Analytical derivation of the scaling law for the inverse participation ratio in quasi-one-dimensional disordered systems

1992 ◽  
Vol 69 (7) ◽  
pp. 1093-1096 ◽  
Author(s):  
Yan V. Fyodorov ◽  
Alexander D. Mirlin
Keyword(s):  
Disordered Systems ◽  
Scaling Law ◽  
Inverse Participation Ratio ◽  
One Dimensional ◽  
Analytical Derivation ◽  
Participation Ratio

scholarly journals Displacement Transformations as a Tool to Study Many-Body Localization

2021 ◽  
Vol 9 ◽  
Author(s):  
Pablo Serna ◽  
Miguel Ortuño ◽  
Andrés M. Somoza
Keyword(s):  
Excited States ◽  
Short Range ◽  
The State ◽  
Large System ◽  
Many Body ◽  
Inverse Participation Ratio ◽  
One Dimensional ◽  
Participation Ratio

We obtain eigenstates of interacting disorder Hamiltonians using unitary displacement transformations that rotate the state of the system. The method generates excited states if the strength of these transformations is chosen to optimize the energy, while decreasing the energy variance. We apply the method to analyse the localization properties of one-dimensional spinless fermions with short range interactions, reaching relatively large system sizes. We quantify the degree of localization through the size and disorder dependence of the inverse participation ratio.

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