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

TL;DR

This study maps the phase diagram and quantum critical behavior of Heisenberg spin chains with Ising-like interchain couplings, revealing incommensurate order, quantum critical points, and Luttinger liquid behavior relevant to YbAlO$_3$.

Contribution

It provides the first large-scale quantum Monte Carlo analysis of the phase diagram and quantum criticality in anisotropic Heisenberg chains with implications for real materials.

Findings

Incommensurate longitudinal spin density wave order at low temperatures.

Quantum critical point with $(3+2)$D XY universality.

Luttinger liquid behavior persists over broad field and temperature ranges.

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.