We study the system of two localized anyons in the lowest Landau level and show how anyonic signatures extrapolating between anti-bunching tendencies of fermions and bunching tendencies of bosons become manifest in the two-particle correlations. Towards probing these correlations, we discuss the influence of a saddle potential on these anyons; we exploit analogies from quantum optics to analyze the time-evolution of such a system. We show that the saddle potential can act as a beam splitter akin to those in bosonic and fermionic systems and can provide a means of measuring the derived anyonic signatures.
We review the general strategy of topologically protected quantum information processing based on non-Abelian anyons, in which quantum information is encoded into the fusion channels of pairs of anyons and in fusion paths for multi-anyon states, realized in two-dimensional fractional quantum Hall systems. The quantum gates which are needed for the quantum information processing in these multi-qubit registers are implemented by exchange or braiding of the non-Abelian anyons that are at fixed positions in two-dimensional coordinate space. As an example we consider the Pfaffian topological quantu…
Fractionalized anyons in counterflowing Quantum Hall Liquids
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大李政道研究所）；Department of Physics, Stockholm University, AlbaNova University Center（斯德哥尔摩大学阿尔巴诺瓦大学中心物理系）；Department of Physics, KTH-Royal Institute of Technology（瑞典皇家理工学院物理系）；Wallenberg Initiative Materials Science for Sustainability, Department of Physics, KTH Royal Institute of Technology（瑞典皇家理工学院物理系瓦伦堡可持续材料科学倡议）
Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor $ν=1/m$ (where m is an odd integer) have been predicted to obey abelian fractional statistics, with a phase $φ$ associated with the exchange of two particles equal to $π/m$. However, despite numerous experimental attempts, clear signatures of fractional statistics remain elusive. Here we experimentally demonstrate abelian fractional statistics at filling factor $ν=1/3$ by measu…
We investigate the response to modular transformations and the fractional statistics of Abelian multi-component fractional quantum Hall (FQH) states. In particular, we analytically derive the modular matrices encoding the statistics of anyonic excitations for general Halperin states using the conformal field theories (CFTs). We validate our theory by several microscopic examples, including the spin-singlet state using anyon condensation picture and the Halperin (221) state in a topological flat-band lattice model using numerical calculations. Our results, uncovering that the modular matrices a…
The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a new type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. We provide analytical wave functions and exact few-body parent Hamiltonians, and we show numerically for several different Hausdorff dimensions between 1 and 2 that the systems host anyons. We also find examples of fractional quantum Hall physics in fractals with Hausdorff dimension 1 and ln(4)/ln(5). Our results suggest that the local structur…
Many-Anyon Braiding in Non-Abelian Fractional Quantum Hall Effect with Hybrid Monte Carlo Simulation
The University of Hong Kong（香港大学）；HK Institute of Quantum Science & Technology（香港量子研究院）；State Key Laboratory of Optical Quantum Materials（光学量子材料国家重点实验室）；Nanyang Technological University（南洋理工大学）
We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For interacting electrons, the statistical transmutation from anyons to bosons allows us to explicitly derive the microscopic statistical interaction between the anyons, in the form of the effective two-body and few-body interactions. This also leads to a number of unexpected topological phases of the single component bosonic fractional quantum Hall effect that…
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 do…
Spin Splitter without Spin-Split Bands: A Reconfigurable Altermagnetic Texture
College of Physics Science and Technology, Yangzhou University（扬州大学物理科学与技术学院）；College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院）；Lanzhou Center for Theoretical Physics, Lanzhou University（兰州大学理论物理中心）；Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University（兰州大学量子理论与应用教育部重点实验室）；School of Mathematics and Physics, Southwest University of Science and Technology（西南科技大学数学与物理学院）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）
Quantum information scrambling is the spread of local information into correlation throughout the entire quantum many-body system. This concept has become a central topic in different contexts. In this work, we restate the connection between anyon condensation and topological quantum information scrambling in quantum Hall interfaces. We consider the interface between the Abelian Halperin-330 state and the non-Abelian Read-Rezayi state. We verify explicitly that the interface can be fully gapped. This allows the transmutation of local pseudospin information carried by an Abelian anyon into topo…
It has been demonstrated numerically, mainly by considering ground state properties, that fractional quantum Hall physics can appear in lattice systems, but it is very difficult to study the anyons directly. Here, I propose to solve this problem by using conformal field theory to build semi-analytical fractional quantum Hall lattice models having anyons in their ground states, and I carry out the construction explicitly for the family of bosonic and fermionic Laughlin states. This enables me to show directly that the braiding properties of the anyons are those expected from analytical continua…
In a Laughlin fractional quantum Hall state, one- and two-quasihole states can be obtained by diagonalizing the many-body Hamiltonian with a trapping potential or, for larger systems, from the linear combination of the edge Jack polynomials. The quasihole states live entirely in the subspace of the lowest-energy branch in the energy spectrum with a fixed number of orbits, or a hard-wall confinement. The reduction in the Hilbert space dimension facilitates the study of time evolution of the quasihole states after, say, the removal of the trapping potential. We explore the quench dynamics under …
The $ν=12/5$ fractional quantum Hall plateau observed in $\mathrm{GaAs}$ semiconductor wells is a suspect in the search for non-Abelian Fibonacci anyons. Using the infinite density matrix renormalization group, we find clear evidence that fillings $ν= 12/5$ and $ν=13/5$ are in the $k = 3$ Read-Rezayi phase in the absence of particle-hole symmetry-breaking effects. The lowest energy charged excitation is identified as a non-Abelian Fibonacci anyon, distinguished from its Abelian counterpart by its local quadrupole moment. However, several experiments at $ν= 13/5$ observe a re-entrant integer qu…
Anyon collision experiments have recently demonstrated the ability to discriminate between fermionic and anyonic statistics. However, only one type of anyons associated with the simple Laughlin state at filling factor $ν=1/3$ has been probed so far. It is now important to establish anyon collisions as quantitative probes of fractional statistics for more complex topological orders, with the ability to distinguish between different species of anyons with different statistics. In this work, we use the anyon collider to compare the Laughlin $ν=1/3$ state, which is used as the reference state, wit…
One remarkable feature of strongly correlated systems is the phenomenon of fractionalization where quasiparticles carry only a fraction of the charge or spin of the elementary constituents. Such quasiparticles often present anyonic statistics in two dimensions and lie at the heart of the fractional quantum Hall effect. We discuss the observation of fractionalization and anyonic statistics already in the integer quantum Hall effect coupled to a metallic island. A continuous fractional emitter is proposed, which sends dilute beams of non-integer charges, and its full counting statistics is obtai…
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this paper, we consider a simple bilayer fractional quantum Hall (FQH) system with the $1/3$ Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous `Fibonacci'anyon, whose non-Abelian statistics is powerful enough for universal TQC. Ou…
We show the low-lying excitations at filling factor $ν=n+1/3$ with realistic interactions are contained completely within the well-defined Hilbert space of "Gaffnian quasiholes". Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like "partons" with "asymptotic freedom" mediated by neutral excitations acting as "gluons". Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bounded and fractionalise with rich dynamical properties. By studying the effective interactions b…
Recent pioneering works have set the stage for exploring anyon braiding statistics from negative current cross-correlations along two intersecting quasiparticle beams. In such a dual-source - analyzer quantum point contact setup, also referred to as 'collider', the anyon exchange phase of fractional quantum Hall quasiparticles is predicted to be imprinted into the cross-correlations characterized by an effective Fano-factor $P$. In the case of symmetric incoming quasiparticle beams, conventional fermions result in a vanishing $P$. In marked contrast, we observe signatures of anyon statistics i…
The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions. As opposed to conventional Landau-Ginzburg-Wilson phases, which are classified on the basis of the spontaneous breaking of an underlying symmetry, topologically ordered phases, such as those occurring in the fractional quantum Hall effect, are absolutely stable, not requiring any such symmetry. Recently, though, it has been realized that symmetries, which may still be present in suc…
