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Register a new userGround-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches
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We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing to calculate the ground state. Using this approach, the phase boundaries between the antiferromagnetic N{e}el, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetery protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in, which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.
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Quantum entanglement and correlations in the spin-1 Heisenberg chain with single-ion anisotropy are investigated using the quantum renormalization group method. Negativity and quantum discord (QD) are calculated with various anisotropy parameters $bigtriangleup$ and single-ion anisotropy parameters $D$. We focus on the relations between two abovementioned physical quantities and on transitions between the Neel, Haldane, and Large-D phases. It is found that both negativity and QD exhibit step-like patterns in different phases as the size of the system increases. Interestingly, the single-ion anisotropy parameter $D$, which can be modulated using nuclear electric resonance (2020 textit{Nature} textbf{579} 205), plays an important role in tuning the quantum phase transition (QPT) of the system. Both the first partial derivative of the negativity and quantum discord with respect to $D$ or $bigtriangleup$ exhibit nonanalytic behavior at the phase transition points, which corresponds directly to the divergence of the correlation length. The quantum correlation critical exponents derived from negativity and QD are equal, and are the reciprocal of the correlation length exponent at each critical point. This work extends the application of quantum entanglement and correlations as tools for depicting QPTs in spin-1 systems.
We consider the dimerized spin-1 $XXZ$ chain with single-ion anisotropy $D$. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.
Using density matrix renormalization group calculations, ground state properties of the spin-1 Heisenberg chain with exchange and single-ion anisotropies in an external field are studied. Our findings confirm and refine recent results by Sengupta and Batista, Physical Review Letters 99, 217205 (2007) (2007), on the same model applying Monte Carlo techniques. In particular, we present evidence for two types of biconical (or supersolid) and for two types of spin-flop (or superfluid) structures. Basic features of the quantum phase diagram may be interpreted qualitatively in the framework of classical spin models.
We construct a new spin-1 model on a chain. Its ground state is determined exactly which is three-fold degenerate by breaking translational invariance. Thus we have trimerization. Excited states cannot be obtained exactly, but we determine a few low-lying ones by using trial states, among them solitons.
Exactly solvable frustrated quantum spin models consisting of a diamond unit structure are presented. The ground states are characterized by tetramer-dimer states with a macroscopic degeneracy in a certain range of isotropic exchange interaction. The lower bound of the excitation gap is exactly calculated to be finite and the bulk entropy in the limit of zero temperature remains finite depending on the shape of the boundary of system. Residual entropy is in a range of 0~6.1% of the entropy at high temperature for hexagonal diamond lattice and 0~8.4% for square diamond lattice. These diamond lattices are generalized to any dimensions and it is likely to be synthesized experimentally.
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