analiza aiqbench
This is foundational quantum many-body theory, not a device or hardware result. It proves that thermal states of quantum spin chains can be written as mixtures of matrix product states with a bond dimension independent of system size, so the Schmidt number stays finite even in the thermodynamic limit. For quantum readers, the practical value is the efficient classical sampling algorithm, which could inform classical simulation of thermal quantum systems and the limits of what entanglement can do at finite temperature.
Entanglement in quantum spin chains is strictly finite at any temperature
arXiv:2602.13386v2 Announce Type: replace Abstract: Entanglement is the hallmark of quantum physics, yet its characterization in interacting many-body systems at thermal equilibrium remains one of the most important challenges in quantum statistical physics. We prove that the Gibbs state of any quantum spin chain can be exactly decomposed into a mixture of matrix product states with a bond dimension that is independent of the system size, at any nonzero temperature. As a consequence, the Schmidt number, arguably the most stringent measure of bipartite entanglement, is strictly finite for thermal states, even in the thermodynamic limit. Our decomposition is explicit and is accompanied by an efficient classical algorithm to sample the resulting matrix product states.
Abstract:Entanglement is the hallmark of quantum physics, yet its characterization in interacting many-body systems at thermal equilibrium remains one of the most important challenges in quantum statistical physics. We prove that the Gibbs state of any quantum spin chain can be exactly decomposed into a mixture of matrix product states with a bond dimension that is independent of the system size, at any nonzero temperature. As a consequence, the Schmidt number, arguably the most stringent measure of bipartite entanglement, is strictly finite for thermal states, even in the thermodynamic limit. Our decomposition is explicit and is accompanied by an efficient classical algorithm to sample the resulting matrix product states.
33 pages, 1 figure. Improved constants
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
arXiv:2602.13386 [quant-ph]
(or arXiv:2602.13386v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2602.13386 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 213 cuvinte
Subiecte conexe
Basis-independent coherence and quantum correlations in two dipole-dipole-coupled electrons in double quantum-dot molecules
arXiv · 24 iul. 2026
Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
arXiv · 19 oct. 2026
Symmetry enforces entanglement at high temperatures
arXiv · 21 sept. 2026
Extensive entanglement between coupled Tomonaga-Luttinger liquids in and out of equilibrium
arXiv · 7 aug. 2026