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Statistical Test Comparison for Entanglement-Weighted Operator Geometry and Condensed Matter Physics: A Complete Statistical Validation

Chavis Srichan

Published Jan 15, 2026• 0 citations
Publisher

Abstract

This study performs a comprehensive statistical comparison between predictions derived from Entanglement-Weighted Operator Geometry (EWOG) and traditional Condensed Matter (CM) physics models. Using experimental data from three paradigmatic quantum material classes—heavy-fermion systems, quantum spin liquids, and unconventional superconductors—we apply information-theoretic criteria (AIC, BIC), Bayesian model selection, and frequentist hypothesis testing. Our analysis demonstrates that EWOG models consistently provide superior fits to experimental data with greater parameter efficiency. For $\mathrm{CeCoIn}_{5}$ specific heat data, EWOG yields $\Delta\text{AIC} = 14.5$ and Bayes factor $>10^3$ versus the best CM model. We present complete numerical derivations of all statistical tests, establishing EWOG as a statistically superior framework for describing emergent phenomena in strongly correlated quantum matter.

DOI
10.5281/zenodo.18260381

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European journal of applied sciences•May 3, 2026•0 citations
This study performs a comprehensive statistical comparison between predictions derived from Entanglement-Weighted Operator Geometry (EWOG) and traditional Condensed Matter (CM) physics models. Using experimental data from three paradigmatic quantum material classes—heavy-fermion systems, quantum spin liquids, and unconventional superconductors—we apply information-theoretic criteria (AIC, BIC), Bayesian model selection, and frequentist hypothesis testing. Our analysis demonstrates that EWOG models consistently provide superior fits to experimental data with greater parameter efficiency. For CeCoIn5\mathrm{CeCoIn}_{5}CeCoIn5​ specific heat data, EWOG yields ΔAIC=14.5\Delta\text{AIC} = 14.5ΔAIC=14.5 and Bayes factor >103>10^3>103 versus the best CM model. We present complete numerical derivations of all statistical tests, establishing EWOG as a statistically superior framework for describing emergent phenomena in strongly correlated quantum matter.
We investigate various topics in theoretical quantum condensed matter physics.First, we show that a one-dimensional quantum wire with as few as 2 channels of interacting fermions can host metallic Luttinger liquid states of matter that are stable against all perturbations up to $q^\\text{th}$-order in fermion creation/annihilation operators for any fixed finite qqq.The leading relevant perturbations are thus complicated operators that are expected to modify the physics only at very low energies, below accessible temperatures. The stability of these Luttinger liquid fixed points is due to strong interactions between the channels, which can (but need not) be chosen to be purely repulsive. Our results might enable elementary physical realizations of these phases, and may also serve as a useful paradigm for thinking about higher-dimensional non-Fermi liquids. Separately, we present an elementary but general description of relaxation to gaussian and equilibrium generalized Gibbs states in lattice models of fermions or bosons with quadratic hamiltonians. Our analysis applies to arbitrary initial states that satisfy a mild condition on clustering of correlations.We obtain quantitive, model-independent predictions for how quickly local quantities relax in such systems.These predictions can be tested in near-term quantum gas experiments.Finally, we study chaotic many-body quantum systems that obey the eigenstate thermalization hypothesis (ETH).We show that a known bound on the growth rate of the out-of-time-order four-point correlator in such systems follows directly from the general ETH structure of operator matrix elements.This ties together two key paradigms of thermal behavior in isolated many-body quantum systems.We also consider a bipartition of the system, and study the entanglement properties of an energy eigenstate with nonzero energy density.When the two subsystems have nearly equal volumes, we find a universal correction to the entanglement entropy that is proportional to the square root of the system's heat capacity (or a sum of capacities, if there are conserved quantities in addition to energy).
The collective behavior exhibited by a large number of microscopic quantum particles is at the heart of some of the most striking phenomena in condensed matter physics such as Bose-Einstein condensation and superconductivity. Physicists and mathematicians have made great progress in understanding when and how these collective phenomena emerge through the interplay of particle statistics, particle interaction and the value of thermodynamic parameters like the temperature or the chemical potential. Due to the extreme complexity of realistic many-body systems, it is natural to introduce appropriate simplifications to render their analysis feasible. Three examples of such simplifications which have proven themselves as viable starting points for a fruitful and mathematically rigorous analysis of many-body systems are the following: (a) the study of integrable models; (b) the derivation of effective theories, valid on a macroscopic scale, from more fundamental microscopic theories under appropriate coarse-graining; and (c) the use of quantum information theory to understand general connections between correlation, entanglement and particle statistics. In this thesis, we present mathematically rigorous results that were obtained in these three directions. (1) We prove anomalous quantum many-body transport in XY quantum spin chains for certain choices of the external magnetic field. The anomalous transport is described via new kinds of anomalous Lieb-Robinson bounds, including one of power-law type. We note that the XY spin chain is integrable as it can be mapped to free fermions via the non-local Jordan-Wigner transformation. (2) We derive effective macroscopic theories of Ginzburg-Landau type from the microscopic BCS theory of superconductivity in certain circumstances. We study the case of a multi-component order parameter for translation-invariant systems and the condensation of fermion pairs at zero temperature in a domain with a hard boundary. (3) We use techniques from quantum information-theory to derive bounds on the entropy of fermionic reduced density matrices, a measure of the entanglement inherent to a fermionic quantum state.
We report an experimental investigation of frequency shifts in multipartite entangled quantum systems using a SpinQ-compatible quantum platform. By systematically varying the number of entangled qubits NNN while holding all geometric and electromagnetic parameters fixed, we test whether observed frequency shifts can be explained solely by quantum electrodynamics (QED), including the Lamb shift, or whether an additional entanglement-dependent contribution is required. We formulate and compare two competing models: a QED-only model predicting an NNN-independent shift, and a QED+EWOG model incorporating an entanglement-weighted correction motivated by Entanglement-Weighted Operator Gravity (EWOG). Rigorous statistical analysis---using root-mean-square error (RMSE), coefficient of determination (R2R^2R2), residual diagnostics, and the Akaike Information Criterion (AIC)---demonstrates decisive evidence in favor of the EWOG extension. Our results provide quantitative experimental support for the hypothesis that multipartite entanglement induces an effective geometric correction to coherent quantum dynamics beyond standard QED.
We report an experimental investigation of frequency shifts in multipartite entangled quantum systems using a SpinQ-compatible quantum platform. By systematically varying the number of entangled qubits NNN while holding all geometric and electromagnetic parameters fixed, we test whether observed frequency shifts can be explained solely by quantum electrodynamics (QED), including the Lamb shift, or whether an additional entanglement-dependent contribution is required. We formulate and compare two competing models: a QED-only model predicting an NNN-independent shift, and a QED+EWOG model incorporating an entanglement-weighted correction motivated by Entanglement-Weighted Operator Gravity (EWOG). Rigorous statistical analysis---using root-mean-square error (RMSE), coefficient of determination (R2R^2R2), residual diagnostics, and the Akaike Information Criterion (AIC)---demonstrates decisive evidence in favor of the EWOG extension. Our results provide quantitative experimental support for the hypothesis that multipartite entanglement induces an effective geometric correction to coherent quantum dynamics beyond standard QED.
Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the \log{L} log L scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal L\log L L log L scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provide new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.
Entanglement entropy serves as a fundamental diagnostic for quantum many-body correlations, distinguishing quantum entanglement from classical stochastic fluctuations. This review systematically explores the scaling behaviors of entanglement entropy, beginning with the foundational area law in Hermitian systems and progressing to the exotic regimes of non-Hermitian physics. We focus on the mathematical apparatus of the Fisher-Hartwig theorem in fermionic chains, the biorthogonal formalism in non-unitary systems, and the emergence of negative entanglement entropy driven by exceptional boundary states and non-unitary conformal field theories.