Fractal dimension and the counting rule of the Goldstone modes
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918147539337216 |
|---|---|
| author | Shi, Qian-Qian Dai, Yan-Wei Zhou, Huan-Qiang McCulloch, Ian P. |
| author_facet | Shi, Qian-Qian Dai, Yan-Wei Zhou, Huan-Qiang McCulloch, Ian P. |
| contents | It is argued that there are a set of orthonormal basis states, which appear as highly degenerate ground states arising from spontaneous symmetry breaking with a type-B Goldstone mode, and they are scale-invariant, with a salient feature that the entanglement entropy $S(n)$ scales logarithmically with the block size $n$ in the thermodynamic limit. As it turns out, the prefactor is half the number of type-B Goldstone modes $N_B$. This is achieved by performing an exact Schmidt decomposition of the orthonormal basis states, thus unveiling their self-similarities in the real space--the essence of a fractal. Combining with a field-theoretic prediction [O. A. Castro-Alvaredo and B. Doyon, Phys. Rev. Lett. \textbf{108}, 120401 (2012)], we are led to the identification of the fractal dimension $d_f$ with the number of type-B Goldstone modes $N_B$ for the orthonormal basis states in quantum many-body systems undergoing spontaneous symmetry breaking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01071 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fractal dimension and the counting rule of the Goldstone modes Shi, Qian-Qian Dai, Yan-Wei Zhou, Huan-Qiang McCulloch, Ian P. Strongly Correlated Electrons It is argued that there are a set of orthonormal basis states, which appear as highly degenerate ground states arising from spontaneous symmetry breaking with a type-B Goldstone mode, and they are scale-invariant, with a salient feature that the entanglement entropy $S(n)$ scales logarithmically with the block size $n$ in the thermodynamic limit. As it turns out, the prefactor is half the number of type-B Goldstone modes $N_B$. This is achieved by performing an exact Schmidt decomposition of the orthonormal basis states, thus unveiling their self-similarities in the real space--the essence of a fractal. Combining with a field-theoretic prediction [O. A. Castro-Alvaredo and B. Doyon, Phys. Rev. Lett. \textbf{108}, 120401 (2012)], we are led to the identification of the fractal dimension $d_f$ with the number of type-B Goldstone modes $N_B$ for the orthonormal basis states in quantum many-body systems undergoing spontaneous symmetry breaking. |
| title | Fractal dimension and the counting rule of the Goldstone modes |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2201.01071 |