Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

• URL: http://arxiv.org/abs/2404.08222v1
• Date: Fri, 12 Apr 2024 03:34:56 GMT
• Title: Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model
• Authors: Xiang-Long Zeng, Wen-Xi Lai, Yi-Wen Wei, Yu-Quan Ma,
• Abstract summary: We derive exactly expressions for the quantum metric and Berry curvature of the energy band electrons. We also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem. Some regions where the Berry curvature is identically zero in the first Brillouin zone results in the degeneracy of the quantum metric.
• Score: 1.3499500088995464
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exactly expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone results in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer "Euler number" provides valuable insights and provide an upper bound for absolute values of the Chern numbers.

Related papers

• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Topological linear response of hyperbolic Chern insulators [0.0]
  We show that the Hall conductivity is quantized to $e2C_ij/h$, where $C_ij$ is the first Chern number. We demonstrate that although it receives contributions from both Abelian and non-Abelian Bloch states, the Chern number can be calculated solely from Abelian states.
  arXiv  Detail & Related papers  (2024-06-12T16:38:43Z)
• Non-Abelian quantum geometric tensor in degenerate topological semimetals [4.00041392024119]
  We propose a generic Hamiltonian with global degenerate ground states, and give a general relation between the corresponding non-Abelian quantum metric and unit Bloch vector. To be concrete, we present and study two topological semimetal models with global degenerate bands under CP and $CT$ symmetries.
  arXiv  Detail & Related papers  (2023-12-02T09:33:37Z)
• Area-law entanglement from quantum geometry [0.0]
  We study the entanglement entropy of a region of linear size $ell$ in fermion systems with nontrivial quantum geometry. We show that the entanglement entropy scales as $S = alpha elld-1 lnell + beta elld-1 + cdots$ where the first term is the well-known area-law violating term for fermions.
  arXiv  Detail & Related papers  (2022-10-24T18:00:59Z)
• Multipartite entanglement of the topologically ordered state in a perturbed toric code [18.589873789289562]
  We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological quantum phase transitions in the spin-$frac12$ toric code model. Our results provide insights to topological phases, which are robust against external disturbances, and are candidates for topologically protected quantum computation.
  arXiv  Detail & Related papers  (2021-09-07T20:20:21Z)
• Chern number and Berry curvature for Gaussian mixed states of fermions [0.0]
  We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase. The Chern number can be expressed as an integral of the Berry curvature of the so-called fictitious Hamiltonian.
  arXiv  Detail & Related papers  (2021-04-25T09:39:32Z)
• 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)
• 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)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain [21.24186888129542]
  We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
  arXiv  Detail & Related papers  (2020-10-14T16:46:11Z)
• Euler characteristic number of the energy band and the reason for its non-integer values [0.0]
  We show that the quantum metric $g_mu nu $ is actually positive semi-definite. We provide an effective topological index for a class of nontrivial topological phases.
  arXiv  Detail & Related papers  (2020-01-14T19:37:15Z)

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.