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Entanglement related properties work as nice fingerprint of the quantummany-body wave function. However, those of fermionic models are hard toevaluate in standard numerical methods because they suffer from finite sizeeffects. We show that a so-called density embedding theory (DET) can evaluatethem without size scaling analysis in comparably high quality with thoseobtained by the large-size density matrix renormalization group analysis. Thismethod projects the large scale original many-body Hamiltonian to the smallnumber of basis sets defined on a local cluster, and optimizes the choice ofthese bases by tuning the local density matrix. The DET entanglement spectrumof one-dimensional interacting fermions perfectly reproduces the exact ones andworks as a marker of the phase transition point. It is further shown that thephase transitions in two-dimension could be determined by the entanglemententropy and the fidelity that reflects the change of the structure of the wavefunction.

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