Bosonic fractional quantum Hall states on a finite cylinder

Rosson, Paolo; Lubasch, Michael; Kiffner, Martin; Jaksch, Dieter

doi:10.1103/physreva.99.033603

Cited by 30 publications

(22 citation statements)

References 68 publications

(82 reference statements)

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“…This condition might be difficult to reach with ultracold atoms; however, as suggested in Refs. [40,43,47], we believe that considering finite-strength interactions instead of the hard-core ones should not modify our results in a considerable way. A comprehensive analysis of the case of soft-core interactions is left for a future work.…”

Section: Discussionmentioning

confidence: 75%

“…In this context, several theoretical studies investigated the adiabatic preparation of different FCI states and the associated phase diagrams [35][36][37][38][39][40]. Some works focused on the numerical characterization of these states by inspecting key quantities such as the many-body Chern number, the particle entanglement spectrum, the behavior of the correlation functions and the topological entanglement entropy [41][42][43], while others proposed ex-perimentally applicable schemes to identify these elusive strongly correlated phases of matter [44,45]. Finally, growing attention has been given to FCI bulk excitations [46][47][48][49], which (similarly to those characterizing the FQH effect) display fractional charge and anyonic statistics.…”

Section: Introductionmentioning

confidence: 99%

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Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

Macaluso

Comparin

Umucalılar

et al. 2020

Phys. Rev. Research

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We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling ν = 1/2, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For this purpose we employ a Tree Tensor Network technique, which allows us to study systems with up to N = 18 particles on a 16 × 16 lattice and experiencing an additional harmonic confinement. First, we observe the quantization of the quasihole charge at fractional values and its robustness against the shape and strength of the impurity potentials used to create and localize such excitations. Then, we numerically characterize quasihole anyonic statistics by applying a discretized version of the relation connecting the statistics of quasiholes in the lowest Landau level to the depletions they create in the density profile [E. Macaluso et al., arxiv:1903.03011]. Our results give a direct proof of the anyonic statistics for quasiholes of fractional Chern insulators, starting from a realistic Hamiltonian. Moreover, they provide strong indications that this property can be experimentally probed through local density measurements, making our scheme readily applicable in state-of-the-art experiments with ultracold atoms and superconducting qubits.arXiv:1910.05222v1 [cond-mat.quant-gas]

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Section: Discussionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

Macaluso

Comparin

Umucalılar

et al. 2020

Phys. Rev. Research

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show abstract

“…We determine the ground state by performing DMRG calculations [45] with our TNT library [46]. To this end, we map the 2D lattice to a 1D chain by sequentially going through each column of the lattice from bottom to top as in [47]. For our model in Eq.…”

Section: N T 7 W Q 1 F F N G U 4 a A O 4 R H C O I C 6 3 E A D M K mentioning

confidence: 99%

Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems

et al. 2020

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We use state-of-the-art density matrix renormalization group calculations in the canonical ensemble to determine the phase diagram of the dipolar Bose-Hubbard model on a finite cylinder. We consider several observables that are accessible in typical optical lattice setups and assess how well these quantities perform as order parameters. We find that, especially for small systems, the occupation imbalance is less susceptible to boundary effects than the structure factor in uncovering the presence of a periodic density modulation. By analysing the non-local correlations, we find that the appearance of supersolid order is very sensitive to boundary effects, which may render it difficult to observe in quantum gas lattice experiments with a few tens of particles. Finally, we show how density measurements readily obtainable on a quantum gas microscope allow distinguishing between superfluid and solid phases using unsupervised machine-learning techniques. arXiv:1909.09099v1 [cond-mat.quant-gas]

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“…We open our discussion on the 1D-2D crossover by focusing on the CDW amplitude of the Laughlin state realized on the N w -leg ladder. We choose to consider a geometry of a cylinder rather than a torus, since it is more realistic in experimental and numerical contexts [59,110]. In 2D, the fate of putting a FQH state on a torus or on a cylinder is different, since the latter has edges.…”

Section: Wire Construction: Charge Density Wave and 1d-2d Crossovermentioning

confidence: 99%

Pretopological fractional excitations in the two-leg flux ladder

Strinati,

Sahoo,

Shtengel

et al. 2019

Preprint

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Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between this topological regime and the Tao-Thouless thin torus quasi-1D limit. Using the wire-construction approach, we analyze an emergent charge density wave (CDW) signifying the break-down of topological order, and relate its phase shifts to Wilson loop operators. The CDW amplitude decreases exponentially with the torus circumference once it exceeds the transverse correlation length controllable by the inter-wire coupling. By means of numerical simulations based on the matrix product states (MPS) formalism, we explore the extreme quasi-1D limit in a two-leg flux ladder and present a simple recipe for probing fractional charge excitations in the ν = 1/2 Laughlin-like state of hard-core bosons. We discuss the possibility of realizing this construction in cold-atom experiments. We also address the implications of our findings to the possibility of producing non-Abelian zero modes. As known from rigorous no-go theorems, topological protection for exotic zero modes such as parafermions cannot exist in 1D fermionic systems and the associated degeneracy cannot be robust. Our theory of the 1D-2D crossover allows to calculate the splitting of the degeneracy, which vanishes exponentially with the number of wires, similarly to the CDW amplitude.

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Bosonic fractional quantum Hall states on a finite cylinder

Cited by 30 publications

References 68 publications

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems

Pretopological fractional excitations in the two-leg flux ladder

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