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Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
- Source :
- npj Quantum Mater. 8, 59 (2023)
- Publication Year :
- 2023
-
Abstract
- The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension $D\le 2$. For long-range interactions with a power-law form ($1/r^{\alpha}$), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when $\alpha\ge 2D$. However, the situation for $\alpha \in (2,4)$ at $D=2$ is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of $SU(2)$ symmetry in the ferromagnetic Heisenberg model with $1/r^{\alpha}$-form long-range interactions at $D=2$. We determine critical exponents through finite-size analysis for $\alpha<3$ (above the upper critical dimension with Gaussian fixed point) and $3\le\alpha<4$ (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem's scope.
- Subjects :
- Condensed Matter - Strongly Correlated Electrons
Subjects
Details
- Database :
- arXiv
- Journal :
- npj Quantum Mater. 8, 59 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2306.01044
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1038/s41535-023-00591-6