Spectral statistics in constrained many-body quantum chaotic systems
We study the spectral statistics of spatially extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert space dimension, we find that the spectral form factor K(t)...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.023176 |
| _version_ | 1797210998550036480 |
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| author | Sanjay Moudgalya Abhinav Prem David A. Huse Amos Chan |
| author_facet | Sanjay Moudgalya Abhinav Prem David A. Huse Amos Chan |
| author_sort | Sanjay Moudgalya |
| collection | DOAJ |
| description | We study the spectral statistics of spatially extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert space dimension, we find that the spectral form factor K(t) of Floquet random circuits can be mapped exactly to a classical Markov circuit, and, at late times, is related to the partition function of a frustration-free Rokhsar-Kivelson (RK) type Hamiltonian. Through this mapping, we show that the inverse of the spectral gap of the RK Hamiltonian lower bounds the Thouless time t_{Th} of the underlying circuit. For systems with conserved higher moments, we derive a field theory for the corresponding RK Hamiltonian by proposing a generalized height field representation for the Hilbert space of the effective spin chain. Using the field theory formulation, we obtain the dispersion of the low-lying excitations of the RK Hamiltonian in the continuum limit, which allows us to extract t_{Th}. In particular, we analytically argue that in a system of length L that conserves the mth multipole moment, t_{Th} scales subdiffusively as L^{2(m+1)}. We also show that our formalism directly generalizes to higher dimensional circuits, and that in systems that conserve any component of the mth multipole moment, t_{Th} has the same scaling with the linear size of the system. Our work therefore provides a general approach for studying spectral statistics in constrained many-body chaotic systems. |
| first_indexed | 2024-04-24T10:19:30Z |
| format | Article |
| id | doaj.art-7678b6cd5ae94a9780fd967c41463599 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:19:30Z |
| publishDate | 2021-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-7678b6cd5ae94a9780fd967c414635992024-04-12T17:10:28ZengAmerican Physical SocietyPhysical Review Research2643-15642021-06-013202317610.1103/PhysRevResearch.3.023176Spectral statistics in constrained many-body quantum chaotic systemsSanjay MoudgalyaAbhinav PremDavid A. HuseAmos ChanWe study the spectral statistics of spatially extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert space dimension, we find that the spectral form factor K(t) of Floquet random circuits can be mapped exactly to a classical Markov circuit, and, at late times, is related to the partition function of a frustration-free Rokhsar-Kivelson (RK) type Hamiltonian. Through this mapping, we show that the inverse of the spectral gap of the RK Hamiltonian lower bounds the Thouless time t_{Th} of the underlying circuit. For systems with conserved higher moments, we derive a field theory for the corresponding RK Hamiltonian by proposing a generalized height field representation for the Hilbert space of the effective spin chain. Using the field theory formulation, we obtain the dispersion of the low-lying excitations of the RK Hamiltonian in the continuum limit, which allows us to extract t_{Th}. In particular, we analytically argue that in a system of length L that conserves the mth multipole moment, t_{Th} scales subdiffusively as L^{2(m+1)}. We also show that our formalism directly generalizes to higher dimensional circuits, and that in systems that conserve any component of the mth multipole moment, t_{Th} has the same scaling with the linear size of the system. Our work therefore provides a general approach for studying spectral statistics in constrained many-body chaotic systems.http://doi.org/10.1103/PhysRevResearch.3.023176 |
| spellingShingle | Sanjay Moudgalya Abhinav Prem David A. Huse Amos Chan Spectral statistics in constrained many-body quantum chaotic systems Physical Review Research |
| title | Spectral statistics in constrained many-body quantum chaotic systems |
| title_full | Spectral statistics in constrained many-body quantum chaotic systems |
| title_fullStr | Spectral statistics in constrained many-body quantum chaotic systems |
| title_full_unstemmed | Spectral statistics in constrained many-body quantum chaotic systems |
| title_short | Spectral statistics in constrained many-body quantum chaotic systems |
| title_sort | spectral statistics in constrained many body quantum chaotic systems |
| url | http://doi.org/10.1103/PhysRevResearch.3.023176 |
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