Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose

• URL: http://arxiv.org/abs/2403.12121v2
• Date: Wed, 21 Aug 2024 14:52:29 GMT
• Title: Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Authors: Nico Kirchner, Wonjune Choi, Frank Pollmann,
• Abstract summary: Entanglement of mixed quantum states can be quantified using the partial transpose and its corresponding entanglement measure, the logarithmic negativity. Recently, the notion of partial transpose has been extended to systems of anyons, which are exotic quasiparticles whose exchange statistics go beyond the bosonic and fermionic case.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Entanglement of mixed quantum states can be quantified using the partial transpose and its corresponding entanglement measure, the logarithmic negativity. Recently, the notion of partial transpose has been extended to systems of anyons, which are exotic quasiparticles whose exchange statistics go beyond the bosonic and fermionic case. Studying the fundamental properties of this anyonic partial transpose, we first reveal that when applied to the special case of fermionic systems, it can be reduced to the fermionic partial transpose or its twisted variant depending on whether or not a boundary Majorana fermion is present. Focusing on ground state properties, we find that the anyonic partial transpose captures both the correct entanglement scaling for gapless systems, as predicted by conformal field theory, and the phase transition between a topologically trivial and a nontrivial phase. For non-abelian anyons and the bipartition geometry, we find a rich multiplet structure in the eigenvalues of the partial transpose, the so-called negativity spectrum, and reveal the possibility of defining both a charge- and an imbalance-resolved negativity.

Related papers

• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Charge-resolved entanglement in the presence of topological defects [0.0]
  We compute the charge-resolved entanglement entropy for a single interval in the low-lying states of the Su-Schrieffer-Heeger model. We find that, compared to the unresolved counterpart and to the pure system, a richer structure of entanglement emerges.
  arXiv  Detail & Related papers  (2023-06-27T15:03:46Z)
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles [0.0]
  We write down a renewal equation for the statistics of the entanglement entropy and show that depending on the spectrum of quasiparticle decay rates different entanglement scaling can arise and even sharp entanglement phase transitions. When applied to a Quantum Ising chain where the transverse magnetization is measured by quantum jumps, our theory predicts a critical phase with logarithmic scaling of the entanglement, an area law phase and a continuous phase transition between them, with an effective central charge vanishing as a square root at the transition point.
  arXiv  Detail & Related papers  (2021-11-05T13:38:04Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Anyonic Partial Transpose I: Quantum Information Aspects [0.0]
  A basic diagnostic of entanglement in mixed quantum states is known as the partial transpose. The corresponding entanglement measure is called the logarithmic negativity. We conjecture that the subspace of states with a vanishing logarithmic negativity is a set of measure zero in the entire space of anyonic states.
  arXiv  Detail & Related papers  (2020-12-03T19:26:35Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Fermionic systems for quantum information people [0.0]
  We develop new tools for the treatment of fermionic systems. We consider variants of the notions of fermionic mode correlation and entanglement.
  arXiv  Detail & Related papers  (2020-06-04T18:18:05Z)
• Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models [0.0]
  Small-polaron transitions are analyzed through the prism of the entanglement spectrum of the excitation-phonon system. The behavior of the entanglement entropy in the vicinity of the critical excitation-phonon coupling strength chiefly originates from one specific entanglement-spectrum eigenvalue.
  arXiv  Detail & Related papers  (2020-01-30T08:41:00Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

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.