The one-dimensional Heisenberg antiferromagnets of large-integer-$S$ spins are studied; their Haldane gaps are estimated by the numerical diagonalization method for $S=5$ and $6$. We successfully obtain a monotonically increasing sequence of finite-size energy difference data corresponding to the Haldane gaps from the huge-scale parallel calculations of diagonalization under the twisted boundary condition and create a monotonically decreasing sequence within the range of system sizes treated in this study from the monotonically increasing sequence. Consequently, the gaps for $S=5$ and $6$ are estimated to be $0.000050 \pm 0.000005$ and $0.0000030 \pm 0.0000005$, respectively. The asymptotic formula of the Haldane gap for $S\rightarrow\infty$ is examined from the new estimates to determine the coefficient in the formula more precisely.
Emergence of Long Period Antiferromagnetic Orders from Haldane Phase in S=1 Heisenberg Chains with D-Modulation
研究了单格点各向异性D的空间调制对S=1海森堡链基态的影响。在周期2调制的情况下，发现相图中包含Haldum相、大D相、Udud型Neel相和U 0 d 0型Neel相。结果表明，隐藏的反铁磁序在Halflies相兼容的D-项的空间调制得到冻结，导致出现各种类型的Neel订单。对具有较长周期D调制的模型的研究也证实了这一点。
The antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling $J$ of the Heisenberg chain. We discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We next study the robustness of the edge states of the spin one chain by studying by the DMRG algorithm a spin one ladder. We show that the peculiar hidden topological order of the spin one chain disappear…
We calculate the Haldane gap of the $\mathrm{SU}(3)$ spin $[3~0~0]$ Heisenberg model using variational uniform fully symmetric $\mathrm{SU}(3)$ matrix product states, and find that the minimal gap $Δ/J = 0.0263 $ is obtained in the $[2~1~0]$ sector at momentum $2π/3$. We also discuss the symmetry protected topological order of the ground state, and determine the full dispersion relation of the elementary excitations and the correlation lengths of the system.
For the Haldane phase, the magnetic field usually tends to break the symmetry and drives the system into a topologically trivial phase. Here, we report a novel reentrance of the Haldane phase at zero temperature in the spin-1 antiferromagnetic Heisenberg model on sawtooth chain. A partial Haldane phase is induced by the magnetic field, which is the combination of the Haldane state in one sublattice and a ferromagnetically ordered state in the other sublattice. Such a partial topological order is a result of the zero-temperature entropy due to quantum fluctuations caused by geometrical frustrat…
We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid similar to a $S=1/2$ Heisenberg antiferromagnetic chain. We furth…
Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-1/2 kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using th…
The Haldane gap of the S=2 Heisenberg antiferromagnet in a one-dimensional linear chain is examined by a numerical-diagonalization method. A precise estimate for the magnitude of the gap is successfully obtained by a multistep convergence-acceleration procedure applied to finite-size diagonalization data under the twisted boundary condition.
Using Quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic Néel phase, a rung singlet product phase, and a topological none trivial Haldane phase, separated by two quantum phase transitions. We show that the two quantum critical points are all in the three-dimensional O(3) universality class. The properties of the two gapped phases, including the finite-size behavior of the string orders in the Haldane phase, are studied. We show that the surface formed by the ladders ends …
The special surface transition at (2+1)-dimensional quantum critical point is precluded in corresponding classical critical point. The mechanism of such behavior which is only found in dimerized Heisenberg models so far is still under debate. To illuminate the role of symmetry protected topological (SPT) phase in inducing such nonordinary behaviors, we study a system on a two-dimensional square lattice consisted by interacting spin-1 Haldane chains, which has a genuine SPT phase--the Haldane phase--at weak interchain interactions and a quantum critical point belonging to the classical 3D O(3) …
Quantum antiferromagnetic Heisenberg half-odd integer spin model as the entanglement Hamiltonian of the integer spin Affleck-Kennedy-Lieb-Tasaki states
We present a study of the spin-1/2 Heisenberg chain with alternating ferro- and antiferromagnetic exchange, focusing on the role of the exchange couplings to cover both, dimer and Haldane limit. Employing a complementary combination of perturbation theory and quantum Monte Carlo simulation, we report results for the magnetic susceptibility as well as the dynamic structure factor over a wide range of coupling constants and for different temperatures to extract the spin gap. For a small ferromagnetic coupling, we find good agreement between perturbation theory and quantum Monte Carlo. For arbitr…
The magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the 1/3 and 2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the 1/3 plateau are obtained by using the approximated state in the unit cell and compared with the nu- merical results of the exact diagonalization of 42 sites.
