arXiv subjects

Wei-Wei Luo

Publications and source records attributed to Wei-Wei Luo.

10 recordsLinked to original sources

arXiv2025

Robust non-Abelian even-denominator fractional Chern insulator in twisted bilayer MoTe$_2$

A recent experiment observes a series of quantum spin Hall effects in transition metal dichalcogenide moiré MoTe$_2$ [K. Kang, et. al, Nature 628, 522-526 (2024)]. Among them, the vanishing Hall signal at the filling factor $ν=3$ implies a possible realization of a time-reversal pair of the even-denominator fractional Chern insulators (FCIs). Inspired by this discovery, we investigate whether a robust incompressible quantum Hall liquid can be stabilized in the half-filled Chern band of twisted MoTe$_2$ bilayers. We use the continuum model with parameters relevant to twisted MoTe$_2$ bilayers and obtain three consecutive nearly flat Chern bands with the same Chern number. Crucially, when the second moiré miniband is half-filled,signatures of non-Abelian frctional quantum Hall state are found via exact diagonalization calculations, including the stable six-fold ground state degeneracy that grows more robust with the lattice size and is consistent with an even-denominator FCI state. We further perform flux insertion simulations to reveal a 1/2 quantized many-body Chern number as direct evidence of topological order. Furthermore, the ground state density structure factors show no sharp peak, indicating no charge density wave order. These evidences signal the potential of realizing the non-Abelian state at zero magnetic field in twisted bilayer MoTe$_2$ at the fractional hole filling 3/2.

cond-mat.str-el↗

arXiv2024

Chiral Spin Liquid on a Shastry-Sutherland Heisenberg Antiferromagnet

We demonstrate the existence of a topological chiral spin liquid in the frustrated Shastry-Sutherland Heisenberg model with an additional spin chirality interaction, using numerically unbiased exact diagonalization and density matrix renormalization group methods. We establish a quantum phase diagram where conventional phases, including dimer singlet, plaquette singlet, N{\' e}el and collinear phase, can be clearly identified by suitable local order parameters. Among them a $SU(2)_1$ chiral spin liquid emerges in the highly frustrated region, which is unambiguously identified by two topologically degenerate ground states, modular matrix, and characteristic level counting in entanglement spectrum, featuring the same topological order of $ν=1/2$ bosonic Laughlin state. The phase boundaries among the different orders are determined by the energy level crossing analysis and wave function fidelity susceptibility.

cond-mat.str-el↗

arXiv2022

Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$1/2$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in spin-$3/2$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian CSL emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in spin-$3/2$ system suggests a new route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.

cond-mat.str-el↗

arXiv2022

Topological states in a dimerized system with staggered magnetic fluxes

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional first-order and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At $\frac{1}{2}$-filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the $\mathcal{C}=2$ Chern insulator states. At $\frac{1}{4}$-filling, we find a $\mathcal{C}=0$ topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.

cond-mat.mes-hall↗

arXiv2021

Bosonic fractional Chern insulating state at integer fillings in multi-band system

The integer quantum Hall state occurs when the Landau levels are fully occupied by the fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by the strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of the hard-core bosons in a multi-band lattice model hosting topological flat bands with high Chern number. The previously proposed $ν=1/3$ fractional Chern insulating state inherited from the high Chern number $C=2$ of the lowest topological flat band is revisited by the infinite density matrix renormalization group algorithm. In particular, we numerically identify a bosonic $1/2$-Laughlin-like fractional Chern insulating state at the integer fillings. We show two lower topological flat bands jointly generate an effective $C=1$ Chern band with half-filling. Furthermore, we find a strictly particle-hole-like symmetry between the $ν$ and $3-ν$ filling in our model. These findings extend our understanding of quantum Hall states and offer a new route to realize the novel fractional states in the system with multi-bands and high-Chern numbers.

cond-mat.str-el↗

arXiv2020

Non-Abelian Fractional Chern Insulator in Disk Geometry

Non-Abelian (NA) fractional topological states with quasi-particles obeying NA braiding statistics have attracted intensive attentions for both its fundamental nature and the prospect for topological quantum computation. To date, there are many models proposed to realize the NA fractional topological states, such as the well-known Moore-Read quantum Hall states and the Non-Abelian fractional Chern insulators (NA-FCIs). Here, we investigate the NA-FCI in disk geometry with three-body hard-core bosons loaded into a topological flat band. This stable $ν= 1$ bosonic NA-FCI is characterized by the edge excitations and the ground-state angular momentum. Based on the generalized Pauli principle and the Jack polynomials, we successfully construct a trial wave function for the NA-FCI. Moreover, a $ν= 1/2$ Abelian FCI state emerges with the increase of the on-site interaction and it can be identified with the help of the trial wave function as well. Our findings not only lead to an optimal wave function for the NA-FCI, but also directly provide an effective approach for future researches on paired topological states.

cond-mat.str-el↗

arXiv2019

Fractional Chern Insulators in Singular Geometries

The fractional quantum anomalous Hall (FQAH) states or fractional Chern insulator (FCI) states have been studied on two-dimensional (2D) flat lattices with different boundary conditions. Here, we propose the geometry-dependent FCI/FQAH states that interacting particles are bounded on 2D singular lattices with arbitrary $n$-fold rotational symmetry. Based on the generalized Pauli principle, we construct trial wave functions for the singular-lattice FCI/FQAH states with the aid of an effective projection approach, and compare them with the exact diagonalization results. High wave-function overlaps show that the singular-lattice FCI/FQAH states are certainly related to the geometric factor $β$. More interestingly, we observe some exotic degeneracy sequences of edge excitations in these singular-lattice FCI/FQAH states, and provide an explanation that two branches of edge excitations mix together.

cond-mat.str-el↗

arXiv2017

Chern Insulators on Singular Geometries

Topological quantum states have been proposed and investigated on two-dimensional flat surfaces or lattices with different geometries like the plane, cylinder and torus. Here, we study quantum anomalous Hall (QAH) or Chern insulator (CI) states on two-dimensional singular surfaces (such as conical and helicoid-like surfaces). Such singular geometries can be constructed based on the disk geometry and a defined unit sector with $n$-fold rotational symmetry. The singular geometry induces novel and intriguing features of CI/QAH states, such as in-gap and in-band core states, charge fractionalization, and multiple branches of edge excitations.

cond-mat.mes-hall↗

arXiv2015

Wave Functions for Fractional Chern Insulators on Disk Geometry

Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands. These systems exhibit similar fractionalization phenomena as the conventional fractional quantum Hall (FQH) systems. Using the mapping relationship between the FQH states and the FCI/FQAH states, we construct the many-body wave functions of the fermionic FCI/FQAH states on the disk geometry with the aid of the generalized Pauli principle (GPP) and the Jack polynomials. Compared with the ground state by exact diagonalization method, the wave-function overlap is higher than $0.97$ even when the Hilbert space dimension is as large as $3\times10^6$. We also use the GPP and the Jack polynomials to construct edge excitations for the ferminoic FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems reproduce the prediction of the chiral Luttinger liquid theory, complementing the exact diagonalization results with larger lattice sizes and more particles.

cond-mat.str-el↗

arXiv2013

Edge Excitations in Fractional Chern Insulators

Recent theoretical works have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role to obtain a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagomé-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.

cond-mat.str-el↗