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

• URL: http://arxiv.org/abs/2403.10725v4
• Date: Fri, 12 Jul 2024 19:12:07 GMT
• Title: Unscrambling of single-particle wave functions in systems localized through disorder and monitoring
• Authors: Marcin Szyniszewski,
• Abstract summary: We develop a process of finding a Slater determinant representation of free-fermion wave functions that accurately characterizes localized particles. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 work, 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 $\mathbb{Z}_2$-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.

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