Kubo-Martin-Schwinger relation for an interacting mobile impurity
arXiv:2308.06482 · doi:10.1103/PhysRevResearch.5.043265
Abstract
In this work we study the Kubo-Martin-Schwinger (KMS) relation in the Yang-Gaudin model of an interacting mobile impurity. We use the integrability of the model to compute the dynamic injection and ejection Green's functions at finite temperatures. We show that due to separability of the Hilbert space with an impurity, the ejection Green's in a canonical ensemble cannot be reduced to a single expectation value as per microcanonical picture. Instead, it involves a thermal average over contributions from different subspaces of the Hilbert space which, due to the integrability, are resolved using the so-called spin rapidity. It is then natural to consider the injection and ejection Green's functions within each subspace. By means of reformulating the original KMS condition as a Riemann-Hilbert problem, we analytically demonstrate that such Green's functions obey a refined analogous relation, which is finally corroborated by numerical evaluation.
20 pages, 3 figures
References in corpus (9)
- Thermalization and its mechanism for generic isolated quantum systems
- Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
- Generalized Thermalization in an Integrable Lattice System
- Quantum transport through a Tonks-Girardeau gas
- Spin dynamics in a one-dimensional ferromagnetic Bose gas
- Bloch oscillations in one-dimensional spinor gas
- Thermal out-of-time-order correlators, KMS relations, and spectral functions
- Impurity Green's function of a one-dimensional Fermi-gas
- Effective free-fermionic form factors and the XY spin chain