Chern number and Berry curvature for Gaussian mixed states of fermions

• URL: http://arxiv.org/abs/2104.12115v2
• Date: Mon, 14 Jun 2021 08:40:56 GMT
• Title: Chern number and Berry curvature for Gaussian mixed states of fermions
• Authors: Lukas Wawer and Michael Fleischhauer
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase (EGP) introduced for one-dimensional lattice models to two dimensions. In contrast to the geometric phase for density matrices suggested by Uhlmann, the EGP leads a proper Chern number for Gaussian, finite-temperature or non-equilibrium steady states. The Chern number can be expressed as an integral of the Berry curvature of the so-called fictitious Hamiltonian, constructed from single-particle correlations, over the two-dimensional Brillouin zone. For the Chern number to be non-zero the fictitious Hamiltonian has to break time-reversal symmetry.

Related papers

• A Non-Invertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra [0.0]
  We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+1d conformal field theory. We use this to determine the universal leading and sub-leading contributions to the non-invertible symmetry-resolved entanglement entropy of a single interval.
  arXiv  Detail & Related papers  (2024-09-04T15:25:05Z)
• 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)
• Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model [1.3499500088995464]
  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.
  arXiv  Detail & Related papers  (2024-04-12T03:34:56Z)
• 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)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Quantum quenches in a pseudo-Hermitian Chern insulator [1.0093662416275693]
  We show the bulk-surface duality of the pseudo-Hermitian phases, then build a concrete relation between the static band topology and quench dynamics. We propose a possible scheme to realize the seemingly challenging model in a bilayer lattice and detect the dynamics with a double-quench protocol.
  arXiv  Detail & Related papers  (2022-09-30T03:20:45Z)
• Penrose dodecahedron, Witting configuration and quantum entanglement [55.2480439325792]
  A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose. The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. Two entangled systems with quantum states described by Witting configurations are discussed in presented work.
  arXiv  Detail & Related papers  (2022-08-29T14:46:44Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• 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)

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.