Phase diagram and quantum criticality of Heisenberg spin chains with Ising-like interchain couplings -- Implication to YbAlO${}_3$

Abstract

Motivated by recent progress on field-induced phase transitions in quasi-one-dimensional quantum antiferromagnets, we study the phase diagram of $S=1/2$ antiferromagnetic Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations. The interchain interactions is shown to enhance longitudinal spin correlations to stabilize an incommensurate longitudinal spin density wave order at low temperatures. With increasing field the ground state changes to a canted antiferromagnetic order until the magnetization fully saturates above a quantum critical point controlled by the $(3+2)$D XY universality. Increasing temperature in the quantum critical regime the system experiences a fascinating dimension crossover to a universal Tomonaga-Luttinger liquid. The calculated NMR relaxation rate $1/T_1$ indicates this Luttinger liquid behavior survives a broad field and temperature regime. Our results determine the global phase diagram and quantitative features of quantum criticality of a general model for quasi-one-dimensional spin chain compounds, and thus lay down a concrete ground to the study on these materials.

arXiv comment4.5+3 pages, 4+6 figures

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Cited by in corpus (11)

• Spin Density Wave versus Fractional Magnetization Plateau in a Triangular Antiferromagnet
• Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain
• Low-energy spin dynamics in rare-earth perovskite oxides
• Quenches and confinement in a Heisenberg-Ising spin ladder
• Confinement in the spectrum of a Heisenberg-Ising spin ladder
• Field-induced antiferromagnetism and Tomonaga-Luttinger liquid behavior in the quasi-one-dimensional Ising-Antiferromagnet SrCo2V2O8
• Confinement of many-body Bethe strings
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• 1/5 and 1/3 magnetization plateaux in the spin 1/2 chain system YbAlO3
• Quantum scaling of the spin lattice relaxation rate in the checkerboard $J$-$Q$ model
• Thermally activated detection of dark particles in a weakly coupled quantum Ising ladder