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.
Recent advancements in our understanding of ordered magnets call for a quantification of their entanglement content on an equal footing with classical thermodynamic quantities, such as the total magnetic moment. We evaluate the entanglement entropy (EE) between the two sublattices of a bipartite ordered antiferromagnet, finding it to scale with volume. Thus, the EE density becomes an intensive property and is evaluated to be a universal dimensionality-dependent constant when exchange is the dominant interaction. Our analytic results are validated against the DMRG-based analysis of a one-dimensional (1D) system, finding good agreement. Furthermore, our evaluated EE per bond provides a useful shortcut towards obtaining the central-cut EE in 1D, and the area law in higher-dimensional magnets.
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.
Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\ensuremath{\alpha}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $\ensuremath{\alpha}>\frac{1}{2}$. A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\ensuremath{\alpha}$, corresponding to a critical behavior with an effective central charge
c=ln(2), independent of $\ensuremath{\alpha}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\ensuremath{\alpha}$. For a wide range of partition size
l, the EE fits a critical behavior with a central charge close to
c=1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\ensuremath{\alpha}=2$. Only for small $l\ensuremath{\ll}L$, in a range which increases with the number of spins
N, we find deviations which are rather consistent with the strong disorder fixed point central charge
c=ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. We also present results obtained with DMRG and find agreement with ED for sufficiently small $\ensuremath{\alpha}<2$, whereas for larger $\ensuremath{\alpha}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.
Magnetic susceptibilities of spin-
(S,s) ferrimagnetic Heisenberg chains are numerically investigated. It is argued how the ferromagnetic and antiferromagnetic features of quantum ferrimagnets are exhibited as functions of
(S,s). Spin-
(S,s) ferrimagnetic chains behave similar to combinations of spin-$(S\ensuremath{-}s)$ ferromagnetic and spin-
(2s) antiferromagnetic chains provided
S=2s.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.