Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1006.1732 · Journal of Physics B Atomic Molecular and Optical Physics

Entanglement entropy in an antiferromagnetic Heisenberg spin chain with boundary impurities

Jie Ren, Shiqun Zhu, Xiang Hao

Published Dec 18, 2008• 19 citations
arXivHTMLPDF

Abstract

The effects of boundary impurities on the entanglement entropy in an antiferromagnetic Heisenberg opened spin-1/2 chain are investigated. The method of the density-matrix renormalization group is used to obtain the bipartite entanglement. The entropy increases when the length of the subsystem increases. It approaches a constant when the system length is very large. With the same impurity interaction, qutrit impurities of spin-1 can increase the entanglement entropy.

DOI
10.1088/0953-4075/42/1/015504

Related papers

Density-matrix renormalization-group study of entanglement and entropy in an antiferromagnetic Heisenberg spin chain with domain walls

Jie Ren, Shiqun Zhu

By using the method of density-matrix renormalization-group theory, the ground-state entanglement in the spin-1/2 isotropic antiferromagnetic Heisenberg chain is studied when there are domain walls generated by a boundary magnetic field. It is found that the pairwise entanglement of odd-bond two qubits decreases and even-bond two qubits increases to stable values alternately when the magnetic field increases. The pairwise entanglement of odd bond can be equal to that of even bond for a suitable value of the magnetic field. When the magnetic field increases further, the entanglement of even bond can be larger than that of odd bond. The entanglement entropy increases and then almost saturates as the number of spin sites increases. Due to the domain walls, the entanglement entropy of even bond decreases to a minimum value and then increases as the magnetic field increases.

Physical Review A•Mar 25, 2008•3 citations

Boundary Quantum Entanglement of the XXZ Spin Chain with Boundary Impurities

Zhuo Wei, Yupeng Wang

The boundary quantum entanglement for the s = 1/2 XXZ spin chain with boundary impurities is studied via the density matrix renormalization group (DMRG) method. It is shown that the entanglement entropy of the boundary bond (the impurity and the chain spin next to it) behaves differently in different phases. The relationship between the singular points of the boundary entropy and boundary quantum critical points is discussed.

Chinese Physics Letters•Dec 1, 2007•1 citation

Critical entanglement of XXZ Heisenberg chains with defects

Jize Zhao, Ingo Peschel, Xiaoqun Wang

We study the entanglement properties of anisotropic open spin one-half Heisenberg chains with a modified central bond. The entanglement entropy between the two half-chains is calculated with the density-matrix renormalization method (DMRG). We find a logarithmic behavior with an effective central charge ${c}^{\ensuremath{'}}$ varying with the length of the system. It flows to one in the ferromagnetic region and to zero in the antiferromagnetic region of the model. In the $XX$ case it has a nonuniversal limit and we recover previous results.

arXiv:cond-mat/0509338•Physical Review B•Jan 24, 2006•56 citations

Magnetic impurity coupled to a Heisenberg chain: Density-matrix renormalization-group study

W. Zhang, J. Igarashi, Peter Fulde

By making use of the Lanczos and the density-matrix renormalization-group methods, we study the zero-temperature properties of a spin-1/2 antiferromagnetic Heisenberg chain system with a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins. A comparison is made with the results for a magnetic impurity coupled only to the nearest-neighbor spin in the chain. The binding energy and the spin correlations are calculated. The matrix elements of the impurity spin operators are also calculated between several low-energy states. By carefully analyzing finite-size effects, we show that the dynamical structure factor of the impurity contains a \ensuremath{\delta}-function contribution at zero frequency which does not vanish in the thermodynamic limit for the case of symmetrical coupling. This indicates a partial decoupling of the impurity spin from the spins in the chain, and therefore the impurity susceptibility is predicted to show a Curie behavior. This contradicts the two-channel Kondo behavior suggested from analytic considerations.

Physical review. B, Condensed matter•Jul 1, 1997•24 citations

Density-Matrix Renormalization Group Study on an Impurity Symmetrically Coupled to a Quantum Heisenberg Chain

Weijie Zhang, Jun-ichi Igarashi, Peter Fulde

We calculate the impurity susceptibility for a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins in an antiferromagnetic Heisenberg spin-1/2 chain. This is done by extending White's density-matrix renormalization group (DMRG) technique to finite temperatures. It is found that the impurity susceptibility satisfies Curie law at low temperatures, and that the Curie constant decreases rapidly with increasing coupling constant between the impurity spin and the spins in the chain. For strong couplings, a logarithmic dependence of the susceptibility on temperature emerges. The Curie law behavior agrees with the DMRG analysis at zero temperature but deviates from the prediction of conformal field theory.

Journal of the Physical Society of Japan•May 15, 1998•4 citations

Intersublattice entanglement entropy of ferrimagnetic spin chains

Jongmin Y. Lee, Se Kwon Kim

Ferrimagnets are antiparallel-ordered magnetic states in a bipartite lattice with two alternating unequal spins, which exhibit both ferromagnetic and antiferromagnetic properties. Several theoretical studies have explored the magnetic properties of ferrimagnets, but the entanglement entropy of ferrimagnets with arbitrary spin combinations has not been studied. In this study, we analytically derive the intersublattice entanglement entropy of a ferrimagnetic spin chain using the method that has been applied to the antiferromagnetic case. The analytical results are numerically verified using the density-matrix renormalization group. Going beyond the results for antiferromagnets, the entanglement entropy of ferrimagnets for fixed anisotropy is shown to solely depend on the difference of spins relative to its geometric average, and the quantity is shown to be stable against small-parameter variations.

arXiv:2410.12354•Physical review. B./Physical review. B•Mar 17, 2025•2 citations
The effects of boundary impurities on the entanglement entropy in an antiferromagnetic Heisenberg opened spin-1/2 chain are investigated. The method of the density-matrix renormalization group is used to obtain the bipartite entanglement. The entropy increases when the length of the subsystem increases. It approaches a constant when the system length is very large. With the same impurity interaction, qutrit impurities of spin-1 can increase the entanglement entropy.
By using the method of density-matrix renormalization-group theory, the ground-state entanglement in the spin-1/2 isotropic antiferromagnetic Heisenberg chain is studied when there are domain walls generated by a boundary magnetic field. It is found that the pairwise entanglement of odd-bond two qubits decreases and even-bond two qubits increases to stable values alternately when the magnetic field increases. The pairwise entanglement of odd bond can be equal to that of even bond for a suitable value of the magnetic field. When the magnetic field increases further, the entanglement of even bond can be larger than that of odd bond. The entanglement entropy increases and then almost saturates as the number of spin sites increases. Due to the domain walls, the entanglement entropy of even bond decreases to a minimum value and then increases as the magnetic field increases.
We study the entanglement properties of anisotropic open spin one-half Heisenberg chains with a modified central bond. The entanglement entropy between the two half-chains is calculated with the density-matrix renormalization method (DMRG). We find a logarithmic behavior with an effective central charge ${c}^{\ensuremath{'}}$ varying with the length of the system. It flows to one in the ferromagnetic region and to zero in the antiferromagnetic region of the model. In the XXXXXX case it has a nonuniversal limit and we recover previous results.
By making use of the Lanczos and the density-matrix renormalization-group methods, we study the zero-temperature properties of a spin-1/2 antiferromagnetic Heisenberg chain system with a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins. A comparison is made with the results for a magnetic impurity coupled only to the nearest-neighbor spin in the chain. The binding energy and the spin correlations are calculated. The matrix elements of the impurity spin operators are also calculated between several low-energy states. By carefully analyzing finite-size effects, we show that the dynamical structure factor of the impurity contains a \ensuremath{\delta}-function contribution at zero frequency which does not vanish in the thermodynamic limit for the case of symmetrical coupling. This indicates a partial decoupling of the impurity spin from the spins in the chain, and therefore the impurity susceptibility is predicted to show a Curie behavior. This contradicts the two-channel Kondo behavior suggested from analytic considerations.
We calculate the impurity susceptibility for a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins in an antiferromagnetic Heisenberg spin-1/2 chain. This is done by extending White's density-matrix renormalization group (DMRG) technique to finite temperatures. It is found that the impurity susceptibility satisfies Curie law at low temperatures, and that the Curie constant decreases rapidly with increasing coupling constant between the impurity spin and the spins in the chain. For strong couplings, a logarithmic dependence of the susceptibility on temperature emerges. The Curie law behavior agrees with the DMRG analysis at zero temperature but deviates from the prediction of conformal field theory.
Ferrimagnets are antiparallel-ordered magnetic states in a bipartite lattice with two alternating unequal spins, which exhibit both ferromagnetic and antiferromagnetic properties. Several theoretical studies have explored the magnetic properties of ferrimagnets, but the entanglement entropy of ferrimagnets with arbitrary spin combinations has not been studied. In this study, we analytically derive the intersublattice entanglement entropy of a ferrimagnetic spin chain using the method that has been applied to the antiferromagnetic case. The analytical results are numerically verified using the density-matrix renormalization group. Going beyond the results for antiferromagnets, the entanglement entropy of ferrimagnets for fixed anisotropy is shown to solely depend on the difference of spins relative to its geometric average, and the quantity is shown to be stable against small-parameter variations.