Unscrambling of single-particle wave functions in systems localized through disorder and monitoring

Journal article

In systems undergoing localization-delocalization quantum phase transitions due to disorder or monitoring, there is a crucial need for robust methods capable of distinguishing phases and uncovering their intrinsic properties. In this paper, we develop a process of finding a Slater determinant representation of free-fermion wave functions that accurately characterizes localized particles, a procedure we dub "unscrambling."The central idea is to minimize the overlap between envelopes of single-particle wave functions or, equivalently, to maximize the inverse participation ratio of each orbital. This numerically efficient methodology can differentiate between distinct types of wave functions: exponentially localized, power-law localized, and conformal critical, also revealing the underlying physics of these states. The method is readily extendable to systems in higher dimensions. Furthermore, we apply this approach to a more challenging problem involving disordered monitored free fermions in one dimension, where the unscrambling process unveils the presence of a conformal critical phase and a localized area-law quantum Zeno phase. Importantly, our method can also be extended to free fermion systems without particle number conservation, which we demonstrate by estimating the phase diagram of Z2-symmetric disordered monitored free fermions. Our results unlock the potential of utilizing single-particle wave functions to gain valuable insights into the localization transition properties in systems such as monitored free fermions and disordered models.

Authors: Szyniszewski, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review B
• Volume: 110
• Issue: 2
• Article number: 024303
• Publication date: 2024-07-01
• Acceptance date: 2024-06-21
• DOI: 10.1103/physrevb.110.024303
• EISSN: 2469-9969
• ISSN: 2469-9950
• Language: English