Bootstrapping the Kronig-Penney Model
Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the Schr\"odinger equation with periodic potentials, payin...
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| description | Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the Schr\"odinger equation with periodic potentials, paying particular attention to the Kronig-Penney model of a particle in a one-dimensional lattice. With an appropriate choice of operator basis involving position and momenta, we find that the bootstrap approach efficiently computes the band gaps of the energy spectrum but has trouble effectively constraining the minimum energy. We show how applying more complex constraints involving higher powers of momenta can potentially remedy such a problem. We also propose an approach for analytically constructing the dispersion relation associated with the Bloch momentum of the system. |
| doi_str_mv | 10.48550/arxiv.2209.09919 |
| format | Article |
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| subjects | Energy gap Energy spectra Field theory Mechanical systems Physics - High Energy Physics - Lattice Physics - High Energy Physics - Theory Physics - Quantum Physics Physics - Statistical Mechanics Physics - Strongly Correlated Electrons Quantum mechanics Statistical methods |
| title | Bootstrapping the Kronig-Penney Model |
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