Unfolding a composed ensemble of energy spectra using singular value decomposition
arXiv:2303.04755 · doi:10.1209/0295-5075/acd5fa
Abstract
In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an ensemble where there are large realization-to-realization fluctuations the canonical methods for unfolding fail. Here we show that singular value decomposition can be used even for the challenging situations where the ensemble is composed out of realizations originating from a different range of parameters resulting in a non-monotonous local density of states. This can be useful in experimental situations for which the physical parameters can not be tightly controlled, of for situations for which the local density of states is strongly fluctuating.
arXiv comment5 pages, 4 figures
References in corpus (16)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Anderson Transitions
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Localization of interacting fermions at high temperature
- Comments on the Sachdev-Ye-Kitaev model
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Statistics of energy levels and eigenfunctions in disordered systems
- The Statistical Theory of Quantum Dots
- Onset of Random Matrix Behavior in Scrambling Systems
- Eigenstate thermalization in the Sachdev-Ye-Kitaev model
- On super-Poissonian behavior of the Rosenzweig-Porter model in the non-ergodic extended regime
- Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
- Random Matrix Spectra as a Time Series
- Probing the metallic energy spectrum beyond the Thouless energy scale using the singular value decomposition
- Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
- Sachdev-Ye-Kitaev model: Non-self-averaging properties of the energy spectrum