We study four different models of Chern insulators in the presence of strong electronic repulsion at partial fillings. We observe that all cases exhibit a Laughlin-like phase at filling fraction 1/3. We provide evidence of such a strongly correlated topological phase by studying both the energy and the entanglement spectra. In order to identify the key ingredients of the emergence of Laughlin physics in these systems, we show how they are affected when tuning the band structure. We also address the question of the relevance of the Berry curvature flatness in this problem. Using three-body interactions, we show that some models can also host a topological phase reminiscent of the ν = 1/2 Pfaffian Moore-Read state. Additionally, we identify the structures indicating cluster correlations in the entanglement spectra.

We introduce a Bloch-like basis in a C-component lowest Landau level fractional quantum Hall (FQH) effect, which entangles the real and internal degrees of freedom and preserves an Nx × Ny full lattice translational symmetry. We implement the Haldane pseudopotential Hamiltonians in this new basis. Their ground states are the model FQH wave functions, and our Bloch basis allows for a mutatis mutandis transcription of these model wave functions to the fractional Chern insulator (FCI) of arbitrary Chern number C, obtaining wave functions different from all previous proposals. For C > 1, our wave functions are related to color-dependent magnetic-flux inserted versions of Halperin and non-Abelian color-singlet states. We then provide large-size numerical results for both the C = 1 and C = 3 cases. This new approach leads to improved overlaps compared to previous proposals. We also discuss the adiabatic continuation from the FCI to the FQH in our Bloch basis, both from the energy and the entanglement spectrum perspectives.

We propose an improved scheme to construct many-body trial wave functions for fractional Chern insulators (FCI), using one-dimensional localized Wannier basis. The procedure borrows from the original scheme on a continuum cylinder, but is adapted to finite-size lattice systems with periodic boundaries. It fixes several issues of the continuum description that made the overlap with the exact ground states insignificant. The constructed lattice states are translationally invariant, and have the correct degeneracy as well as the correct relative and total momenta. Our prescription preserves the (possible) inversion symmetry of the lattice model, and is isotropic in the limit of flat Berry curvature. By relaxing the maximally localized hybrid Wannier orbital prescription, we can form an orthonormal basis of states which, upon gauge fixing, can be used in lieu of the Landau orbitals. We find that the exact ground states of several known FCI models at ν = 1/3 filling are well captured by the lattice states constructed from the Laughlin wave function. The overlap is higher than 0.99 in some models when the Hilbert space dimension is as large as 3 × 10 4 in each total momentum sector.

Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z3 ReadRezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z3 Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function.PACS numbers: 05.30. Pr, 73.43.Cd, 03.67.Mn Non-Abelian anyons have been the focus of much theoretical and experimental interest due to the exciting prospect of topologically fault-tolerant quantum computing . As noted by Kitaev [1], the topological degeneracy of these exotic excitations allows nonlocal storage of quantum information, while adiabatic braiding implements unitary quantum gates. Candidates [22][23][24] for their physical realization are the quasiholes in certain fractional quantum Hall states [25], in particular, those around the plateaus at fillings ν = 5/2 and 12/5 [26][27][28]. Their model wave functions, namely, the Moore-Read [29] (MR) and the Z 3 Read-Rezayi [30] (RR) states, enjoy an elegant first-quantized rewriting [29,31] in terms of conformal field theory [32-34] (CFT) correlators, from which many physical properties can be predicted. The strengths of this approach rest on a crucial conjecture [29]: quasihole braiding statistics can be directly read off from the monodromy of the CFT correlators. Under this conjecture, the MR quasiholes are Ising anyons, while the Z 3 RR ones are Fibonacci anyons. But the proof of the conjecture itself is lacking.The relation between statistics and monodromy was originally established for the Laughlin state [35] through the plasma analogy [36]. Assuming sufficient quasihole separations, the statistics-monodromy equivalence holds true when the plasma is in the screening phase. With considerable effort, this line of argument was recently extended to the MR state [37][38][39], in agreement with finite-size numerics [40][41][42]. More complicated states like the Z 3 RR still remain uncharted territory for both analytics and numerics, despite their capacity for universal quantum computation [2][3][4]. Moreover, wave functions constructed from nonunitary field theories (such as the Gaffnian [43]) are conjectured not to give rise to sensible statistics [38], yet the microscopic symptom of such pathology is still under investigation [44].In this Letter, we aim to settle the aforementioned issues through numerical studies of certain model wave functions. Until very recently, this was a daunting task due to the exponentially larg...

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one-and two-component FQH systems at total filling fraction ν = n + 2/3, for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here, we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2/3, including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2/3 bilayers, we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in singlecomponent systems at ν = 8/3, we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8/3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively.