2017/12/31 by Michael Pretko, Rahul Nandkishore, Rahul M. Nandkishore
Mathematics · Physics and Astronomy · #Anderson localization #Cosmic string #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Randomness #String (physics) #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el #cond-mat.supr-con #hep-th
paper · pdf · doi:10.1103/physrevb.98.134301
published as Phys. Rev. B 98, 134301 (2018) · 16 pages
openalex publication_date 2018/10/03 · arxiv created 2018/10/04 · arxiv updated 2018/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions. We generalize this concept to a system of extended objects, such as strings and membranes, arguing that such a system can also exhibit localization in the presence of sufficiently strong disorder (randomness) in the Hamiltonian. We show that localization of large extended objects can be mapped to a lower-dimensional many-body localization problem. For example, motion of a string involves propagation of pointlike signals down its length to keep the different segments in causal contact. For sufficiently strong disorder, all such internal modes will exhibit many-body localization, resulting in the localization of the entire string. The eigenstates of the system can then be constructed perturbatively through a convergent ``string locator expansion.'' We propose a type of out-of-time-order string correlator as a diagnostic of such a string localized phase. Localization of other higher-dimensional objects, such as membranes, can also be studied through a hierarchical construction by mapping onto the localization of lower-dimensional objects. Our arguments are ``asymptotic'' (i.e., valid up to rare regions) but they extend the notion of localization (and localization protected order) to a host of settings where such ideas previously did not apply. These include high-dimensional ferromagnets with domain wall excitations, three-dimensional topological phases with looplike excitations, and three-dimensional type-II superconductors with flux line excitations. In type-II superconductors, localization of flux lines could stabilize superconductivity at energy densities where a normal state would arise in thermal equilibrium.