Two-Site Entropy and Quantum Phase Transitions in Low-Dimensional Models

We propose a new approach to study quantum phase transitions in low-dimensional lattice models. It is based on studying the von Neumann entropy of two neighboring central sites in a long chain. It is demonstrated that the procedure works equally well for fermionic and spin models, and the two-site entropy is a better indicator of quantum phase transition than calculating gaps, order parameters, or the single-site entropy. The method is especially convenient when the density-matrix renormalization-group algorithm is used.

Figure 1

$\theta$ dependence of the single-site entropy of the central site of the isotropic spin-1 chain, determined for different chain lengths.

Figure 2

(a) $\theta$ dependence of the two-site entropy $s_{i,i+1}$ for $i=N/2$ and $i=N/2+1$ of the isotropic spin-1 chain for different chain lengths. The results for $i=N/2$ are displayed for $N=400$ only. (b) Dimerization of the two-site entropy.

Figure 3

(a) Dimer order parameter of the ionic Hubbard model for $t/\Delta =1$ for different chain lengths. (b) Entropy of the central site.

Figure 4

Two-site entropy $s_{i,i+1}$ for $i=N/2$ and $i=N/2+1$ of the ionic Hubbard model for $t/\Delta =1$ for different chain lengths.

Figure 5

Single-site entropy of the donor-acceptor model for $t/\Delta =1$ for different chain lengths.

Figure 6

Two-site entropy of the donor-acceptor model for $t/\Delta =1$ for different chain lengths.

Figure 7

Entropy of blocks of $N/2$ and $N/2+1$ sites of the bilinear-biquadratic $S=1$ model for a chain with $N=200$ sites.