Abstract
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.
| Original language | English (US) |
|---|---|
| Article number | 104406 |
| Journal | Physical Review B |
| Volume | 97 |
| Issue number | 10 |
| DOIs | |
| State | Published - Mar 7 2018 |
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ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
Cite this
Exploring one-particle orbitals in large many-body localized systems. / Villalonga, Benjamin; Yu, Xiongjie; Luitz, David J.; Clark, Bryan K.
In: Physical Review B, Vol. 97, No. 10, 104406, 07.03.2018.Research output: Contribution to journal › Article
}
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.
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.
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U2 - 10.1103/PhysRevB.97.104406
DO - 10.1103/PhysRevB.97.104406
M3 - Article
AN - SCOPUS:85043981786
VL - 97
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 10
M1 - 104406
ER -