The presence of symmetries can lead to nontrivial dynamics of operator entanglement in open quantum many-body systems, which characterizes the cost of a matrix product density operator representation of the density matrix in tensor-network methods and provides insights into the corresponding classical simulability. One example is $\mathrm{U}(1)$ -symmetric open quantum systems with dephasing, in which the operator entanglement increases logarithmically at late times instead of being suppressed by the dephasing. Here we numerically study the far-from-equilibrium dynamics of operator entanglement in a dissipative quantum many-body system with the more complicated $\mathrm{SU}(2)$ symmetry and dissipations beyond dephasing. We show that after the initial rise and fall, the operator entanglement increases again in a logarithmic manner at late times in the $\mathrm{SU}(2)$ -symmetric case. We find that this behavior can be fully understood from the corresponding $\mathrm{U}(1)$ subsymmetry by considering the symmetry-resolved operator entanglement. Especially, the probability distribution of different $\mathrm{U}(1)$ sectors also follows the Gaussian distribution observed in the $\mathrm{U}(1)$ -symmetric case with dephasing, with the variance growing as a power law. But unlike the latter, both the classical Shannon entropy associated with the probabilities for the half system to be in different symmetry sectors and the corresponding symmetry-resolved operator entanglement now make nontrivial contributions to the late-time logarithmic growth of operator entanglement in our $\mathrm{SU}(2)$ -symmetric case. Our results show evidence that the logarithmic growth of operator entanglement at long times is a generic behavior of dissipative quantum many-body dynamics with $\mathrm{U}(1)$ as the symmetry or subsymmetry and for broader dissipations beyond dephasing, although more analytical and numerical proof from future studies is still required for this conjecture. By breaking the $\mathrm{SU}(2)$ symmetry of our quantum many-body dynamics to $\mathrm{U}(1)$ , we also show that the latter property---the logarithmic growth behavior of operator entanglement for broader dissipations beyond dephasing---is valid even for open quantum systems with only $\mathrm{U}(1)$ symmetry.The presence of symmetries can lead to nontrivial dynamics of operator entanglement in open quantum many-body systems, which characterizes the cost of a matrix product density operator representation of the density matrix in tensor-network methods and provides insights into the corresponding classical simulability. One example is $\mathrm{U}(1)$-symmetric open quantum systems with dephasing, in which the operator entanglement increases logarithmically at late times instead of being suppressed by the dephasing. Here we numerically study the far-from-equilibrium dynamics of operator entanglement in a dissipative quantum many-body system with the more complicated $\mathrm{SU}(2)$ symmetry and dissipations beyond dephasing. We show that after the initial rise and fall, the operator entanglement increases again in a logarithmic manner at late times in the $\mathrm{SU}(2)$-symmetric case. We find that this behavior can be fully understood from the corresponding $\mathrm{U}(1)$ subsymmetry by considering the symmetry-resolved operator entanglement. Especially, the probability distribution of different $\mathrm{U}(1)$ sectors also follows the Gaussian distribution observed in the $\mathrm{U}(1)$-symmetric case with dephasing, with the variance growing as a power law. But unlike the latter, both the classical Shannon entropy associated with the probabilities for the half system to be in different symmetry sectors and the corresponding symmetry-resolved operator entanglement now make nontrivial contributions to the late-time logarithmic growth of operator entanglement in our $\mathrm{SU}(2)$-symmetric case. Our results show evidence that the logarithmic growth of operator entanglement at long times is a generic behavior of dissipative quantum many-body dynamics with $\mathrm{U}(1)$ as the symmetry or subsymmetry and for broader dissipations beyond dephasing, although more analytical and numerical proof from future studies is still required for this conjecture. By breaking the $\mathrm{SU}(2)$ symmetry of our quantum many-body dynamics to $\mathrm{U}(1)$, we also show that the latter property---the logarithmic growth behavior of operator entanglement for broader dissipations beyond dephasing---is valid even for open quantum systems with only $\mathrm{U}(1)$ symmetry.

arXiv:2410.18468Physical review. B./Physical review. BSep 23, 20250 citations

Dephasing-induced growth of discrete time-crystalline order in spin networks

Akitada Sakurai, V. M. Bastidas, Marta P. Estarellas +2 more

A discrete time crystal (DTC) is a quantum phase of matter related to the symmetries of a periodically driven system. It can appear when the initial state breaks these symmetries, and hence the observation of DTCs is intimately related to the symmetry of the initial state. In this paper, we investigate a nontrivial situation in which two interacting regions are simultaneously prepared in two initial states that preserve and break this symmetry. Specifically, we discuss the behavior of such a system under the influence of an environment by extending Floquet theory to the Liouvillian dynamics. Our analysis shows that the entire system evolves toward a DTC phase and is stabilized by the effect of dephasing. Our results provide a new understanding of quantum phases emerging from the competition between the coherent and incoherent dynamics in dissipative nonequilibrium quantum systems.A discrete time crystal (DTC) is a quantum phase of matter related to the symmetries of a periodically driven system. It can appear when the initial state breaks these symmetries, and hence the observation of DTCs is intimately related to the symmetry of the initial state. In this paper, we investigate a nontrivial situation in which two interacting regions are simultaneously prepared in two initial states that preserve and break this symmetry. Specifically, we discuss the behavior of such a system under the influence of an environment by extending Floquet theory to the Liouvillian dynamics. Our analysis shows that the entire system evolves toward a DTC phase and is stabilized by the effect of dephasing. Our results provide a new understanding of quantum phases emerging from the competition between the coherent and incoherent dynamics in dissipative nonequilibrium quantum systems.

arXiv:2106.02765Physical review. B./Physical review. BAug 20, 20213 citations

Time symmetry and quantum measurements

Michel Bitbol

Physics Letters AMay 1, 19863 citations

Quantum Time-Reversal Symmetry

Woon Siong Gan

Springer eBooksJan 1, 20210 citations

Distinguishing between Quantum and Classical Markovian Dephasing Dissipation

Alireza Seif, Yu-Xin Wang, Aashish A. Clerk

Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider n qubits subject to correlated Markovian dephasing and present a sufficient condition for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry plays a crucial role: broken time-reversal symmetry is required for dissipative entanglement generation. Further, simply having nonzero bath susceptibilities is not enough for the dissipation to be quantum. We also present an explicit experimental protocol for identifying truly quantum dephasing dissipation and lay the groundwork for studying more complex dissipative systems and finding optimal noise mitigating strategies.Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider n qubits subject to correlated Markovian dephasing and present a sufficient condition for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry plays a crucial role: broken time-reversal symmetry is required for dissipative entanglement generation. Further, simply having nonzero bath susceptibilities is not enough for the dissipation to be quantum. We also present an explicit experimental protocol for identifying truly quantum dephasing dissipation and lay the groundwork for studying more complex dissipative systems and finding optimal noise mitigating strategies.

arXiv:2109.06155Physical Review LettersFeb 17, 202225 citations

\mathrm{U}(1)

-symmetric open quantum systems with dephasing, in which the operator entanglement increases logarithmically at late times instead of being suppressed by the dephasing. Here we numerically study the far-from-equilibrium dynamics of operator entanglement in a dissipative quantum many-body system with the more complicated

\mathrm{SU}(2)

symmetry and dissipations beyond dephasing. We show that after the initial rise and fall, the operator entanglement increases again in a logarithmic manner at late times in the

\mathrm{SU}(2)

-symmetric case. We find that this behavior can be fully understood from the corresponding

\mathrm{U}(1)

subsymmetry by considering the symmetry-resolved operator entanglement. Especially, the probability distribution of different

\mathrm{U}(1)

sectors also follows the Gaussian distribution observed in the

\mathrm{U}(1)

-symmetric case with dephasing, with the variance growing as a power law. But unlike the latter, both the classical Shannon entropy associated with the probabilities for the half system to be in different symmetry sectors and the corresponding symmetry-resolved operator entanglement now make nontrivial contributions to the late-time logarithmic growth of operator entanglement in our

\mathrm{SU}(2)

-symmetric case. Our results show evidence that the logarithmic growth of operator entanglement at long times is a generic behavior of dissipative quantum many-body dynamics with

\mathrm{U}(1)

as the symmetry or subsymmetry and for broader dissipations beyond dephasing, although more analytical and numerical proof from future studies is still required for this conjecture. By breaking the

\mathrm{SU}(2)

symmetry of our quantum many-body dynamics to

\mathrm{U}(1)

, we also show that the latter property---the logarithmic growth behavior of operator entanglement for broader dissipations beyond dephasing---is valid even for open quantum systems with only

\mathrm{U}(1)

symmetry.