Abstract
We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical \mathcal{Y}𝒴-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.
Highlights
The equilibration phenomena of quantum many-body systems have become a vigorous research topic for both theoretical and experimental studies of condensed matter systems in recent years
One of the key findings of this work is that in thermodynamic/large-N limit the canonical structure is superseded by an emergent equilibrium landscape, encoded in non-trivial node terms λj and generically non- meromorphic thermodynamic Y -functions involving branch points inside P
We have developed a robust and unified framework which encompasses both the Thermodynamic Bethe Ansatz and the two-dimensional vertexmodel regularisation approaches to thermodynamics
Summary
The equilibration phenomena of quantum many-body systems have become a vigorous research topic for both theoretical and experimental studies of condensed matter systems in recent years. The unconventional equilibration exhibited by (nearly) integrable systems has drawn substantial interest, leading to the notion of the Generalized Gibbs Ensemble (GGE) [4,5,6]. The majority of the literature on equilibration in integrable systems has focused on non-interacting models, where the concept of a generalised Gibbs ensemble is synonymous to prescribing the occupations of single-particle modes [8, 9]. Interacting integrable systems on the other hand exhibit rich spectra of stable excitations which undergo non-trivial completely factorizable scattering [10]. This places interacting integrable systems in a distinguished position, and raises the question whether interactions induce physically discernible features among equilibrium states.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
