Solvable entanglement dynamics in quantum circuits with generalized space-time duality
We study the nonequilibrium dynamics of kicked Ising models in 1 + 1 dimensions which have interactions alternating between odd and even bonds in time. These models can be understood as quantum circuits tiling space-time with the generalized space-time dual properties of triunitarity (three “arrows...
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.L012011 |
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| author | Chuan Liu Wen Wei Ho |
| author_facet | Chuan Liu Wen Wei Ho |
| author_sort | Chuan Liu |
| collection | DOAJ |
| description | We study the nonequilibrium dynamics of kicked Ising models in 1 + 1 dimensions which have interactions alternating between odd and even bonds in time. These models can be understood as quantum circuits tiling space-time with the generalized space-time dual properties of triunitarity (three “arrows of time”) at the global level, and also second-level dual unitarity at the local level, which constrains the behavior of pairs of local gates underlying the circuit under a space-time rotation. We identify a broad class of initial product states wherein the effect of the environment on a small subsystem can be exactly represented by influence matrices with simple Markovian structures, resulting in the subsystem's full dynamics being efficiently computable. We further find additional conditions under which the dynamics of entanglement can be solved for all times, yielding rich phenomenology ranging from linear growth at half the maximal speed allowed by locality, followed by saturation to maximum entropy (i.e., thermalization to infinite temperature), to entanglement growth with saturation to extensive but submaximal entropy. Intriguingly, for certain parameter regimes, we find a nonchaotic class of dynamics which is neither integrable nor Clifford, exemplified by nonzero operator entanglement growth but with a spectral form factor which exhibits large, apparently time-quasiperiodic revivals. |
| format | Article |
| id | doaj-art-0af16ee574ae4cfebef1b173edb04d86 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-0af16ee574ae4cfebef1b173edb04d862025-01-17T15:03:41ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-0171L01201110.1103/PhysRevResearch.7.L012011Solvable entanglement dynamics in quantum circuits with generalized space-time dualityChuan LiuWen Wei HoWe study the nonequilibrium dynamics of kicked Ising models in 1 + 1 dimensions which have interactions alternating between odd and even bonds in time. These models can be understood as quantum circuits tiling space-time with the generalized space-time dual properties of triunitarity (three “arrows of time”) at the global level, and also second-level dual unitarity at the local level, which constrains the behavior of pairs of local gates underlying the circuit under a space-time rotation. We identify a broad class of initial product states wherein the effect of the environment on a small subsystem can be exactly represented by influence matrices with simple Markovian structures, resulting in the subsystem's full dynamics being efficiently computable. We further find additional conditions under which the dynamics of entanglement can be solved for all times, yielding rich phenomenology ranging from linear growth at half the maximal speed allowed by locality, followed by saturation to maximum entropy (i.e., thermalization to infinite temperature), to entanglement growth with saturation to extensive but submaximal entropy. Intriguingly, for certain parameter regimes, we find a nonchaotic class of dynamics which is neither integrable nor Clifford, exemplified by nonzero operator entanglement growth but with a spectral form factor which exhibits large, apparently time-quasiperiodic revivals.http://doi.org/10.1103/PhysRevResearch.7.L012011 |
| spellingShingle | Chuan Liu Wen Wei Ho Solvable entanglement dynamics in quantum circuits with generalized space-time duality Physical Review Research |
| title | Solvable entanglement dynamics in quantum circuits with generalized space-time duality |
| title_full | Solvable entanglement dynamics in quantum circuits with generalized space-time duality |
| title_fullStr | Solvable entanglement dynamics in quantum circuits with generalized space-time duality |
| title_full_unstemmed | Solvable entanglement dynamics in quantum circuits with generalized space-time duality |
| title_short | Solvable entanglement dynamics in quantum circuits with generalized space-time duality |
| title_sort | solvable entanglement dynamics in quantum circuits with generalized space time duality |
| url | http://doi.org/10.1103/PhysRevResearch.7.L012011 |
| work_keys_str_mv | AT chuanliu solvableentanglementdynamicsinquantumcircuitswithgeneralizedspacetimeduality AT wenweiho solvableentanglementdynamicsinquantumcircuitswithgeneralizedspacetimeduality |