Eigenstates of fully many-body localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called l bits. These spin algebras define quasilocal l -bit measurement (τiz) and l -bit flip (τix) 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 (L2) 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.
Physical Review B
- Pub Date:
- March 2019
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics;
- Quantum Physics
- 10 pages, 7 figures, added references