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Register a new userExact Ground States of Frustrated Spin-1 Ising-Heisenberg and Heisenberg Ladders in a Magnetic Field
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Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung. The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations. It is demonstrated that both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and three-quarters of the saturation magnetization.
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The Heisenberg-Ising spin ladder is one of the few short-range models showing confinement of elementary excitations without the need of an external field, neither transverse nor longitudinal. This feature makes the model suitable for an experimental realization with ultracold atoms. In this paper, we combine analytic and numerical techniques to precisely characterize its spectrum in the regime of Hamiltonian parameters showing confinement. We find two kinds of particles, which we dub intrachain and interchain mesons, that correspond to bound states of kinks within the same chain or between different ones, respectively. The ultimate physical reasons leading to the existence of two families of mesons is a residual double degeneracy of the ground state: the two types of mesons interpolate either between the same vacuum (intrachain) or between the two different ones (interchain). While the intrachain mesons can also be qualitatively assessed through an effective mean field description and were previously known, the interchain ones are new and they represent general features of spin ladders with confinement.
The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices is exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical--quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model.
A full energy spectrum of the spin-1/2 Heisenberg cubic cluster is used to investigate a low-temperature magnetization process and adiabatic demagnetization of this zero-dimensional 2x2x2 quantum spin system. It is shown that the antiferromagnetic spin-1/2 Heisenberg cube exhibits at low enough temperatures a stepwise magnetization curve with four intermediate plateaux at zero, one quarter, one half, and three quarters of the saturation magnetization. We have also found the enhanced magnetocaloric effect close to level-crossing fields that determine transitions between the intermediate plateaux.
Using (infinite) density matrix renormalization group techniques, ground state properties of antiferromagnetic S=1 Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid as well as the spin-liquid and the ferromagnetic phases. Analyzing spin correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.
In this paper, we determine the geometric phase for the one-dimensional $XXZ$ Heisenberg chain with spin-$1/2$, the exchange couple $J$ and the spin anisotropy parameter $Delta$ in a longitudinal field(LF) with the reduced field strength $h$. Using the Jordan-Wigner transformation and the mean-field theory based on the Wicks theorem, a semi-analytical theory has been developed in terms of order parameters which satisfy the self-consistent equations. The values of the order parameters are numerically computed using the matrix-product-state(MPS) method. The validity of the mean-filed theory could be checked through the comparison between the self-consistent solutions and the numerical results. Finally, we draw the the topological phase diagrams in the case $J<0$ and the case $J>0$.
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