Approximating observables on eigenstates of large manybody localized systems
Abstract
Eigenstates of fully manybody localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called l bits. These spin algebras define quasilocal l bit measurement (τ_{i}^{z}) and l bit flip (τ_{i}^{x}) operators. For a disordered Heisenberg spin chain in the MBL regime we approximate l bit flip operators by first calculating them exactly on small windows of systems using an algorithm called operator localization optimization. We then extend the l bit operators onto the whole system by exploiting their quasilocal nature. We subsequently use these operators to represent approximate eigenstates of the Hamiltonian. Finally, we describe a method to calculate products of local observables on these eigenstates for systems of size L in O (L^{2}) time. This method is used to calculate the variance of the energy of the approximate eigenstates, yielding an estimate of the error of the approximation.
 Publication:

Physical Review B
 Pub Date:
 March 2019
 DOI:
 10.1103/PhysRevB.99.104201
 arXiv:
 arXiv:1811.00442
 Bibcode:
 2019PhRvB..99j4201K
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 10 pages, 7 figures, added references