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

摘要

Entanglement-related properties work as a 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 a size scaling analysis, in comparably high quality with those obtained by a large-size density matrix renormalization group analysis. This method projects the large-scale original many-body Hamiltonian to a 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 dimensions could be determined by the entanglement entropy and the fidelity that reflects the change of the structure of the wave function.