Zirnbauer, Martin R. (2021). Particle-hole symmetries in condensed matter. J. Math. Phys., 62 (2). MELVILLE: AIP Publishing. ISSN 1089-7658
Full text not available from this repository.Abstract
The term particle-hole symmetry is beset with conflicting meanings in contemporary physics. Conceived and written from a condensed-matter standpoint, the present paper aims to clarify and sharpen the terminology. In that vein, we propose to define the operation of particle-hole conjugation as the tautological algebra automorphism that simply swaps single-fermion creation and annihilation operators, and we construct its invariant lift to the Fock space. Particle-hole symmetries then arise for gapful or gapless free-fermion systems at half filling, as the concatenation of particle-hole conjugation with one or another involution that reverses the sign of the first-quantized Hamiltonian. We illustrate that construction principle with a series of examples including the Su-Schrieffer-Heeger model and the Kitaev-Majorana chain. For an enhanced perspective, we contrast particle-hole symmetries with the charge-conjugation symmetry of relativistic Dirac fermions. We go on to present two major applications in the realm of interacting electrons. For one, we offer a heuristic argument that the celebrated Haldane phase of antiferromagnetic quantum spin chains is adiabatically connected to a free-fermion topological phase protected by a particle-hole symmetry. For another, we review the recent proposal by Son [Phys. Rev. X 5, 031027 (2015)] for a particle-hole conjugation symmetric effective field theory of the half-filled lowest Landau level, and we comment on the emerging microscopic picture of the composite fermion.
| Item Type: | Journal Article | ||||||||
| Creators: |
|
||||||||
| URN: | urn:nbn:de:hbz:38-564075 | ||||||||
| DOI: | 10.1063/5.0035358 | ||||||||
| Journal or Publication Title: | J. Math. Phys. | ||||||||
| Volume: | 62 | ||||||||
| Number: | 2 | ||||||||
| Date: | 2021 | ||||||||
| Publisher: | AIP Publishing | ||||||||
| Place of Publication: | MELVILLE | ||||||||
| ISSN: | 1089-7658 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
|
||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/56407 |
Downloads
Downloads per month over past year
Altmetric
Export
Actions (login required)
 |
View Item |