Utilizing the matrix product formalism, we have studied the variation of entanglement and fidelity measures in the MP ground states of a generic anisotropic spin 2 chain with nearest neighbour interactions and shared symmetries. These MP states represent the exact Ground State solutions of the system and display distinctive characteristics determined by a maximum of three parameters exhibiting one antiferromagnetic Haldane phase (AFMH), together with a secondary weak antiferromagnetic (WAFM) and a weak ferromagnetic phase (WFM). Using Transfer Matrix Method (TM), we have obtained nontrivial features in the variation of Quantum Correlation measures and QIT Measures around the VBS point for an acritical choice of the parameters, and a Quantum Critical Point, for a critical choice of the parameters, of the AFMH spin liquid phase of the system.
We use the matrix product approach to construct all optimum ground states of general anisotropic spin-2 chains with nearest-neighbour interactions and common symmetries. These states are exact ground states of the model and their properties depend on up to three parameters. We find three different antiferromagnetic Haldane phases, one weak antiferromagnetic and one weak ferromagnetic phase. The antiferromagnetic phases can be described as spin liquids with exponentially decaying correlation functions. The variety of phases found with the matrix product ansatz also gives insight into the behaviour of spin chains with arbitrary higher spins.
In this paper, we study the entanglement properties of a spin-1 model, the exact ground state of which is given by a matrix product (MP) state. The model exhibits a critical point transition at a parameter value
a=0. The longitudinal and transverse correlation lengths are known to diverge as $a\ensuremath{\rightarrow}0$. We use three different entanglement measures
S(i) (the one-site von Neumann entropy),
S(i,j) (the two-body entanglement), and
G(2,n) (the generalized global entanglement) to determine the entanglement content of the MP ground state as the parameter
a is varied. The entanglement length, associated with
S(i,j), is found to diverge in the vicinity of the quantum critical point
a=0. The first derivative of the entanglement measure
E [=S(i),S(i,j)] with respect to the parameter
a also diverges. The first derivative of
G(2,n) with respect to
a does not diverge as $a\ensuremath{\rightarrow}0$ but attains a maximum value at
a=0. At the quantum critical point itself all three entanglement measures become zero. We further show that multipartite correlations are involved in the quantum phase transitions at
a=0.
We consider a spin ladder model which is known to have matrix product states as exact ground states with spin liquid characteristics. The model has two critical-point transitions at the parameter values
u=0 and $\ensuremath{\infty}$. We study the variation of entanglement and fidelity measures in the ground states as a function of
u and specially look for signatures of quantum phase transitions at
u=0 and $\ensuremath{\infty}$. The two different entanglement measures used are
S(i) (the single-site von Neumann entropy) and
S(i,j) (the two-body entanglement). At the quantum critical point (QCP) $u=\ensuremath{\infty}$, the entanglement measure
E [=S(i),S(i,j)] vanishes but remains nonzero at the other QCP
u=0. The first and second derivatives of
E with respect to the parameter
u and the entanglement length associated with
S(i,j) are further calculated to identify special features, if any, near the QCPs. We further determine the GS fidelity
F and a quantity
ln∣D∣ related to the second derivative of
F and show that these quantities calculated for finite-sized systems are good indicators of QPTs occurring in the infinite system.
In the present work, we study the fidelity susceptibility and the entanglement entropy in an antiferromagnetic spin-1 chain with additional next-nearest neighbor interactions and three-site interactions, which are given by H=(J1SiSi+1+ J2SiSi+2)+[J3(SiSi+1)(Si+1Si+2)+ h.c.]. By using the density matrix renormalization group method, the ground-state properties of the system are calculated with very high accuracy. We investigate the effect of the three-site interaction J3 on the fidelity susceptibility numerically, and then analyze its relation with the quantum phase transition (QPT). The fidelity measures the similarity between two states, and the fidelity susceptibility describes the associated changing rate. The QPT is intuitively accompanied by an abrupt change in the structure of the ground-state wave function, so generally a peak of the fidelity susceptibility indicates a QPT and the location of the peak denotes the critical point. For the case of J2=0, a peak of the fidelity susceptibility is found by varying J3, and the height of the peak grows as the system size increases. The location of the peak shifts to a slightly lower J3 up to a particular value as the system size increases. Through a finite size scaling, the critical point J3c=0.111 of the QPT from the Haldane spin liquid to the dimerized phase is identified. We also study the effect of the three-site interaction on the entanglement entropy between the right half part and the rest. It is noted that the peak of the entanglement entropy does not coincide with the critical point. Instead, the critical point is determined by the position at which the first-order derivative of the entanglement entropy takes its minimum, since a second-order QPT is signaled by the first derivative of density matrix element. Moreover, the entanglement entropy disappears when J3=1/6, which corresponds to the size-independent Majumdar-Ghosh point. The positions of quantum critical points extracted from these two quantum information observables agree well with those obtained by the string order parameters, which characterizes the topological order in the Haldane phase. Secondly, we also study the case of J20, and obtain the critical points by both the fidelity susceptibility and the entanglement entropy. Finally we provide a ground-state phase diagram of the system. To sum up, the quantum information observables are effective tools for detecting diverse QPTs in spin-1 models.
Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-1 2 anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases.The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains.Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization.Dispersion relations, spin gap and several ground state orders have been obtained.Dimer order and string orders are found to coexist in the ground state.Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain.This spin gap along with the string orders attribute to the Haldane phase.The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.