TY - JOUR
T1 - Exploring one-particle orbitals in large many-body localized systems
AU - Villalonga, Benjamin
AU - Yu, Xiongjie
AU - Luitz, David J.
AU - Clark, Bryan K.
N1 - We thank Fabian Heidrich-Meisner for useful discussions. D.J.L. also would like to thank Jens Bardarson and David Pekker for interesting discussions on one-particle orbitals and l-bits. B.K.C. would like to thank David Pekker for valuable discussions and collaboration on related projects involving correlation lengths of MBL phases. This project was supported in part by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4305 at the University of Illinois, and has received support from the US Department of Energy, Office of Science, Basic Energy Sciencs under Award No. DE-FG02-11ER16211, as well as funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 747914 (QMBDyn). D.J.L. acknowledges PRACE for awarding access to HLRS's Hazel Hen computer based in Stuttgart, Germany, under Grant No. 2016153659. Our SIMPS code used in this work is built on top of the ITensor library. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.
We thank Fabian Heidrich-Meisner for useful discussions. D.J.L. also would like to thank Jens Bardarson and David Pekker for interesting discussions on one-particle orbitals and l-bits. B.K.C. would like to thank David Pekker for valuable discussions and collaboration on related projects involving correlation lengths of MBL phases. This project was supported in part by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4305 at the University of Illinois, and has received support from the US Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-FG02-11ER16211, as well as funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 747914 (QMBDyn). D.J.L. acknowledges PRACE for awarding access to HLRS's Hazel Hen computer based in Stuttgart, Germany, under Grant No. 2016153659. Our SIMPS code used in this work is built on top of the ITensor library. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.
PY - 2018/3/7
Y1 - 2018/3/7
N2 - Strong disorder in interacting quantum systems can give rise to the phenomenon of many-body localization (MBL), which defies thermalization due to the formation of an extensive number of quasilocal integrals of motion. The one-particle operator content of these integrals of motion is related to the one-particle orbitals (OPOs) of the one-particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.046603; Ann. Phys. 529, 1600356 (2017)ANPYA20003-380410.1002/andp.201600356]. We study the properties of the OPOs of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS, a matrix product state method to target highly excited many-body eigenstates introduced previously [Phys. Rev. Lett. 118, 017201 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.017201], we are able to obtain accurate results for large systems of sizes up to L=64. We find that the OPOs drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the OPOs decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find that the probability distribution of the strength of the large-range coupling constants of the number operators generated by the OPOs approach a log-uniform distribution at strong disorder.
AB - Strong disorder in interacting quantum systems can give rise to the phenomenon of many-body localization (MBL), which defies thermalization due to the formation of an extensive number of quasilocal integrals of motion. The one-particle operator content of these integrals of motion is related to the one-particle orbitals (OPOs) of the one-particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.046603; Ann. Phys. 529, 1600356 (2017)ANPYA20003-380410.1002/andp.201600356]. We study the properties of the OPOs of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS, a matrix product state method to target highly excited many-body eigenstates introduced previously [Phys. Rev. Lett. 118, 017201 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.017201], we are able to obtain accurate results for large systems of sizes up to L=64. We find that the OPOs drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the OPOs decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find that the probability distribution of the strength of the large-range coupling constants of the number operators generated by the OPOs approach a log-uniform distribution at strong disorder.
UR - http://www.scopus.com/inward/record.url?scp=85043981786&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85043981786&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.97.104406
DO - 10.1103/PhysRevB.97.104406
M3 - Article
AN - SCOPUS:85043981786
SN - 2469-9950
VL - 97
JO - Physical Review B
JF - Physical Review B
IS - 10
M1 - 104406
ER -