Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet

TL;DR

This paper investigates the finite-temperature phase diagram of a frustrated quantum antiferromagnet, revealing a line of critical points and a quantum critical end point, with detailed numerical analysis confirming their universality classes.

Contribution

It demonstrates the existence of finite-temperature critical points and a quantum critical end point in the frustrated bilayer Heisenberg model, using advanced quantum Monte Carlo and tensor-network methods.

Findings

Finite-temperature critical points are in the Ising universality class.

A quantum critical end point exists where the zero-temperature transition terminates.

High-precision simulations confirm the nature of phase transitions.

Abstract

We consider the finite-temperature phase diagram of the $S = 1/2$ frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of first-order transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer and the dimer-singlet state terminates on the first-order line, giving a quantum critical end point, and we use tensor-network calculations to follow the first-order discontinuities in its vicinity.