Abstract
Although free-fermion systems are considered exactly solvable, they generically do not admit closed expressions for nonlocal quantities such as topological string correlations or entanglement measures. We derive closed expressions for such quantities for a dense subclass of certain classes of topological fermionic wires (classes BDI and AIII). Our results also apply to spin chains called generalised cluster models. While there is a bijection between general models in these classes and Laurent polynomials, restricting to polynomials with degenerate zeros leads to a plethora of exact results: (1) we derive closed expressions for the string correlation functions - the order parameters for the topological phases in these classes; (2) we obtain an exact formula for the characteristic polynomial of the correlation matrix, giving insight into ground state entanglement; (3) the latter implies that the ground state can be described by a matrix product state (MPS) with a finite bond dimension in the thermodynamic limit - an independent and explicit construction for the BDI class is given in a concurrent work [Phys. Rev. Res. 3 (2021), 033265, 26 pages, arXiv:2105.12143]; (4) for BDI models with even integer topological invariant, all non-zero eigenvalues of the transfer matrix are identified as products of zeros and inverse zeros of the aforementioned polynomial. General models in these classes can be obtained by taking limits of the models we analyse, giving a further application of our results. To the best of our knowledge, these results constitute the first application of Day's formula and Gorodetsky's formula for Toeplitz determinants to many-body quantum physics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Symmetry, Integrability and Geometry: Methods and Applications
Disclaimer: 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.