arXiv subjects

Zhao Liu

Publications and source records attributed to Zhao Liu.

At least 127 records · Page 7Linked to original sources

arXiv2017

Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States

We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.

cond-mat.str-el↗

arXiv2017

Transport properties of an interacting Majorana chain

We study a one-dimensional (1D) chain of $2N$ Majorana bound states, which interact through a local quartic interaction. This model describes for example the edge physics of a quasi 1D stack of $2N$ Kitaev chains with modified time-reversal symmetry $Tγ_iT^{-1}=γ_i$, which precludes the presence of quadratic coupling. The ground state of our 1D Majorana chain displays a four-fold periodicity in $N$, corresponding to the four distinct topological classes of the stacked Kitaev chains. We analyze the transport properties of the 1D Majorana chain, when probed by local conductors located at its ends. We find that for finite but large $N$, the scattering matrix partially reflects the four-fold periodicity, and the chain exhibits strikingly different transport properties for different chain lengths. In the thermodynamic limit, the 1D Majorana chain hosts a robust many-body zero mode, which indicates that the corresponding stacked two-dimensional bulk system realizes a weak topological phase.

cond-mat.mes-hall↗

arXiv2017

BP_5 Monolayer with Multiferroicity and Negative Poisson's Ratio: A Prediction by Global Optimization Method

Based on variable components global optimization algorithm, we predict a stable two-dimensional (2D) phase of boron phosphide with 1:5 stoichiometry, i.e. boron pentaphosphide (BP_5) monolayer, which has a lower formation energy than that of the commonly believed graphitic phase (g-BP). BP_5 monolayer is a multiferroic material with coupled ferroelasticity and ferroelectricity. The predicted reversible strain is up to 41.41%, which is the largest among all reported ferroelastic materials. Due to the non-centrosymmetric structure and electronegativity differences between boron and phosphorus atoms, an in-plane spontaneous polarization of 326.0 pC/m occurs in BP_5. Moreover, the recently hunted negative Poisson's ratio property, is also observed in BP_5. As an indirect semiconductor with a band gap of 1.34 eV, BP_5 displays outstanding optical and electronic properties, for instance strongly anisotropic visible-light absorption and high carrier mobility. The rich and extraordinary properties of BP_5 make it a potential nanomaterial for designing electromechanical or optoelectronic devices, such as nonvolatile memory with conveniently readable/writeable capability. Finally, we demonstrate that AlN (010) surface could be a suitable substrate for epitaxy growth of BP_5 monolayer.

cond-mat.mtrl-sci↗

arXiv2016

Largest Particle Simulations Downgrade the Runaway Electron Risk for ITER

Fusion energy will be the ultimate clean energy source for mankind. One of the most visible concerns of the future fusion device is the threat of deleterious runaway electrons (REs) produced during unexpected disruptions of the fusion plasma. Both efficient long-term algorithms and super-large scale computing power are necessary to reveal the complex dynamics of REs in a realistic fusion reactor. In the present study, we deploy the world's fastest supercomputer, Sunway TaihuLight, and the newly developed relativistic volume-preserving algorithm to carry out long-term particle simulations of 10^7 sampled REs in 6D phase space, which involves simulation scale of 10^18 particle-steps, the largest ever achieved in fusion research. Our simulations show that in a realistic fusion reactor, the concern of REs is not as serious as previously thought. Specifically, REs are confined much better than previously predicted and the maximum average energy is in the range of 150MeV, less than half of previous estimate.

physics.plasm-ph↗

arXiv2016

Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids

We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder -- the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.

cond-mat.str-el↗

arXiv2016

Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase

Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil "finger print" evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian $(331)$ Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a "proof-of-principle" demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral $p-$wave pairing states.

cond-mat.str-el↗

arXiv2016

Model Fractional Chern Insulators

We devise local lattice models whose ground states are model fractional Chern insulators---Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement gaps. Most saliently, we construct exact parent Hamiltonians for two distinct families of bosonic lattice generalizations of the $\mathcal{Z}_k$ parafermion quantum Hall states: (i) color-entangled fractional Chern insulators at band filling fractions $ν=k/(\mathcal{C}+1)$ and (ii) nematic states at $ν=k/2$, where $\mathcal{C}$ is the Chern number of the lowest band in our models. In spite of a fluctuating Berry curvature, our construction is partially frustration free: the ground states reside entirely within the lowest band and exactly minimize a local $(k+1)$-body repulsion term by term. In addition to providing the first known models hosting intriguing states such as higher Chern number generalizations of the Fibonacci anyon quantum Hall states, the remarkable stability and finite-size properties make our models particularly well-suited for the study of novel phenomena involving e.g. twist defects and proximity induced superconductivity, as well as being a guide for designing experiments.

cond-mat.str-el↗

arXiv2015

Phase diagram of $ν=\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings

We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $ν=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the inter-layer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both inter-layer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Inter-layer interactions favor a ferromagnetic phase when the system is $SU(2)$ symmetric, while the inter-layer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the $(220)$ Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.

cond-mat.str-el↗

arXiv2015

Non-Abelian phases in two-component $ν=2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons

Recent theoretical insights into the possibility of non-Abelian phases in $ν=2/3$ fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body interlayer couplings on the $(330)$ bilayer state and exactly solve the Hamiltonian for up to $14$ electrons on sphere and torus geometries. We consider interlayer tunneling, short-ranged repulsive/attractive pseudopotential interactions and Coulomb repulsion. We find a 6-fold ground-state degeneracy on the torus when the interlayer hollow-core interaction is dominant. To identify the topological nature of this phase we measure the orbital-cut entanglement spectrum, quasihole counting, topological entanglement entropy, and wave-function overlap. Comparing the numerical results to the theoretical predictions, we interpret this 6-fold ground-state degeneracy phase to be the non-Abelian bilayer Fibonacci state.

cond-mat.str-el↗

arXiv2015

Fermionic non-Abelian fractional Chern insulators from dipolar interactions

We study fermions on a triangular lattice model that exhibits topological flatbands characterized by nonzero Chern numbers. Our scheme stems from the well-known Hofstadter model but the next-nearest-neighbor hopping is introduced, which is crucial for tuning the lowest band to be nearly flat. Differing from previous proposals with the necessity of multiparticle interactions, we consider the more realistic long-range dipolar interaction combined with two-body short-range attractions between fermions. We show the realization of the non-Abelian $ν=1/2$ Moore-Read fractional Chern insulators, and strong evidence for the existence of the more exotic $ν=3/5$ Read-Rezayi fractional Chern insulators. Our results provide insights for the experimental realization of these exotic states by realistic two-body interactions and thus facilitates the implementation of the universal topological quantum computation.

cond-mat.str-el↗

arXiv2015

Characterization of quasiholes in fractional Chern insulators

We provide a detailed study of the Abelian quasiholes of $ν=1/2$ bosonic fractional quantum Hall states on the torus geometry and in fractional Chern insulators. We find that the density distribution of a quasihole in a fractional Chern insulator can be related to that of the corresponding fractional quantum Hall state by choosing an appropriate length unit on the lattice. This length unit only depends on the lattice model that hosts the fractional Chern insulator. Therefore, the quasihole size in a fractional Chern insulator can be predicted for any lattice model once the quasihole size of the corresponding fractional quantum Hall state is known. We discuss the effect of the lattice embedding on the quasihole size. We also perform the braiding of quasiholes for fractional Chern insulator models to probe the fractional statistics of these excitations. The numerical values of the braiding phases accurately match the theoretical predictions.

cond-mat.str-el↗

arXiv2015

Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators

We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall state. By contrast, in the three-dimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates.

cond-mat.str-el↗

arXiv2014

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

cond-mat.str-el↗

arXiv2013

Non-Abelian Fractional Chern Insulators from Long-Range Interactions

The recent theoretical discovery of fractional Chern insulators (FCIs) has provided an important new way to realize topologically ordered states in lattice models. In earlier works, on-site and nearest neighbor Hubbard-like interactions have been used extensively to stabilize Abelian FCIs in systems with nearly flat, topologically nontrivial bands. However, attempts to use two-body interactions to stabilize non-Abelian FCIs, where the ground state in the presence of impurities can be massively degenerate and manipulated through anyon braiding, have proven very difficult in uniform lattice systems. Here, we study the remarkable effect of long-range interactions in a lattice model that possesses an exactly flat lowest band with a unit Chern number. When spinless bosons with two-body long-range interactions partially fill the lowest Chern band, we find convincing evidence of gapped, bosonic Read-Rezayi (RR) phases with non-Abelian anyon statistics. We characterize these states through studying topological degeneracies, the overlap between the ground states of two-body interactions and the exact RR ground states of three- and four-body interactions, and state counting in the particle-cut entanglement spectrum. Moreover, we demonstrate how an approximate lattice form of Haldane's pseudopotentials, analogous to that in the continuum, can be used as an efficient guiding principle in the search for lattice models with stable non-Abelian phases.

cond-mat.str-el↗

arXiv2013

Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices

Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C|=1 and |C|>1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.

cond-mat.str-el↗

arXiv2013

Topological Flat Band Models and Fractional Chern Insulators

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating phases, with an altogether much richer and less explored phenomenology. Most saliently, lattice generalizations of fractional quantum Hall states, dubbed fractional Chern insulators, have recently been predicted to be stabilized by interactions within nearly dispersionless bands with non-zero Chern number, $C$. Contrary to their continuum analogues, these states do not require an external magnetic field and may potentially persist even at room temperature, which make these systems very attractive for possible applications such as topological quantum computation. This review recapitulates the basics of tight-binding models hosting nearly flat bands with non-trivial topology, $C\neq 0$, and summarizes the present understanding of interactions and strongly correlated phases within these bands. Emphasis is made on microscopic models, highlighting the analogy with continuum Landau level physics, as well as qualitatively new, lattice specific, aspects including Berry curvature fluctuations, competing instabilities as well as novel collective states of matter emerging in bands with $|C|>1$. Possible experimental realizations, including oxide interfaces and cold atom implementations as well as generalizations to flat bands characterized by other topological invariants are also discussed.

cond-mat.str-el↗

arXiv2013

Bulk-edge correspondence in fractional Chern insulators

It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems -- fractional Chern insulators and the fractional quantum Hall states -- via generalization of a gauge-fixed Wannier-Qi construction in the cylinder geometry. Our setup offers a number of important advantages compared to the earlier exact diagonalization studies on a torus. Most notably, it gives access to edge states and to a single-cut orbital entanglement spectrum, hence to the physics of bulk-edge correspondence. It is also readily implemented in the state-of-the-art density matrix renormalisation group method that allows for numerical simulations of significantly larger systems. We demonstrate our general approach on examples of flat-band models on ruby and kagome lattices at bosonic filling fractions $ν=1/2$ and $ν=1$, which show the signatures of (non)-Abelian phases, and establish the correspondence between the physics of edge states and the entanglement in the bulk. Notably, we find that the non-Abelian $ν=1$ phase can be stabilized by purely on-site interactions in the presence of a confining potential.

cond-mat.str-el↗

arXiv2013

From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum

The possibility of realizing lattice analogs of fractional quantum Hall (FQH) states, so-called fractional Chern insulators (FCIs), in nearly flat topological (Chern) bands has attracted a lot of recent interest. Here, we make the connection between Abelian as well as non-Abelian FQH states and FCIs more precise. Using a gauge-fixed version of Qi's Wannier basis representation of a Chern band, we demonstrate that the interpolation between several FCI states, obtained by short-range lattice interactions in a spin-orbit-coupled kagome lattice model, and the corresponding continuum FQH states is smooth: the gap remains approximately constant and extrapolates to a finite value in the thermodynamic limit, while the low-lying part of the orbital entanglement spectrum remains qualitatively unaltered. The orbital entanglement spectra also provide a first glimpse of the edge physics of FCIs via the bulk-boundary correspondence. Corroborating these results, we find that the squared overlaps between the FCI and FQH ground states are as large as 98.7% for the 8-electron Laughlin state at $ν=1/3$ (consistent with an earlier study) and 97.8% for the 10-electron Moore-Read state at $ν=1/2$. For the bosonic analogs of these states, the adiabatic continuity is also shown to hold, albeit with somewhat smaller associated overlaps, etc. Although going between the Chern bands to the Landau level problem is often smooth, we show that this is not always the case by considering fermions at filling fraction $ν=4/5$, where the interpolation between Hamiltonians describing the two systems results in a phase transition.

cond-mat.str-el↗