Bootstrapping Disordered Quantum Systems
Abstract
We present a bootstrap framework that yields rigorous two-sided bounds on ground-state observables of quantum systems with quenched disorder. The key idea is to extend the operator algebra to include classical disorder variables and to encode the disorder distribution through a set of moments. The method directly bounds disorder-averaged expectation values for finite or infinite lattice systems and for arbitrary disorder distributions. In contrast to conventional approaches, we do not need to sample disorder realizations, which enables us to make thorough use of symmetries that hold only on average rather than for each disorder realization. Additionally, we show that multi-replica operators can be used to access disorder fluctuations such as the variance of an observable. We apply the method to the one-dimensional random transverse-field Ising model (RTFIM) with discrete, uniform, and Gaussian disorder, obtaining tight bounds on the disorder-averaged ground-state energy density and short-range spin-spin correlators, as well as bounds on the disorder variance of the energy density. Additionally, we show that the difference between the upper and lower bounds on the disorder-averaged ground-state energy density, which we term the bootstrap gap, can be used to map out the phase diagram of the RTFIM. The bootstrap gap is small and flat within the paramagnetic and ferromagnetic phases at weak disorder, grows upon entering the Griffiths regions, and peaks along the critical line.
Related
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- Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
- Bootstrapping Classical Systems with Quenched Disorder
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- Locking transition in coupled disordered systems
BibTeX
@misc{onder2026bootstrapping,
title = {{Bootstrapping Disordered Quantum Systems}},
author = {Yaprak Önder and Michael G. Scheer and Minjae Cho and Eslam Khalaf},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20916},
eprint = {2609.20916},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20916},
}
RIS
TY - UNPB
TI - Bootstrapping Disordered Quantum Systems
AU - Yaprak Önder
AU - Michael G. Scheer
AU - Minjae Cho
AU - Eslam Khalaf
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20916
UR - https://arxiv.org/abs/2609.20916
AB - We present a bootstrap framework that yields rigorous two-sided bounds on ground-state observables of quantum systems with quenched disorder. The key idea is to extend the operator algebra to include classical disorder variables and to encode the disorder distribution through a set of moments. The method directly bounds disorder-averaged expectation values for finite or infinite lattice systems and for arbitrary disorder distributions. In contrast to conventional approaches, we do not need to sample disorder realizations, which enables us to make thorough use of symmetries that hold only on average rather than for each disorder realization. Additionally, we show that multi-replica operators can be used to access disorder fluctuations such as the variance of an observable. We apply the method to the one-dimensional random transverse-field Ising model (RTFIM) with discrete, uniform, and Gaussian disorder, obtaining tight bounds on the disorder-averaged ground-state energy density and short-range spin-spin correlators, as well as bounds on the disorder variance of the energy density. Additionally, we show that the difference between the upper and lower bounds on the disorder-averaged ground-state energy density, which we term the bootstrap gap, can be used to map out the phase diagram of the RTFIM. The bootstrap gap is small and flat within the paramagnetic and ferromagnetic phases at weak disorder, grows upon entering the Griffiths regions, and peaks along the critical line.
ER -