A modular-invariant modified Weierstrass sigma-function as a building block for lowest-Landau-level wavefunctions on the torus
- Princeton Univ., NJ (United States). Dept. of Physics
A “modified” variant of the Weierstrass sigma, zeta, and elliptic functions is proposed whereby the zeta function is redefined by $$ζ(z) \mapsto \tilde{ζ}(z) ≡ ζ(z) - γ_2z$$, where γ2 is a lattice invariant related to the almost-holomorphic modular invariant of the quasi-modular-invariant weight-2 Eisenstein series. If ωi is a primitive half-period, $$\tilde{ζ}(ω_i) = πω^{*}_{i}/A$$, where A is the area of the primitive cell of the lattice. The quasiperi-odicity of the modified sigma function is much simpler than that of the original, and it becomes the building-block for the modular-invariant formulation of lowest-Landau-level wavefunctions on the torus. It is suggested that the “modified” sigma function is more natural than the original Weierstrass form, which was formulated before quasi-modular forms were understood. Finally, for the high-symmetry (square and hexagonal) lattices, the modified and original sigma functions coincide.
- Research Organization:
- Princeton Univ., NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0002140
- OSTI ID:
- 1540241
- Alternate ID(s):
- OSTI ID: 1459239
- Journal Information:
- Journal of Mathematical Physics, Vol. 59, Issue 7; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Elliptic Functions According to Eisenstein and Kronecker: An Update
|
journal | January 2016 |
A new construction of Eisenstein’s completion of the Weierstrass zeta function
|
journal | July 2015 |
The origin of holomorphic states in Landau levels from non-commutative geometry and a new formula for their overlaps on the torus
|
journal | August 2018 |
Dirac Fermion Hierarchy of Composite Fermi Liquids
|
journal | June 2019 |
Hall viscosity of composite fermions
|
journal | February 2020 |
| Lattice Monte Carlo for Quantum Hall States on a Torus | text | January 2017 |
| Dirac Fermion Hierarchy of Composite Fermi Liquids | text | January 2018 |
| Hall Viscosity of Composite Fermions | text | January 2019 |
Similar Records
Landau automorphic functions on C{sup n} of magnitude {nu}
Light-Front Holography, Light-Front Wavefunctions, and Novel QCD Phenomena