Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1612.09184

Creating a bosonic fractional quantum Hall state by pairing fermions

Cécile Repellin·Tarik Yefsah·Antoine Sterdyniak
View original source ↗Read source document ↗Export metadata ↓

Abstract

We numerically study the behavior of spin--$1/2$ fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the non-interacting case where each spin population is prepared in a quantum Hall state with unity filling, we follow the evolution of the system as the interaction strength is increased. Above a critical value and for sufficiently low flux density, we observe the emergence of a twofold quasidegeneracy accompanied by the opening of an energy gap to the third level. Analysis of the entanglement spectra shows that the gapped ground state is the bosonic $1/2$ Laughlin state. Our work therefore provides compelling evidence of a topological phase transition from the fermionic quantum Hall state at unity filling to the bosonic Laughlin state at a critical attraction strength.

Explore related subjects

cond-mat.str-elcond-mat.quant-gas

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Cécile Repellin, Tarik Yefsah, Antoine Sterdyniak. 2016-12-29. Creating a bosonic fractional quantum Hall state by pairing fermions. https://doi.org/10.1103/physrevb.96.161111

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exotic Spin Excitation Continuum in a Weakly Coupled Quantum Chainsaw Antiferromagnet

Collective motions in strongly interacting magnets involve many spins and are often described in terms of integer-spin excitations. However, in certain cases, the collective motion can behave as if these integer excitations break apart into smaller, particle-like entities with unusual properties. Such fractionalized excitations in quantum magnets are commonly associated either with topological order in two dimensions or with criticality in one dimension. It remains unclear how these distinct mechanisms are connected across a dimensional crossover. Here we investigate the Ti-based quantum antiferromagnet, $Cs_{8}LiNa_{3}Ti_{12}F_{48}$, in which $Ti^{3+}$ ($3d^{1}$, $S=1/2$) ions interact antiferromagnetically within distorted kagome planes. Our inelastic neutron scattering study on a single crystal reveals a frustrated network of weakly coupled spin-$1/2$ chainsaws, realizing a regime of dimensional frustration in which interchain couplings fail to establish coherent two-dimensional order. The magnetic excitation spectrum exhibits a strong continuum spanning the full measured momentum and energy phase space. In addition, the dynamic spin correlation function displays rod-like scattering in momentum space, indicating a quasi-one-dimensional nature of the magnetic correlations. These results point to fractionalized excitations with intrinsically directional character, demonstrating that signatures of one-dimensional criticality can persist within a two-dimensional lattice. Our findings establish anisotropic fractionalization as a distinct organizing principle for quantum-disordered states.

cond-mat.str-el↗
arXiv2026

Quantum-interference-driven orbital density wave and high-temperature superconductivity in trilayer nickelates

Intertwined charge-density-wave (CDW) and spin-density-wave (SDW) orders are a hallmark of high-temperature superconducting multilayer nickelates. In trilayer La4Ni3O_{10}, charge correlations develop at temperatures above the onset of long-range spin order, and the characteristic ordering wavevectors satisfy $Q_{cdw} \approx 2Q_{sdw}$. Here, using a density-wave equation with vertex corrections, we show that quantum interference between short-range SDW fluctuations at $q \approx Q_{sdw}$ on the outer NiO2 layers generates an inter-outer-layer bond order at $Q_{cdw} \approx 2 Q_{sdw}$. This bond order induces a pronounced inner-layer-centered orbital order, with antiphase modulations of the Ni $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ occupations, producing strong orbital polarization but only weak total charge modulation. This intertwined bond-and-orbital order accounts for the layer-selective electronic reconstruction inferred from NMR/NQR and is consistent with Raman spectroscopy and scanning tunnelling microscopy measurements. The same orbital and spin fluctuations also cooperate to stabilize $s_{\pm}$-wave superconductivity through $M_z$ mirror-parity selection rules. Our results provide a unified microscopic framework for intertwined density-wave order and high-Tc superconductivity in multilayer nickelates.

cond-mat.str-el↗
arXiv2026

Model Fractional Quantum Hall States on Lattices: Exact Parent Hamiltonians and Routes to Realization

Recent advances in engineered quantum platforms have enabled the realization of bosonic Laughlin states at $ν=1/2$ and brought non-Abelian topological phases within experimental reach. A central theoretical challenge is to develop a unified framework connecting lattice fractional quantum Hall (FQH) model states, exact parent Hamiltonians, and experimentally accessible interactions. We systematically construct Hermitian parent Hamiltonians for which continuum lowest Landau level (LLL) model states sampled on lattice sites are exact zero modes. Using these model manifolds as quantitative references, we find that, within the projected lattice LLL at the flux densities studied, short-range density interactions stabilize Laughlin ground-state manifolds at $ν=1/3$ and $1/4$, while two-body onsite repulsion supports a Moore--Read triplet at $ν=1$. Full multiband calculations reveal a sharp contrast: the Laughlin manifolds remain robust against interband mixing on the studied tori, whereas the Moore--Read triplet becomes less spectrally isolated and eventually undergoes a level crossing with competing states near the interband scale. Our framework provides a theoretical foundation for using lattice model states to guide the search for experimentally accessible Abelian and non-Abelian FQH states.

cond-mat.str-el↗