Integral formula for the propagator of the one-dimensional Hubbard model
Taiki Ishiyama, Kazuya Fujimoto, Tomohiro Sasamoto
TL;DR
This paper derives an exact integral formula for the multi-particle propagator of the one-dimensional Hubbard model, facilitating precise analysis of its nonequilibrium dynamics without relying on the string hypothesis.
Contribution
It introduces a novel integral representation of the propagator using the nested Bethe ansatz, applicable to finite-particle wave functions and related quantum models.
Findings
Exact integral formula for the Hubbard model propagator
Enables explicit time evolution analysis of finite-particle states
Applicable to open quantum systems
Abstract
We present an exact integral formula for the multi-particle propagator of the one-dimensional Fermi--Hubbard model on an infinite lattice. The proof is based on the nested Bethe ansatz without relying on the string hypothesis. Our formula enables an explicit integral representation of the time evolution of arbitrary finite-particle wave functions and thereby provides a foundation for the exact analysis of nonequilibrium dynamics in the Hubbard model. It can further be applied to related open quantum models.
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Taxonomy
TopicsQuantum many-body systems · Algebraic structures and combinatorial models · Cold Atom Physics and Bose-Einstein Condensates