Relationship between two-particle topology and fractional Chern insulator

• URL: http://arxiv.org/abs/2209.13215v1
• Date: Tue, 27 Sep 2022 07:33:20 GMT
• Title: Relationship between two-particle topology and fractional Chern insulator
• Abstract summary: We investigate a relationship between the topological band structure in the two-particle problem and the fractional Chern insulators. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases. Our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of the guiding principles for the FCI search. In this paper, we investigate a relationship between the topological band structure in the two-particle problem and the FCI ground states in the many-body problem. We first formulate the two-particle problem of a bosonic on-site interaction projected onto the lowest band of a given tight-binding Hamiltonian. We introduce a reduced Hamiltonian whose eigenvalues correspond to the two-particle bound-state energies. By using the reduced Hamiltonian, we define the two-particle Chern number and numerically check the bulk-boundary correspondence that is predicted by the two-particle Chern number. We then propose that a nontrivial two-particle Chern number of dominant bands roughly indicates the presence of bosonic FCI ground states at filling factor $\nu=1/2$. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases, albeit two-band models being exceptions. Although the two-particle topology is neither a necessary nor a sufficient condition for the FCI state as other indicators in previous studies, our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.

Related papers

• Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response [5.803135196608668]
  We show that staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry.<n>In this work, we analyze fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law.
  arXiv  Detail & Related papers  (2026-03-05T19:18:46Z)
• Sensing the binding and unbinding of anyons at impurities [0.13812010983144798]
  We study how quasihole anyons in a $nu=1/3$ Laughlin fractional quantum Hall state can be bound together by a sufficiently strong attractive impurity potential.<n>We propose methods for studying these states experimentally, for example using scanning tunneling microscopy and exciton spectroscopy.
  arXiv  Detail & Related papers  (2025-07-11T18:00:00Z)
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators [0.0]
  We investigate the relationship between topological effective interactions and fractional Chern insulators (FCIs)<n>We find a notable correlation between the fact that the dominant two-particle bands carry a unit Chern number and the realization of a robust FCI at the filling fraction $nu = 1/3$.<n>Our findings suggest that the topology inherent in the interaction itself can obstruct trivial ground states.
  arXiv  Detail & Related papers  (2025-06-30T15:23:37Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Biorthogonal basis approach to fractional Chern physics [0.0]
  A fractional Chern insulator is thought to emerge from the competition between one-particle band topology and strong repulsive interactions. We introduce a biorthogonal basis constructed from coherent-like states on the von Neumann lattice. We numerically find that it is possible to construct a self-consistent solution where the band dispersion is nearly real.
  arXiv  Detail & Related papers  (2025-03-25T14:51:11Z)
• Tripartite entanglement and Bell non-locality in loop-induced Higgs boson decays [0.21756081703275998]
  We study entanglement properties of the three-body $Htogamma lbarl$ decays (for $l=e,mu,tau$) within the context of the Standard Model. Our aim is to elucidate the distribution of entanglement between the final photon, lepton and antilepton across the phase-space.
  arXiv  Detail & Related papers  (2024-03-26T18:21:10Z)
• Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
  We study the Hamiltonian for a Bose gas in three dimensions of $N geq 3$ spinless particles interacting via zero-range or contact interactions.
  arXiv  Detail & Related papers  (2024-03-19T10:00:12Z)
• Recent Developments in Fractional Chern Insulators [3.926187111157589]
  Fractional Chern insulators (FCIs) are lattice generalizations of the conventional fractional quantum Hall effect (FQHE) FCIs can exist at zero magnetic field and be protected by a large energy gap. Recent development of this field in moir'e materials have turned out to be a remarkably versatile platform for FCIs.
  arXiv  Detail & Related papers  (2022-08-17T18:00:01Z)
• Frustration shapes multi-channel Kondo physics: a star graph perspective [0.31317409221921144]
  We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalization group (URG) technique. Our results display the importance of ground state degeneracy in explaining various important properties.
  arXiv  Detail & Related papers  (2022-05-02T10:21:24Z)
• Spectral form factor in a minimal bosonic model of many-body quantum chaos [1.3793594968500609]
  We study spectral form factor in periodically-kicked bosonic chains. We numerically find a nontrivial systematic system-size dependence of the Thouless time.
  arXiv  Detail & Related papers  (2022-03-10T15:56:24Z)
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids [58.720142291102135]
  We advance a second-quantization framework that helps reveal an exact fusion mechanism for particle fractionalization in FQH fluids. We also uncover the fundamental structure behind the condensation of non-local operators characterizing topological order in the lowest-Landau-level (LLL)
  arXiv  Detail & Related papers  (2021-10-12T18:00:00Z)
• Measurement of Bell-type inequalities and quantum entanglement from $\Lambda$-hyperon spin correlations at high energy colliders [0.0]
  Spin correlations of $Lambda$-hyperons embedded in the QCD strings formed in high energy collider experiments provide unique insight into their locality and entanglement features. We show that while the Clauser-Horne-Shimony-Holt inequality is less stringent for such states, they provide a benchmark for quantum-to-classical transitions induced by varying i) the associated hadron, ii) the spin of nucleons,iii) the separation in rapidity between pairs, and iv) the kinematic accessed.
  arXiv  Detail & Related papers  (2021-07-27T18:00:02Z)
• Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons [58.720142291102135]
  We establish quantum features of an atomic soliton Josephson junction (SJJ) device. We show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present.
  arXiv  Detail & Related papers  (2020-11-26T09:26:19Z)
• On the complex behaviour of the density in composite quantum systems [62.997667081978825]
  We study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We prove that it is a non-perturbative property and we find out a large/small coupling constant duality. Inspired by the proof of KAM theorem, we are able to deal with this problem by introducing a cut-off in energies that eliminates these small denominators.
  arXiv  Detail & Related papers  (2020-04-14T21:41:15Z)
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit [58.720142291102135]
  Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties. We experimentally study a synthetic quantum Hall effect with a two-tone drive.
  arXiv  Detail & Related papers  (2020-04-07T15:00:41Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.