The origin of holomorphic states in Landau levels from non-commutative geometry and a new formula for their overlaps on the torus
- Princeton Univ., NJ (United States)
Holomorphic functions that characterize states in a two-dimensional Landau level have been central to key developments such as the Laughlin state. Their origin has historically been attributed to a special property of “Schrödinger wavefunctions” of states in the “lowest Landau level.” In this work, it is shown that they instead arise in any Landau level as a generic mathematical property of the Heisenberg description of the non-commutative geometry of guiding centers. When quasiperiodic boundary conditions are applied to compactify the system on a torus, a new formula for the overlap between holomorphic states, in the form of a discrete sum rather than an integral, is obtained. The new formula is unexpected from the previous “lowest-Landau level Schrödinger wavefunction” interpretation.
- Research Organization:
- Princeton Univ., NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- SC0002140
- OSTI ID:
- 1512960
- Alternate ID(s):
- OSTI ID: 1464994
- Journal Information:
- Journal of Mathematical Physics, Vol. 59, Issue 8; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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