Emergent symmetries and Interactions: An isolated fixed point Vs a manifold of strongly interacting fixed points
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911886475264000 |
|---|---|
| author | Zhou, Fei |
| author_facet | Zhou, Fei |
| contents | In this article, we study conditions of continuous emergent symmetries in gapless states, either as topological quantum critical points (TQCPs) or a stable phase with protecting symmetries and connections to smooth deformations of the gapped states around. We illustrate that for a wide class of gapless states that can be associated with fully-isolated scale invariant fixed points, there shall always be emergent continuous symmetries that are directly related to smooth deformations of gapped states with symmetries lower than the protecting ones $G_p$. For a 3D TQCP in DIII classes with $G_p=Z^T_2$, $U_{EM}=U(1)$ and $N_f=\frac{1}{2}$ fermions but without charge $U(1)$ symmetry, we explicitly construct a corresponding boundary representation based on a $4D$ topological state with lattice symmetry $H=Z^T_2 \ltimes U(1)$ and $N_f={1}$ fermions. Although emergent continuous symmetries appear to be robust at weakly interacting TQCPs, we further show the breakdown of such one-to-one correspondence between deformations of gapped states and emergent continuous symmetries when gapless states become strongly interacting. In a strongly interacting limit, gapless states can be represented by a smooth manifold of conformal-field-theory fixed points rather than a fully isolated one. A smooth manifold of strong coupling fixed points hinders emergence of a continuous emergent symmetry in the strongly interacting gapless limit, as deformations no longer leave a gapless state or a TQCP invariant, unlike in the more conventional weakly interacting case. This typically reduces continuous emergent symmetries to a discrete symmetry originating from duality transformations under the protection symmetry $G_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12252 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Emergent symmetries and Interactions: An isolated fixed point Vs a manifold of strongly interacting fixed points Zhou, Fei Strongly Correlated Electrons Statistical Mechanics Superconductivity In this article, we study conditions of continuous emergent symmetries in gapless states, either as topological quantum critical points (TQCPs) or a stable phase with protecting symmetries and connections to smooth deformations of the gapped states around. We illustrate that for a wide class of gapless states that can be associated with fully-isolated scale invariant fixed points, there shall always be emergent continuous symmetries that are directly related to smooth deformations of gapped states with symmetries lower than the protecting ones $G_p$. For a 3D TQCP in DIII classes with $G_p=Z^T_2$, $U_{EM}=U(1)$ and $N_f=\frac{1}{2}$ fermions but without charge $U(1)$ symmetry, we explicitly construct a corresponding boundary representation based on a $4D$ topological state with lattice symmetry $H=Z^T_2 \ltimes U(1)$ and $N_f={1}$ fermions. Although emergent continuous symmetries appear to be robust at weakly interacting TQCPs, we further show the breakdown of such one-to-one correspondence between deformations of gapped states and emergent continuous symmetries when gapless states become strongly interacting. In a strongly interacting limit, gapless states can be represented by a smooth manifold of conformal-field-theory fixed points rather than a fully isolated one. A smooth manifold of strong coupling fixed points hinders emergence of a continuous emergent symmetry in the strongly interacting gapless limit, as deformations no longer leave a gapless state or a TQCP invariant, unlike in the more conventional weakly interacting case. This typically reduces continuous emergent symmetries to a discrete symmetry originating from duality transformations under the protection symmetry $G_p$. |
| title | Emergent symmetries and Interactions: An isolated fixed point Vs a manifold of strongly interacting fixed points |
| topic | Strongly Correlated Electrons Statistical Mechanics Superconductivity |
| url | https://arxiv.org/abs/2310.12252 |