The zero-temperature dynamics of the spin-boson model with strong dissipation has been a challenging problem for more than 20 years. To solve this and quantum dynamics of dissipative systems at large, we recently proposed a mixed random-deterministic method. This scheme has been successfully used to simulate the time evolution of the spin-boson model at zero temperature for weak to moderate dissipation. For a better numerical performance, the approach is further modified so that it is flexible to convert a certain part of the random treatment to a deterministic one a la hierarchical equations. Applying the new method to the strong dissipated spin-boson model at zero temperature, we observe that the population in the localized state obeys a simple decay dynamics and the time scale is proportional to the reciprocal of the cutoff frequency.The zero-temperature dynamics of the spin-boson model with strong dissipation has been a challenging problem for more than 20 years. To solve this and quantum dynamics of dissipative systems at large, we recently proposed a mixed random-deterministic method. This scheme has been successfully used to simulate the time evolution of the spin-boson model at zero temperature for weak to moderate dissipation. For a better numerical performance, the approach is further modified so that it is flexible to convert a certain part of the random treatment to a deterministic one a la hierarchical equations. Applying the new method to the strong dissipated spin-boson model at zero temperature, we observe that the population in the localized state obeys a simple decay dynamics and the time scale is proportional to the reciprocal of the cutoff frequency.

The Journal of Chemical PhysicsJan 16, 200875 citations

Dissipation driven quantum phase transition in a spin chain

Philipp Werner, Matthias Troyer, Klaus Voelker +1 more

APSMar 1, 20040 citations

Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{PT}$ Symmetry BreakingDissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{PT}$ Symmetry Breaking

Zihao Qi, Yuan Xue

Exactly solvable dissipative models provide an analytical tool for studying the relaxation dynamics in open quantum systems. In this work, we study an exactly solvable model based on an anisotropic variant of the Yao-Lee spin-orbital model, with dissipation acting in the spin sector. We map Liouvillian dynamics to fermions hopping in a doubled Hilbert space under a non-Hermitian Hamiltonian and demonstrate the model's exact solvability. We analyze the model's strong and weak symmetries, which protect an exponentially large manifold of non-equilibrium steady states, establishing the system as a physically feasible dissipative spin liquid. Furthermore, we analyze the transient dynamics in a translationally invariant sector and discover that the single-particle Liouvillian spectrum hosts an exceptional ring in momentum space. We map out a characteristic $\mathcal{PT}$ symmetry breaking transition driven by the dissipation strength, which governs the crossover from oscillatory to decaying relaxation of physical observables. Our work provides a physically motivated, solvable setting for exploring the coexistence of dissipative spin liquid physics and Liouvillian spectral singularities.Exactly solvable dissipative models provide an analytical tool for studying the relaxation dynamics in open quantum systems. In this work, we study an exactly solvable model based on an anisotropic variant of the Yao-Lee spin-orbital model, with dissipation acting in the spin sector. We map Liouvillian dynamics to fermions hopping in a doubled Hilbert space under a non-Hermitian Hamiltonian and demonstrate the model's exact solvability. We analyze the model's strong and weak symmetries, which protect an exponentially large manifold of non-equilibrium steady states, establishing the system as a physically feasible dissipative spin liquid. Furthermore, we analyze the transient dynamics in a translationally invariant sector and discover that the single-particle Liouvillian spectrum hosts an exceptional ring in momentum space. We map out a characteristic $\mathcal{PT}$ symmetry breaking transition driven by the dissipation strength, which governs the crossover from oscillatory to decaying relaxation of physical observables. Our work provides a physically motivated, solvable setting for exploring the coexistence of dissipative spin liquid physics and Liouvillian spectral singularities.

quant-pharXiv:2512.04155Physical review. B./Physical review. BDec 5, 20250 citations

Effective quantum Zeno dynamics in dissipative quantum systems

Vladislav Popkov, Simon Essink, Carlo Presilla A +1 more

We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\mathcal{H}}_{0}$ of the system, and targeting a unique dark state in ${\mathcal{H}}_{0}$ . We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace ${\mathcal{H}}_{0}$ , evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\mathcal{H}}_{0}$ of the system, and targeting a unique dark state in ${\mathcal{H}}_{0}$. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace ${\mathcal{H}}_{0}$, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.

arXiv:1806.10422Physical Review ANov 7, 201839 citations

Geometric Aspects of Spin Dynamics

Xiao-Chuan Wu, Ran Cheng, Di Xiao

Bulletin of the American Physical SocietyMar 17, 20170 citations

Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and

\mathcal{PT}

Symmetry Breaking

\mathcal{PT}

symmetry breaking transition driven by the dissipation strength, which governs the crossover from oscillatory to decaying relaxation of physical observables. Our work provides a physically motivated, solvable setting for exploring the coexistence of dissipative spin liquid physics and Liouvillian spectral singularities.

We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom

{\mathcal{H}}_{0}

of the system, and targeting a unique dark state in

{\mathcal{H}}_{0}

. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace

{\mathcal{H}}_{0}

, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.