# Entanglement spectrum and Wannier center flow of the Hofstadter problem

@article{Huang2012EntanglementSA, title={Entanglement spectrum and Wannier center flow of the Hofstadter problem}, author={Zhoushen Huang and Daniel P. Arovas}, journal={Physical Review B}, year={2012}, volume={86}, pages={245109} }

We examine the quantum entanglement spectra and Wannier functions of the square lattice Hofstadter model. Consistent with previous work on entanglement spectra of topological band structures, we find that the entanglement levels exhibit a spectral flow similar to that of the full system's energy spectrum. While the energy spectra are continuous, with open boundary conditions the entanglement spectra exhibit discontinuities associated with the passage of an energy edge state through the Fermi…

## Figures from this paper

## 33 Citations

Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly

- Physics
- 2016

We perform an analytical study of the energy and entanglement spectrum of non-interacting fermionic bilayer honeycomb lattices in the presence of trigonal warping in the energy spectrum, on-site…

Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers

- Physics
- 2013

We study Hofstadter bilayers, i.e. coupled hopping models on two-dimensional square lattices in a perpendicular magnetic field. Upon tracing out one of the layers, we find an explicit expression for…

Free-fermion entanglement spectrum through Wannier interpolation

- Physics, Mathematics
- 2015

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…

Position-momentum duality in the entanglement spectrum of free fermions

- Physics, Mathematics
- 2013

We propose an exact equivalence between the entanglement spectra of two completely different free-fermion systems at zero temperature. This equivalence follows from a position-momentum duality where…

Entanglement spectrum and entanglement Hamiltonian of a Chern insulator with open boundaries

- Physics, Mathematics
- 2014

We study the entanglement spectrum of a Chern insulator on a cylinder geometry, with the cut separating two partitions parallel to the cylinder edge at varying distances from the edge. In contrast to…

Relation of the entanglement spectrum to the bulk polarization

- Physics
- 2021

The bulk polarization is a Z2 topological invariant characterizing non-interacting systems in one dimension with chiral or particle-hole symmetries. We show that the bulk polarization can always be…

Entanglement entropy and entanglement spectrum of Bi1-x Sb x (1 1 1) bilayers.

- Physics, MedicineJournal of physics. Condensed matter : an Institute of Physics journal
- 2018

The topologically non-trivial nature of the bismuth bilayer is proved by the presence of spectral flow in the entanglement spectrum, which shows a finite discontinuity in the first derivative.

Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models

- Physics
- 2020

The polaron concept captures physical situations involving an itinerant quantum particle (excitation) that interacts strongly with bosonic degrees of freedom and becomes heavily boson-dressed. While…

Free-Fermion entanglement and orthogonal polynomials

- Mathematics, PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2019

We present a simple construction for a tridiagonal matrix $T$ that commutes with the hopping matrix for the entanglement Hamiltonian ${\cal H}$ of open finite free-Fermion chains associated with…

Entanglement Chern number for an extensive partition of a topological ground state

- Physics
- 2014

If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the…