Quantum phase transitions are a cornerstone of many-body physics at low temperatures but have remained elusive far from equilibrium. Driven open quantum systems -- a prominent non-equilibrium platform where coherent dynamics competes with Markovian dissipation from the environment -- often exhibit an effective classical behavior. In this work, we present a nontrivial quantum phase transition that is stabilized, rather than destroyed, by Markovian dissipation. We consider a variant of the paradigmatic spin-boson model where the spin is driven and bosons are subject to Markovian loss proportional to frequency (hence, vanishing at low frequencies). We show that the steady state exhibits a localization phase transition where the spin's dynamics is frozen, to be contrasted with the ground-state transition in the absence of dissipation. Furthermore, this transition occurs when the steady state becomes pure. The latter is not simply a dark state of dissipation but rather emerges from a nontrivial renormalization of the spin dynamics by low-frequency bosonic modes. Our work provides a nontrivial example where quantumness, typically reserved for ground states, also emerges in dynamical settings, with potential applications in quantum computation.
Quantum phase transitions are a cornerstone of many-body physics at low temperatures but have remained elusive far from equilibrium. Driven open quantum systems -- a prominent non-equilibrium platform where coherent dynamics competes with Markovian dissipation from the environment -- often exhibit an effective classical behavior. In this work, we present a nontrivial quantum phase transition that is stabilized, rather than destroyed, by Markovian dissipation. We consider a variant of the paradigmatic spin-boson model where the spin is driven and bosons are subject to Markovian loss proportional to frequency (hence, vanishing at low frequencies). We show that the steady state exhibits a localization phase transition where the spin's dynamics is frozen, to be contrasted with the ground-state transition in the absence of dissipation. Furthermore, this transition occurs when the steady state becomes pure. The latter is not simply a dark state of dissipation but rather emerges from a nontrivial renormalization of the spin dynamics by low-frequency bosonic modes. Our work provides a nontrivial example where quantumness, typically reserved for ground states, also emerges in dynamical settings, with potential applications in quantum computation.
Open driven quantum systems have defined a powerful paradigm of nonequilibrium phases and phase transitions; however, quantum phase transitions are generically not expected in this setting due to the decohering effect of dissipation. In this Letter, we consider a quantum Ising model subject to bulk dissipation (at rate Γ) and show that, although the correlation length remains finite (hence no phase transition), it develops a pronounced peak close to the ground-state quantum critical point. While standard techniques fail in this regime, we develop a versatile analytical approach that becomes exact with vanishing dissipation (Γ→0 but finite Γt). On a technical level, our approach builds on previous work where the state of the system is described by a slowly evolving generalized Gibbs ensemble that accounts for the integrability of the Hamiltonian while treating dissipation perturbatively. Finally, we demonstrate a kind of universality in that integrability-breaking perturbations of the Hamiltonian lead to the same behavior. To this end, we first show that the steady state of a chaotic Ising Hamiltonian under local Markovian dissipation that preserves the Ising symmetry, and in the limit Γ→0, is identical to that of quench dynamics in the absence of dissipation. This intriguing connection then allows us to draw on recent findings about quantum phase transition signatures in quench dynamics.
A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.
Open quantum systems exhibit a range of novel out-of-equilibrium behavior due to the interplay between coherent quantum dynamics and dissipation. Of particular interest in these systems are driven, dissipative transitions, the emergence of dynamical phases with novel broken symmetries, and critical behavior that lies beyond the conventional paradigm of Landau-Ginzburg phenomenology. Here, we consider a parametrically driven two-mode system in the presence of non-Markovian system-reservoir interactions. We show that the non-Markovian dynamics modifies the phase diagram of this system, resulting in the emergence of a broken symmetry phase in a universality class that has no counterpart in the corresponding Markovian system. This emergent phase is accompanied by enhanced two-mode entanglement that remains robust at finite temperatures. Such reservoir-engineered dynamical phases can potentially shed light on universal aspects of dynamical phase transitions in a wide range of nonequilibrium systems, and aid in the development of techniques for the robust generation of entanglement and quantum correlations at finite temperatures with potential applications to quantum control, state preparation, and metrology.
By considering a solvable driven-dissipative quantum model, we demonstrate that continuous phase transitions in dissipative systems may occur without an accompanying symmetry breaking. As such, the underlying mechanism for this type of transition is qualitatively different from that of continuous equilibrium phase transitions. In our model, the transition is solely a result of the interplay between Hamiltonian and dissipative dynamics and manifests as a nonanalyticity in the steady state ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{\mathrm{ss}}$ in the thermodynamic limit. Based on knowledge from critical classical models we suggest that this behavior derives from a rounding of a first-order phase transition into a continuous one due to large environment-induced fluctuations. Despite being conceptually different from the traditional continuous transitions, we show that expectations of local observables can still be characterized by a set of critical exponents.
The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.
We present numerically exact inchworm quantum Monte Carlo results for the real-time dynamics of the spin polarization in the sub-Ohmic spin-boson model at finite temperature. We focus in particular on the localization and coherence behavior of the model, extending our previous study at low temperature [Phys. Rev. Lett. 134, 056502 (2025)]. As the temperature increases, the system becomes less localized and less coherent. The loss of coherence, which is controlled by two independent mechanisms -- a smooth damping-driven crossover and a sharp frequency-driven transition -- exhibits a nontrivial temperature dependence. While both types of coherence loss occur at lower coupling in the high temperature regime, the frequency exhibits a sharper drop at high temperatures and this drop is observed for all values of the sub-Ohmic exponent, in contrast to the zero-temperature case. We discuss the full temperature-dependent dynamical phase diagram of the system and the interplay between coherence and localization across a wide range of physical parameters.