We compare the accuracy of two prime time evolution algorithms involving matrix product states---tDMRG (time-dependent density matrix renormalization group) and TDVP (time-dependent variational principle). The latter is supposed to be superior within a limited and fixed auxiliary space dimension. Surprisingly, we find that the performance of algorithms depends on the model considered. In particular, many-body localized systems as well as the crossover regions between localized and delocalized phases are better described by tDMRG, contrary to the delocalized regime where TDVP indeed outperforms tDMRG in terms of accuracy and reliability. As an example, we study many-body localization transition in a large size Heisenberg chain. We discuss drawbacks of previous estimates [Phys. Rev. B 98, 174202 (2018)] of the critical disorder strength for large systems.We compare the accuracy of two prime time evolution algorithms involving matrix product states---tDMRG (time-dependent density matrix renormalization group) and TDVP (time-dependent variational principle). The latter is supposed to be superior within a limited and fixed auxiliary space dimension. Surprisingly, we find that the performance of algorithms depends on the model considered. In particular, many-body localized systems as well as the crossover regions between localized and delocalized phases are better described by tDMRG, contrary to the delocalized regime where TDVP indeed outperforms tDMRG in terms of accuracy and reliability. As an example, we study many-body localization transition in a large size Heisenberg chain. We discuss drawbacks of previous estimates [Phys. Rev. B 98, 174202 (2018)] of the critical disorder strength for large systems.

arXiv:1908.06524Physical review. B./Physical review. BJan 29, 202091 citations

Long range interaction and breakdown of many-body localization

Alexander L. Burin

Sep 29, 20140 citations

Entanglement scaling of excited states in large one-dimensional many-body localized systems

Dante Marvin Kennes, Christoph Karrasch

We study the properties of excited states in one-dimensional many-body localized (MBL) systems using a matrix product state algorithm. First, the method is tested for a large disordered noninteracting system, where for comparison we compute a quasiexact reference solution via a Monte Carlo sampling of the single-particle levels. Thereafter, we present extensive data obtained for large interacting systems of $L\ensuremath{\sim}100$ sites and large bond dimensions $\ensuremath{\chi}\ensuremath{\sim}1700$, which allows us to quantitatively analyze the scaling behavior of the entanglement $S$ in the system. The MBL phase is characterized by a logarithmic growth $S(L)\ensuremath{\sim}log(L)$ over a large scale separating the regimes where volume and area laws hold. We check the validity of the eigenstate thermalization hypothesis. Our results are consistent with the existence of a mobility edge.We study the properties of excited states in one-dimensional many-body localized (MBL) systems using a matrix product state algorithm. First, the method is tested for a large disordered noninteracting system, where for comparison we compute a quasiexact reference solution via a Monte Carlo sampling of the single-particle levels. Thereafter, we present extensive data obtained for large interacting systems of $L\ensuremath{\sim}100$ sites and large bond dimensions $\ensuremath{\chi}\ensuremath{\sim}1700$, which allows us to quantitatively analyze the scaling behavior of the entanglement $S$ in the system. The MBL phase is characterized by a logarithmic growth $S(L)\ensuremath{\sim}log(L)$ over a large scale separating the regimes where volume and area laws hold. We check the validity of the eigenstate thermalization hypothesis. Our results are consistent with the existence of a mobility edge.

arXiv:1511.02205Physical review. B./Physical review. BJun 14, 201634 citations

One-body density-matrix characterization of many-body localization

Fabian Heidrich‐Meisner, Soumya Bera, Thomas Martynec +2 more

Bulletin of the American Physical SocietyJun 7, 20170 citations

Encoding the structure of many-body localization with matrix product operators

David Pekker, Bryan K. Clark

Anderson insulators are noninteracting disordered systems which have localized single-particle eigenstates. The interacting analog of Anderson insulators are the many-body localized (MBL) phases. The spectrum of the many-body eigenstates of an Anderson insulator is efficiently represented as a set of product states over the single-particle modes. We show that product states over matrix product operators of small bond dimension is the corresponding efficient description of the spectrum of an MBL insulator. In this language all of the many-body eigenstates are encoded by matrix product states (i.e., density matrix renormalization group wave functions) consisting of only two sets of low bond dimension matrices per site: the ${G}_{i}$ matrices corresponding to the local ground state on site $i$ and the ${E}_{i}$ matrices corresponding to the local excited state. All ${2}^{n}$ eigenstates can be generated from all possible combinations of these sets of matrices.Anderson insulators are noninteracting disordered systems which have localized single-particle eigenstates. The interacting analog of Anderson insulators are the many-body localized (MBL) phases. The spectrum of the many-body eigenstates of an Anderson insulator is efficiently represented as a set of product states over the single-particle modes. We show that product states over matrix product operators of small bond dimension is the corresponding efficient description of the spectrum of an MBL insulator. In this language all of the many-body eigenstates are encoded by matrix product states (i.e., density matrix renormalization group wave functions) consisting of only two sets of low bond dimension matrices per site: the ${G}_{i}$ matrices corresponding to the local ground state on site $i$ and the ${E}_{i}$ matrices corresponding to the local excited state. All ${2}^{n}$ eigenstates can be generated from all possible combinations of these sets of matrices.

arXiv:1410.2224Physical review. B./Physical review. BJan 10, 201742 citations

S

in the system. The MBL phase is characterized by a logarithmic growth $S(L)\ensuremath{\sim}log(L)$ over a large scale separating the regimes where volume and area laws hold. We check the validity of the eigenstate thermalization hypothesis. Our results are consistent with the existence of a mobility edge.

{G}_{i}

matrices corresponding to the local ground state on site

i

and the

{E}_{i}

matrices corresponding to the local excited state. All

{2}^{n}

eigenstates can be generated from all possible combinations of these sets of matrices.