HAL CCSD
Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains
Monthus, Cécile
Institut de Physique Théorique - UMR CNRS 3681 (IPHT) ; Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
International audience
ISSN: 0022-3719
Journal of Physics C: Solid State Physics
Institute of Physics (IOP)
cea-01321388
https://cea.hal.science/cea-01321388
https://cea.hal.science/cea-01321388/document
https://cea.hal.science/cea-01321388/file/1602.03064v1.pdf
https://cea.hal.science/cea-01321388
Journal of Physics C: Solid State Physics, 2016, 49, pp.305002. ⟨10.1088/1751-8113/49/30/305002⟩
ARXIV: 1602.03064
info:eu-repo/semantics/altIdentifier/arxiv/1602.03064
DOI: 10.1088/1751-8113/49/30/305002
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/49/30/305002
https://iopscience.iop.org/article/10.1088/1751-8113/49/30/305002
en
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
info:eu-repo/semantics/article
Journal articles
The iterative methods to diagonalize matrices and many-body Hamiltonians can be reformulated as flows of Hamiltonians towards diagonalization driven by unitary transformations that preserve the spectrum. After a comparative overview of the various types of discrete flows (Jacobi, QR-algorithm) and differential flows (Toda, Wegner, White) that have been introduced in the past, we focus on the random XXZ chain with random fields in order to determine the best closed flow within a given subspace of running Hamiltonians. For the special case of the free-fermion random XX chain with random fields, the flow coincides with the Toda differential flow for tridiagonal matrices which is related to the classical integrable Toda chain and which can be seen as the continuous analog of the discrete QR-algorithm. For the random XXZ chain with random fields that displays a Many-Body-Localization transition, the present differential flow should be an interesting alternative to compare with the discrete flow that has been proposed recently to study the Many-Body-Localization properties in a model of interacting fermions (L. Rademaker and M. Ortuno, Phys. Rev. Lett. 116, 010404 (2016)).
t16/041
2016-06-16
info:eu-repo/semantics/OpenAccess