Multi-fractality of the entanglement Hamiltonian eigen-modes

Abstract

We study the fractal properties of single-particle eigen-modes of entanglement Hamiltonian in free fermion models. One of these modes that has the highest entanglement information and thus called maximally entangled mode (MEM) is specially considered. In free Fermion models with Anderson localization, fractality of MEM is obtained numerically and compared with the fractality of Hamiltonian eigen-mode at Fermi level. We show that both eigen-modes have similar fractal properties: both have same single fractal dimension in delocalized phase which equals the dimension of the system, and both show multi-fractality at phase transitio point. Therefore, we conclude that, fractal behavior of MEM -- in addition to the fractal behavior of Hamiltonian eigen-mode -- can be used as a quantum phase transition characterization.

8 pages, 9 figures

References in corpus (14)

• Anderson Transitions
• Multifractal statistics of Lagrangian velocity and acceleration in turbulence
• Exact relations between multifractal exponents at the Anderson transition
• Detecting and interpreting distortions in hierarchical organization of complex time series
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Entanglement entropy and multifractality at localization transitions
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition
• Entropy of entanglement and multifractal exponents for random states
• Finite Size Scaling of Topological Entanglement Entropy
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization

Cited by in corpus (6)

• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Flat-band-based multifractality in the all-band-flat diamond chain
• The Mean-Field Bose Glass in Quasicrystalline Systems
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement Measures