable flux is an important geometry for studying quantum Hall physics, but its experimental realization in real space is still challenging. Here, we propose to realize a synthetic Hall tube with tunable flux in a…

The warping effect on the fractional quantum Hall (FQH) states in topological insulators is studied theoretically. Based on the perturbed wavefunctions, which include contributions from the warping term, analytical expressions for Haldane's…