Universal features of higher-form symmetries at phase transitions
| Autor: | Chao-Ming Jian, Cenke Xu, Xiao-Chuan Wu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Quantum phase transition Wilson loop Strongly Correlated Electrons (cond-mat.str-el) Operator (physics) QC1-999 General Physics and Astronomy FOS: Physical sciences Field (mathematics) Expectation value Combinatorics Loop (topology) Condensed Matter - Strongly Correlated Electrons Homogeneous space Symmetry (geometry) |
| Zdroj: | SciPost Physics, Vol 11, Iss 2, p 033 (2021) |
| ISSN: | 2542-4653 |
| Popis: | We investigate the behavior of higher-form symmetries at various quantum phase transitions. We consider discrete 1-form symmetries, which can be either part of the generalized concept "categorical symmetry" (labelled as $\tilde{Z}_N^{(1)}$) introduced recently, or an explicit $Z_N^{(1)}$ 1-form symmetry. We demonstrate that for many quantum phase transitions involving a $Z_N^{(1)}$ or $\tilde{Z}_N^{(1)}$ symmetry, the following expectation value $ \langle \left( \log O_\mathcal{C} \right)^2 \rangle$ takes the form $\langle \left( \log O_\mathcal{C} \right)^2 \rangle \sim - \frac{A}{\epsilon} P+ b \log P $, where $O_\mathcal{C}$ is an operator defined associated with loop $\mathcal{C}$ (or its interior $\mathcal{A}$), which reduces to the Wilson loop operator for cases with an explicit $Z_N^{(1)}$ 1-form symmetry. $P$ is the perimeter of $\mathcal{C}$, and the $b \log P$ term arises from the sharp corners of the loop $\mathcal{C}$, which is consistent with recent numerics on a particular example. $b$ is a universal microscopic-independent number, which in (2+1)d is related to the universal conductivity at the quantum phase transition. $b$ can be computed exactly for certain transitions using the dualities between (2+1)d conformal field theories developed in recent years. We also compute the "strange correlator" of $O_\mathcal{C}$: $S_{\mathcal{C}} = \langle 0 | O_\mathcal{C} | 1 \rangle / \langle 0 | 1 \rangle$ where $|0\rangle$ and $|1\rangle$ are many-body states with different topological nature. Comment: 9 pages, 2 figures |
| Databáze: | OpenAIRE |
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