$c=-2$ conformal field theory in quadratic band touching
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911277483294720 |
|---|---|
| author | Masaoka, Rintaro |
| author_facet | Masaoka, Rintaro |
| contents | Quadratic band touching in fermionic systems defines a universality class distinct from that of linear Dirac points, yet its characterization as a quantum critical point remains incomplete. In this work, I show that a $(d+1)$-dimensional free-fermion model with quadratic band touching exhibits spatial conformal invariance, and that its equal-time ground-state correlation functions are exactly captured by the $d$-dimensional symplectic fermion theory. I establish this correspondence by constructing explicit mappings between physical fermionic operators and the fields of the symplectic fermion theory. I further explore the implications of this correspondence in two spatial dimensions, where the symplectic fermion theory is a logarithmic conformal field theory with central charge $c=-2$. In the corresponding $(2+1)$-dimensional systems, I identify anyonic excitations originating from the underlying symplectic fermion theory, even though the Hamiltonian is gapless. Transporting these excitations along non-contractible loops generates transitions among topologically degenerate ground states, in close analogy with those in topologically ordered phases. Moreover, the action of a $2π$ rotation on these excitations is represented by a Jordan block, reflecting the logarithmic character of the associated conformal field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $c=-2$ conformal field theory in quadratic band touching Masaoka, Rintaro Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quadratic band touching in fermionic systems defines a universality class distinct from that of linear Dirac points, yet its characterization as a quantum critical point remains incomplete. In this work, I show that a $(d+1)$-dimensional free-fermion model with quadratic band touching exhibits spatial conformal invariance, and that its equal-time ground-state correlation functions are exactly captured by the $d$-dimensional symplectic fermion theory. I establish this correspondence by constructing explicit mappings between physical fermionic operators and the fields of the symplectic fermion theory. I further explore the implications of this correspondence in two spatial dimensions, where the symplectic fermion theory is a logarithmic conformal field theory with central charge $c=-2$. In the corresponding $(2+1)$-dimensional systems, I identify anyonic excitations originating from the underlying symplectic fermion theory, even though the Hamiltonian is gapless. Transporting these excitations along non-contractible loops generates transitions among topologically degenerate ground states, in close analogy with those in topologically ordered phases. Moreover, the action of a $2π$ rotation on these excitations is represented by a Jordan block, reflecting the logarithmic character of the associated conformal field theory. |
| title | $c=-2$ conformal field theory in quadratic band touching |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.16496 |