Renyi Entanglement Entropy of Interacting Fermions Calculated Using the Continuous-Time Quantum Monte Carlo Method

We present a new algorithm for calculating the Renyi entanglement entropy of interacting fermions using the continuous-time quantum Monte Carlo method. The algorithm only samples the interaction correction of the entanglement entropy, which by design ensures the efficient calculation of weakly interacting systems. Combined with Monte Carlo reweighting, the algorithm also performs well for systems with strong interactions. We demonstrate the potential of this method by studying the quantum entanglement signatures of the charge-density-wave transition of interacting fermions on a square lattice.

Figure 1

Key concepts of the algorithm. (a) A configuration with $k_1=2$ vertices in the time interval $[0,\beta )$ and $k_2=1$ vertex in $[\beta ,2\beta )$. The weights of this configuration are given in Eqs. (8) and (9). (b) The extended configuration space combines two ensembles, ${\mathcal{Z}}^2$ and ${\mathcal{Z}}^A$. MC updates, Eqs. (10) and (11), change the vertex configuration and Eq. (12) switches between the two ensembles.

Figure 2

Renyi EE of an eight-site open chain with equal partitions. The black solid lines are the exact diagonalization results, which agree perfectly with the results calculated by our algorithm (circles).

Figure 3

The rank-two Renyi entanglement entropy versus the subregion size $N_A$ of a cylinder embedded in a $8\times 8$ torus for (a) $T=0.5t$ and (b) $V=2t$.

Figure 4

The scaled mutual information for various system sizes at (a) $T/t=0.5$ and (b) $V/t=2$. The crossing point agrees with the transition point determined in Ref. [40] using correlation functions.