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arXiv:1908.08467 · Physical Review Research

Phase diagram and quantum criticality of Heisenberg spin chains with Ising anisotropic interchain couplings

Yuchen Fan, Jiahao Yang, Weiqiang Yu, Jianda Wu, Rong Yu

Published Mar 19, 2020• 19 citations
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Abstract

The authors find that the interchain Ising anisotropy of coupled spin-1/2 Heisenberg chains enhances longitudinal spin correlations and stabilizes an incommensurate antiferromagnetic order under a longitudinal magnetic field. The system shows a dimensional crossover in the quantum critical regime and exhibits Tomonaga-Luttinger liquid behavior over a broad field and temperature regime.

DOI
10.1103/physrevresearch.2.013345

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The authors find that the interchain Ising anisotropy of coupled spin-1/2 Heisenberg chains enhances longitudinal spin correlations and stabilizes an incommensurate antiferromagnetic order under a longitudinal magnetic field. The system shows a dimensional crossover in the quantum critical regime and exhibits Tomonaga-Luttinger liquid behavior over a broad field and temperature regime.
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We study isotropic antiferromagnetic Heisenberg chains coupled by antiferromagnetic Ising interaction as an effective spin model for the ytterbium aluminum perovskite YbAlO3{\mathrm{YbAlO}}_{3}YbAlO3​. Using the density-matrix renormalization group (DMRG) method we calculate the magnetization curve, local spin, central charge, and dynamical spin structure factors in the presence of magnetic field. From the fitting of the experimental magnetization curve, the effective intrachain and interchain couplings are estimated as J=2.3J=2.3J=2.3 K and Jic=0.8{J}_{\mathrm{ic}}=0.8Jic​=0.8 K, respectively. We can quantitatively explain the experimental observations: (i) phase transition from antiferromagnetic to incommensurate order at field 0.35 T, and (ii) quantum critical behaviors at the saturation field of 1.21 T. Furthermore, the low-energy excitations in the experimental inelastic neutron scattering spectra can be well described by our DMRG results of the dynamical structure factors.
We present a study of XYZXYZXYZ Heisenberg spin-12\frac{1}{2}21​ chain, along with its variant (XYXYXY Heisenberg spin-12\frac{1}{2}21​ Hamiltonian), under a transverse magnetic field. It reveals from our study that two competitive massive phases are separated by a gapless line (critical line). We find in our analysis that the critical points (trivial and nontrivial) are non-Gaussian in nature. There is no phase crossover owing to the change of the critical point from the trivial to the nontrivial one. There is no evidence of magnetization plateau, however the system is in the Ising criticality. The positive and negative values of umklapp-like scattering favor a short range antiferromagnetic order because of the XYXYXY anisotropy and the transverse field, respectively. Higher value of Luttinger liquid parameter (K)(K)(K) also favors the short range antiferromagnetic order due to the in-plane exchange anisotropy.
The thermodynamic properties of the weakly interacting spin-1/2 and spin-1 chains with the intrachain coupling J and interchain coupling $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$ are studied by using the linear renormalization-group method. The magnetic susceptibility of the weakly interacting s=1/2s=1/2s=1/2 quantum anisotropic Heisenberg chains in the longitudinal field (h) is investigated. The scaling shifts of the parallel susceptibility maxima in the external magnetic field are considered. The same method is used to study the specific heat and susceptibility of the weakly interacting S=1S=1S=1 Ising models. In the special case (Blume-Capel model) the phase diagram with critical and first-order transition lines is found. The location of the tricritical point for $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}/J=0.2$ is estimated.
Based on exact diagonalization and density matrix renormalization group method, we show that an anisotropic triangular lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an anisotropic spin structure factor with an exponential-decay spin correlator along the weaker coupling direction, consistent with the Cs2CuCl4{\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}Cs2​CuCl4​ compounds. In the obtained phase diagram, the spin-liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio ${J}^{\ensuremath{'}}∕J=0.78$, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime.
Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo_{2}V_{2}O_{8} in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.