Ground-state phases of $S = 1/2$ Heisenberg models on the body-centered cubic lattice

TL;DR

This study uses neural quantum states to map the ground-state phases of frustrated quantum spin models on the body-centered cubic lattice, revealing phase transition points and the absence of a quantum paramagnetic phase in a model relevant to certain materials.

Contribution

First application of neural quantum states to 3D frustrated spin models on the BCC lattice, providing detailed phase diagrams and insights into material-specific models.

Findings

Identified a first-order transition between Néel and collinear phases at (J2/J1)_c=0.705.

Found no evidence of a quantum paramagnetic ground state in the tetragonally-distorted model.

Determined a phase transition between Néel and chain phases at (J2ab/J1)_c=1.0375.

Abstract

Simulating low-temperature properties of three-dimensional frustrated quantum magnets is challenging due to the sign problem and the system sizes required to mitigate substantial finite-size effects. However, there are many experimental examples of three-dimensional crystals that could host exotic low-temperature states of matter, such as quantum spin liquids. We calculate the ground-state phase diagrams of frustrated quantum spin models on the body-centered cubic lattice using neural quantum states. First, we study the antiferromagnetic $J_1-J_2$ model where we find a direct first-order phase transition between N\'eel and collinear long-range-ordered phases at $(J_2/J_1)_c = 0.705$, consistent with previous studies. Then, in a tetragonally-distorted variant, proposed as a minimal model of NaCa$_2$Cu$_2$(VO$_4$)$_3$, we find no evidence of a quantum paramagnetic ground state, with a first-order phase transition between N\'eel and chain phases at $(J_{2ab}/J_1)_c = 1.0375$. Therefore, the ground state of the tetragonally-distorted model does not reproduce the low-temperature magnetic properties of NaCa$_2$Cu$_2$(VO$_4$)$_3$, and the inclusion of other effects is necessary to rationalize experimental observations.