# Emergent criticality in fully frustrated quantum magnets

**Authors:** Yuchen Fan, Ning Xi, Changle Liu, Bruce Normand, Rong Yu  
**arXiv:** [2306.16288](https://arxiv.org/abs/2306.16288)  
**Date:** 2023-06-28  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.16288v1/

## Key points

- Phase transitions in condensed matter physics are associated with the emergence of exotic properties.
- A recent study focused on the fully frustrated bilayer Heisenberg antiferromagnet and discovered a novel emergent criticality when a magnetic field is applied.
- The quantum phase diagram of this system consists of four distinct states: DS, DTAF, TC, and FM.
- The thermal phase diagram is dominated by a discontinuous wall extending from the zero-field DTAF-DS transition to a quantum critical endpoint.
- At the quantum critical endpoint, the magnetic field drives both the DTAF and TC states into the FM state.
- The first-order wall is terminated at finite temperatures by a line of critical points where two important transitions occur: BKT transition of DTAF and thermal Ising transition of TC.
- Extensive quantum Monte Carlo simulations demonstrate that while the BKT transition does not change the Ising nature of the DTAF-DS critical line, there is a unique phenomenon occurring at the multicritical point where symmetries merge on the DTAF-TC line.
- This phenomenon leads to a 4-state Potts universality associated with an Ashkin-Teller model that is not explicitly contained in the microscopic Hamiltonian.
- The researchers provide additional information in their Supplementary Information regarding calculations, simulations, data analysis, and discussions related to emergent criticality in fully frustrated bilayer Heisenberg antiferromagnets.
- Relevant literature including papers on universality and interfaces at critical endpoints, BKT transition, and fully frustrated XY model are referenced.
- Data and code supporting this study are available from corresponding author upon request.

## Summary

In condensed matter physics, phase transitions are often associated with the emergence of exotic properties. A recent study focused on the fully frustrated bilayer Heisenberg antiferromagnet and discovered that applying a magnetic field leads to a novel emergent criticality. The quantum phase diagram of this system consists of four distinct states: DS (singlets on every interlayer dimer bond), DTAF (all triplets with antiferromagnetic order), TC (a singlet-triplet checkerboard), and FM (saturated ferromagnet). The thermal phase diagram is dominated by a discontinuous wall that extends from the zero-field DTAF-DS transition to a quantum critical endpoint. At this endpoint, the magnetic field drives both the DTAF and TC states into the FM state. This first-order wall is terminated at finite temperatures by a line of critical points, where two important transitions occur: the Berezinskii-Kosterlitz-Thouless (BKT) transition of the DTAF and the thermal Ising transition of the TC. Through extensive quantum Monte Carlo simulations, researchers demonstrated that while the BKT transition does not change the Ising nature of the DTAF-DS critical line, there is a unique phenomenon occurring at the multicritical point where symmetries merge on the DTAF-TC line. This phenomenon leads to a 4-state Potts universality that is not explicitly contained in the microscopic Hamiltonian but can be associated with an Ashkin-Teller model. The researchers provide additional information in their Supplementary Information regarding their calculations, simulations, data analysis, and discussions related to emergent criticality in fully frustrated bilayer Heisenberg antiferromagnets. They also reference relevant literature including papers on universality and interfaces at critical endpoints, BKT transition, and fully frustrated XY model. The data and code supporting this study are available from corresponding author upon request.