We consider a quantum wire connected to the leads and subjected to dissipation along its length. The dissipation manifests as tunneling into (out of) the chain from (to) a memoryless environment. The evolution of the system is described by the Lindblad equation. Already infinitesimally small dissipation along the chain induces a quantum phase transition (QPT). This is a decoherence QPT: the reduced density matrix of a subsystem in the nonequilibrium steady state (far from the ends of the chain) can be represented as the tensor product of single-site density matrices. The QPT is identified from the jump of the current and the entropy per site as the dissipation becomes nonzero. We also explore the properties of the boundaries of the chain close to the transition point and observe that the boundaries behave as if they undergo a second-order phase transition as a function of the dissipation strength: the particle-particle correlation functions and the response to the electric field exhibit a power-law divergence. Disorder is known to localize one-dimensional systems, but the coupling to the memoryless environment pushes the system back into the delocalized state even in the presence of disorder. Interestingly, we observe a similar transition in the classical dissipative counterflow model: the current has a jump at the ends of the chain introducing an infinitely small dissipation.
We consider a quantum wire connected to the leads and subjected to dissipation along its length. The dissipation manifests as tunneling into (out of) the chain from (to) a memoryless environment. The evolution of the system is described by the Lindblad equation. Already infinitesimally small dissipation along the chain induces a quantum phase transition (QPT). This is a decoherence QPT: the reduced density matrix of a subsystem in the nonequilibrium steady state (far from the ends of the chain) can be represented as the tensor product of single-site density matrices. The QPT is identified from the jump of the current and the entropy per site as the dissipation becomes nonzero. We also explore the properties of the boundaries of the chain close to the transition point and observe that the boundaries behave as if they undergo a second-order phase transition as a function of the dissipation strength: the particle-particle correlation functions and the response to the electric field exhibit a power-law divergence. Disorder is known to localize one-dimensional systems, but the coupling to the memoryless environment pushes the system back into the delocalized state even in the presence of disorder. Interestingly, we observe a similar transition in the classical dissipative counterflow model: the current has a jump at the ends of the chain introducing an infinitely small dissipation.
We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two noncommuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a nonmonotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The nonmonotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as an entanglement measure that encodes the internal quantum correlations in the chain.
We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms which include local pumping and decay of particles.
Recent theoretical work has shown that the competition between coherent unitary dynamics and stochastic measurements, performed by the environment, along wave function trajectories can give rise to transitions in the entanglement scaling. In this work, complementary to these previous studies, we analyze a situation where the role of Hamiltonian and dissipative dynamics is reversed. We consider an engineered dissipation, which stabilizes an entangled phase of a quantum $\mathrm{spin}\text{\ensuremath{-}}\frac{1}{2}$ chain, while competing single-particle or interacting Hamiltonian dynamics induce a disentangled phase. Focusing on the single-particle unitary dynamics, we find that the system undergoes an entanglement transition from a logarithmic growth with system size to an area law when the competition ratio between the unitary evolution and the nonunitary dynamics increases. We evidence that the transition manifests itself in state-dependent observables at a finite competition ratio for Hamiltonian and measurement dynamics. On the other hand, it is absent in trajectory-averaged steady-state dynamics, governed by a Lindblad master equation: although purely dissipative dynamics stabilizes an entangled state, for any nonvanishing Hamiltonian contribution the system ends up irremediably in a disordered phase. In addition, a single trajectory analysis reveals that the distribution of the entanglement entropy constitutes an efficient indicator of the transition. Complementarily, we explore the competition of the dissipation with coherent dynamics generated by an interacting Hamiltonian, and demonstrate that the entanglement transition also occurs in this second model. Our results suggest that this type of transition takes place for a broader class of Hamiltonians, underlining its robustness in monitored open quantum many-body systems.
We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a noninteger power law decay for late times, representing dissipation-induced Luttinger liquid behavior. However, the crossover between the two regions occurs due to dissipation-induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as -t ln t initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.
We study the behavior of an extended fermionic wire coupled to a local stochastic field. Since the quantum jump operator is Hermitian and quadratic in fermionic operators, it renders the model soluble, allowing investigation of the properties of the nonequilibrium steady state and the role of dissipation-induced fluctuations. We derive a closed set of equations of motion solely for the two-point correlator; on the other hand, we find, surprisingly, that the many-body state exhibits non-Gaussian correlations. Density-density correlation function demonstrates a crossover from a regime of weak dissipation characterized by moderate heating and stimulated fluctuations to a quantum Zeno regime ruled by strong dissipation, which tames quantum fluctuations. Instances of soluble dissipative impurities represent an experimentally viable platform to understand the interplay between dissipation and Hamiltonian dynamics in many-body quantum systems.
When only local observables of a many-body quantum system are of interest, it is desirable to formulate a reduced description within the Hilbert space of the corresponding subsystem, with the remaining degrees of freedom traced out and acting as an environment. Assuming initially uncorrelated states and Gaussian environments, we develop a framework for reconstructing the local dynamical generator of noninteracting quantum chains, with polynomial computational complexity. As an application, we consider two representative models: a bipartitioned Kitaev chain and a Kitaev chain boundary-coupled to a fully connected free-fermion environment. In both models, strong subsystem-environment coupling leads to non-Markovian dynamics characterized by ballistic spreading of the Lindblad dissipator support within the subsystem. On the other hand, weak coupling to a fully connected environment yields predominantly boundary-localized, Markovian dissipation. Our work highlights the implications of subsystem-environment correlations on the generator of local dynamics, beyond the conventional weak-coupling approximations.