Université de Toulouse, CNRS, UPS (France); Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with nonergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. Here, we find that a localized many-body ground state of a given interacting disordered Hamiltonian H0 is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to H0 but more disordered. Lastly, this construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to L=256 sites.
Dupont, Maxime and Laflorencie, Nicolas. "Many-body localization as a large family of localized ground states." Physical Review B, vol. 99, no. 2, Jan. 2019. https://doi.org/10.1103/PhysRevB.99.020202
Dupont, Maxime, & Laflorencie, Nicolas (2019). Many-body localization as a large family of localized ground states. Physical Review B, 99(2). https://doi.org/10.1103/PhysRevB.99.020202
Dupont, Maxime, and Laflorencie, Nicolas, "Many-body localization as a large family of localized ground states," Physical Review B 99, no. 2 (2019), https://doi.org/10.1103/PhysRevB.99.020202
@article{osti_1506401,
author = {Dupont, Maxime and Laflorencie, Nicolas},
title = {Many-body localization as a large family of localized ground states},
annote = {Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with nonergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. Here, we find that a localized many-body ground state of a given interacting disordered Hamiltonian H0 is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to H0 but more disordered. Lastly, this construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to L=256 sites.},
doi = {10.1103/PhysRevB.99.020202},
url = {https://www.osti.gov/biblio/1506401},
journal = {Physical Review B},
issn = {ISSN PRBMDO},
number = {2},
volume = {99},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2019},
month = {01}}
Devakul, Trithep; Khemani, Vedika; Pollmann, Frank
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 375, Issue 2108https://doi.org/10.1098/rsta.2016.0431