Density Matrix for an Impurity Center

Bernd Esser

López García, Alberto, Cerrillo Moreno, Javier

This work presents a quantum simulation of impurity-induced noise in nitrogen-vacancy (NV) centers in diamond using quantum computing platforms. The study aims to model how spin–spin interactions and environmental impurities affect coherence and entanglement within two-qubit systems. Quantum State Tomography (QST) is employed to reconstruct the density matrix and quantify entanglement through state purity, the Peres–Horodecki criterion, and CHSH inequalities. The results indicate limited entanglement fidelity and the absence of CHSH violation, highlighting the strong influence of impurity noise on the system’s quantum correlations. Future work will focus on improving pulse control (3LS) and leveraging high-performance computational resources to enhance entanglement fidelity, test optimized pulse sequences, and explore more complex quantum simulation scenarios involving NV centers.

Erik Schwartz Sørensen, Ian K. Affleck

The s=1 Heisenberg antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with J'\ensuremath{\ne}J at the center of an even-length open chain is considered. Using the density-matrix renormalization-group method we find that, for sufficiently strong or weak J', a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on s=1/2 chain-end excitations, both in the weak- and strong-coupling limit. In a region around the uniform limit, J'=J, no states are found with energy below the Haldane gap. Second, a s=1/2 impurity at the center of an otherwise even-length open chain is considered. The coupling to the s=1/2 impurity is varied. Bound states in the Haldane gap are found only for sufficiently weak (antiferromagnetic) coupling. For a s=1/2 impurity coupled with a strong (antiferromagnetic) bond, no states are found in the Haldane gap. Our results are in good qualitative agreement with recent experiments on doped NENP and ${\mathrm{Y}}_{2}$${\mathrm{BaNiO}}_{5}$.

Karl Blum

Ebad Kamil, Thomas Pruschke, Peter E. Blöchl

We discuss an open quantum system approach for the evaluation of reduced density-matrix functional in the local approximation that approximates a correlated electron system by a correlated impurity. Using a resolvent approach, we calculate the impurity density matrix and from this the density-matrix functional.

Karl Blum