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

Abstract

Motivated by recent progress on field-induced phase transitions in quasi-one-dimensional quantum antiferromagnets, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations. The interchain interaction is shown to enhance longitudinal spin correlations and stabilize an incommensurate longitudinal spin density wave order at intermediate fields. With increasing field, the ground state changes to a canted antiferromagnetic order and the magnetization fully saturates above a quantum critical point, which is shown to fall into the (3+2)D XY universality. In the quantum critical regime, the system experiences a fascinating dimensional crossover to a universal Tomonaga-Luttinger liquid (TLL) as demonstrated by the continuous change of the critical exponent of the specific heat. The TLL behavior extends to a broad field and temperature regime, as characterized by the calculated NMR relaxation rate 1/T_{1}. Our results not only explain a number of puzzling observations in a quasi-one-dimensional antiferromagnet YbAlO_{3} but also lay down a concrete ground to the study on these materials in general.