Entanglement spectrum as a marker for phase transitions in the density embedding theory for interacting spinless fermionic models

TL;DR

This paper demonstrates that the density embedding theory (DET) effectively evaluates entanglement properties and detects phase transitions in interacting fermionic models, matching large-scale methods without finite size effects.

Contribution

The study introduces DET as a reliable, size-independent method for analyzing entanglement spectra and phase transitions in fermionic systems.

Findings

DET reproduces exact entanglement spectra in 1D models.

Entanglement entropy and fidelity identify phase transitions in 2D models.

DET achieves high-quality results comparable to large-scale density matrix renormalization group methods.

Abstract

Entanglement related properties work as nice fingerprint of the quantum many-body wave function. However, those of fermionic models are hard to evaluate in standard numerical methods because they suffer from finite size effects. We show that a so-called density embedding theory (DET) can evaluate them without size scaling analysis in comparably high quality with those obtained by the large-size density matrix renormalization group analysis. This method projects the large scale original many-body Hamiltonian to the small number of basis sets defined on a local cluster, and optimizes the choice of these bases by tuning the local density matrix. The DET entanglement spectrum of one-dimensional interacting fermions perfectly reproduces the exact ones and works as a marker of the phase transition point. It is further shown that the phase transitions in two-dimension could be determined by the entanglement entropy and the fidelity that reflects the change of the structure of the wave function.