Free-fermion Entanglement Spectrum through Wannier Interpolation
arXiv:1410.8670 · doi:10.1103/PhysRevB.91.085119
Abstract
Quantum Entanglement plays an ubiquitous role in theoretical physics, from the characterization of novel phases of matter to understanding the efficacy of numerical algorithms. As such, there have been extensive studies on the entanglement spectrum (ES) of free-fermion systems, particularly in the relation between its spectral flow and topological charge pumping. However, far less has been studied about the \emph{spacing} between adjacent entanglement eigenenergies, which affects the truncation error in numerical computations involving Matrix Product States (MPS) or Projected Entangled-Pair States (PEPS). In this paper, we shall hence derive asymptotic bounds for the ES spacings through an interpolation argument that utilizes known results on Wannier function decay. For translation invariant systems, the Entanglement energies are shown to decay at a rate monotonically related to the complex gap between the filled and occupied bands. This interpolation also demonstrates the one-to-one correspondence between the ES and the edge states. Our results also provide asymptotic bounds for the eigenvalue distribution of certain types of Block Toeplitz matrices common in physics, even for those not arising from entanglement calculations.
14 pages, 3 figures Keywords: Entanglement, Wannier function, complex decay, imaginary gap, Toeplitz spectrum
References in corpus (14)
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Criticality, the area law, and the computational power of PEPS
- Wannier representation of Z_2 topological insulators
- Three dimensional resonating valence bond liquids and their excitations
- Entanglement entropy in quantum spin chains with finite range interaction
- Entanglement signatures of quantum Hall phase transitions
- Symmetries and boundary theories for chiral Projected Entangled Pair States
- Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
- Position momentum Duality in the Entanglement Spectrum of Free Fermions
- Phase transitions in full counting statistics for periodic pumping
- Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state
- Asymptotics of block Toeplitz determinants and the classical dimer model
- Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
- A simple model for multiple-choice collective decision making