Work

Markov inequality as a tool for linear-scaling estimation of local observables

Year: 2026

Type: article

Abstract: We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive semidefinite estimators, the sampling error at each site can be rigorously bounded relative to the mean via the Markov inequality, overcoming the lack of self-averaging and enabling accurate estimates even under strong spatial fluctuations. The approach extends to nondiagonal observables, such as local currents, through local unitary transformations and its effectiveness is showcased by benchmark calculations in the disordered two-dimensional π -flux model, where the local density of states and steady-state current maps are computed. This method will enable simulations of disorder-driven mesoscopic physics in realistically large lattices and accelerate real-space self-consistent mean-field calculations.

Source: Physical Review Research

DOI: 10.1103/qb1w-44r1

Authors: H. P. Veiga, D. R. Pinheiro, J. P. Santos Pires, J. M. Viana Parente Lopes

Institutions: Universidade do Porto, Centro de Física das Universidades do Minho e do Porto, University of York

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funder: Fundação para a Ciência e a Tecnologia