Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929379412541440 |
|---|---|
| author | Schumm, Gabe Shao, Hui Guo, Wenan Mila, Frédéric Sandvik, Anders W. |
| author_facet | Schumm, Gabe Shao, Hui Guo, Wenan Mila, Frédéric Sandvik, Anders W. |
| contents | Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated (Villain) transverse-field Ising model on the square lattice. We consider a "primary" spin order parameter and a "secondary" dimer order parameter, which both lead to the same phase diagram but detect $Z_8$ and $Z_4$ symmetry, respectively. The spin order scales with conventional exponents, both in the finite temperature critical phase and at the $T = 0$ quantum critical point. The scaling of the dimer order requires more detailed investigations of the applicable low-energy theories; the height model at $T > 0$ and the $O(2)$ model in 2+1 dimensions at $T = 0$. Relating the order parameters to operators in these effective models, we predict the secondary critical exponents and confirm them numerically. The relationships between the primary and secondary order parameters have not been previously discussed in this context and provide insight more broadly for Ising models whose low-energy physics involves dimer degrees of freedom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02407 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice Schumm, Gabe Shao, Hui Guo, Wenan Mila, Frédéric Sandvik, Anders W. Strongly Correlated Electrons High Energy Physics - Lattice Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated (Villain) transverse-field Ising model on the square lattice. We consider a "primary" spin order parameter and a "secondary" dimer order parameter, which both lead to the same phase diagram but detect $Z_8$ and $Z_4$ symmetry, respectively. The spin order scales with conventional exponents, both in the finite temperature critical phase and at the $T = 0$ quantum critical point. The scaling of the dimer order requires more detailed investigations of the applicable low-energy theories; the height model at $T > 0$ and the $O(2)$ model in 2+1 dimensions at $T = 0$. Relating the order parameters to operators in these effective models, we predict the secondary critical exponents and confirm them numerically. The relationships between the primary and secondary order parameters have not been previously discussed in this context and provide insight more broadly for Ising models whose low-energy physics involves dimer degrees of freedom. |
| title | Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice |
| topic | Strongly Correlated Electrons High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2309.02407 |