Universal properties of single particle excitations across the many-body localization transition
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911934158209024 |
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| author | Jana, Atanu Chandra, V. Ravi Garg, Arti |
| author_facet | Jana, Atanu Chandra, V. Ravi Garg, Arti |
| contents | Understanding the nature of the transition from the delocalized to the many-body localized (MBL) phase is an important unresolved issue. To probe the nature of the MBL transition, we investigate the universal properties of single-particle excitations produced in highly excited many-body eigenstates of a disordered interacting quantum many-body system. In a class of one-dimensional spinless fermionic models with random disorder, we study the finite size scaling of the ratio of typical to average values of the single-particle local density of states and the scattering rates across the MBL transition. Our results indicate that the MBL transition in this class of one-dimensional models of spinless fermions is continuous in nature. For various ranges of interactions in the system, the critical exponent $ν$ with which the correlation length $ξ$ diverges at the transition point $W_c$, $ξ\sim |W-W_c|^{-ν}$, satisfies the Chayes-Chayes-Fisher-Spencer(CCFS) bound $ν\ge 2/d$ where $d$ is the physical dimension of the system. We also discuss why the critical exponent obtained from finite-size scaling of the conventional diagnostic of many-body localization, the level-spacing ratio, strongly violates the CCFS bound while the single-particle density of states and scattering rates are consistent with the CCFS criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08480 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Universal properties of single particle excitations across the many-body localization transition Jana, Atanu Chandra, V. Ravi Garg, Arti Disordered Systems and Neural Networks Statistical Mechanics Understanding the nature of the transition from the delocalized to the many-body localized (MBL) phase is an important unresolved issue. To probe the nature of the MBL transition, we investigate the universal properties of single-particle excitations produced in highly excited many-body eigenstates of a disordered interacting quantum many-body system. In a class of one-dimensional spinless fermionic models with random disorder, we study the finite size scaling of the ratio of typical to average values of the single-particle local density of states and the scattering rates across the MBL transition. Our results indicate that the MBL transition in this class of one-dimensional models of spinless fermions is continuous in nature. For various ranges of interactions in the system, the critical exponent $ν$ with which the correlation length $ξ$ diverges at the transition point $W_c$, $ξ\sim |W-W_c|^{-ν}$, satisfies the Chayes-Chayes-Fisher-Spencer(CCFS) bound $ν\ge 2/d$ where $d$ is the physical dimension of the system. We also discuss why the critical exponent obtained from finite-size scaling of the conventional diagnostic of many-body localization, the level-spacing ratio, strongly violates the CCFS bound while the single-particle density of states and scattering rates are consistent with the CCFS criterion. |
| title | Universal properties of single particle excitations across the many-body localization transition |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2212.08480 |