Steady-state Phase Transitions Research Articles

Diagnostics of entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition

We utilize the concept of a measurement-induced entanglement transition to analyze the interplay and competition of processes that generate and destroy entanglement in a one-dimensional quantum spin chain evolving under a locally noisy and disordered Hamiltonian. We employ continuous measurements of variable strength to induce a transition from volume to area-law scaling of the steady-state entanglement entropy. While static background disorder systematically reduces the critical measurement strength, this critical value depends nonmonotonically on the strength of nonstatic noise. According to the extracted finite-size scaling exponents, the universality class of the transition is independent of the noise and disorder strength. We interpret the results in terms of the effect of static and nonstatic disorder on the intricate dynamics of the entanglement generation rate due to the Hamiltonian in the absence of measurement, which is fully reflected in the behavior of the critical measurement strength. Our results establish a firm connection between this entanglement growth and the steady-state behavior of the measurement-controlled systems, which therefore can serve as a tool to quantify and investigate features of transient entanglement dynamics in complex many-body systems via a steady-state phase transition.

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

Quantum and Classical Temporal Correlations in (1+1)D Quantum Cellular Automata.

We employ (1+1)-dimensional quantum cellular automata to study the evolution of entanglement and coherence near criticality in quantum systems that display nonequilibrium steady-state phase transitions. This construction permits direct access to the entire space-time structure of the underlying nonequilibrium dynamics, and allows for the analysis of unconventional correlations, such as entanglement in the time direction between the "present" and the "past." We show how the uniquely quantum part of these correlations-the coherence-can be isolated and that, close to criticality, its dynamics displays a universal power-law behavior on approach to stationarity. Focusing on quantum generalizations of classical nonequilibrium systems: the Domany-Kinzel cellular automaton and the Bagnoli-Boccara-Rechtman model, we estimate the universal critical exponents for both the entanglement and coherence. As these models belong to the one-dimensional directed percolation universality class, the latter provides a key new critical exponent, one that is unique to quantum systems.

Building Continuous Time Crystals from Rare Events.

Symmetry-breaking dynamical phase transitions (DPTs) abound in the fluctuations of nonequilibrium systems. Here, we show that the spectral features of a particular class of DPTs exhibit the fingerprints of the recently discovered time-crystal phase of matter. Using Doob's transform as a tool, we provide a mechanism to build classical time-crystal generators from the rare event statistics of some driven diffusive systems. An analysis of the Doob's smart field in terms of the order parameter of the transition then leads to the time-crystal lattice gas (TCLG), a model of driven fluid subject to an external packing field, which presents a clear-cut steady-state phase transition to a time-crystalline phase characterized by a matter density wave, which breaks continuous time-translation symmetry and displays rigidity and long-range spatiotemporal order, as required for a time crystal. A hydrodynamic analysis of the TCLG transition uncovers striking similarities, but also key differences, with the Kuramoto synchronization transition. Possible experimental realizations of the TCLG in colloidal fluids are also discussed.

Steady-state phase diagram of quantum gases in a lattice coupled to a membrane

In a recent experiment [Vochezer {\it et al.,} Phys. Rev. Lett. \textbf{120}, 073602 (2018)], a novel kind of hybrid atom-opto-mechanical system has been realized by coupling atoms in a lattice to a membrane. While such system promises a viable contender in the competitive field of simulating non-equilibrium many-body physics, its complete steady-state phase diagram is still lacking. Here we study the phase diagram of this hybrid system based on an atomic Bose-Hubbard model coupled to a quantum harmonic oscillator. We take both the expectation value of the bosonic operator and the mechanical motion of the membrane as order parameters, and thereby identify four different quantum phases. Importantly, we find the atomic gas in the steady state of such non-equilibrium setting undergoes a superfluid-Mott-insulator transition when the atom-membrane coupling is tuned to increase. Such steady-state phase transition can be seen as the non-equilibrium counterpart of the conventional superfluid-Mott-insulator transition in the ground state of Bose-Hubbard model. Further, no matter which phase the quantum gas is in, the mechanic motion of the membrane exhibits a transition from an incoherent vibration to a coherent one when the atom-membrane coupling increases, agreeing with the experimental observations. Our present study provides a simple way to study non-equilibrium many-body physics that is complementary to ongoing experiments on the hybrid atomic and opto-mechanical systems.

Non-equilibrium critical phenomena from probe brane holography in Schr\xf6dinger spacetime

We study the non-equilibrium steady-state phase transition from probe brane holography in z = 2 Schrödinger spacetime. Concerning differential conductivity, a phase transition could occur in the conductor state. Considering constant current operator as the external field and the conductivity as an order parameter, we derive scaling behavior of order parameter near the critical point. We explore the critical exponents of the nonequilibrium phase transition in two different Schrödinger spacetimes, which originated 1) from supergravity, and 2) from AdS blackhole in the light-cone coordinates. Interestingly, we will see that even at the zero charge density, in our first geometry, the dynamical critical exponent of z = 2 has a major effect on the critical exponents.

The steady-state solutions of coagulation equations

A theoretical description of the steady-state phase transition process of particle coarsening due to a combined effect of coalescence and coagulation is considered. A complete analytical solution of integro-differential equations is found in cases of equal coagulation rates of particles and encounter mechanism of particle collisions.

Solvable Family of Driven-Dissipative Many-Body Systems.

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.

Minimisers of the Allen–Cahn equation on hyperbolic graphs

We investigate minimal solutions of the Allen-Cahn equation on a Gromov-hyperbolic graph. Under some natural conditions on the graph, we show the existence of non-constant uniformly-bounded minimal solutions with prescribed asymptotic behaviours. For a phase field model on a hyperbolic graph, such solutions describe energy-minimising steady-state phase transitions that converge towards prescribed phases given by the asymptotic directions on the graph.

Instability of a liquid–vapor phase transition front in inhomogeneous wettable porous media

The stability of vertical flows through a horizontally extended two-dimensional region of a porous medium is considered in the case of presence of a phase transition front. It is shown that the plane steady-state phase transition front may have several steady-state positions in the wettable porous medium and the necessary condition of their existence is obtained. The spectral stability of the plane phase transition interface is investigated. It is found that in the presence of capillary forces exerted on the phase transition front in the wettable medium the plane front can be destabilized on the mode with both infinite and zero wavenumbers (short- and long-wave instabilities); the short-wave instability can then exist even in the case of the sole steady-state position of the front.

Critical exponents of steady-state phase transitions in fermionic lattice models

We discuss reservoir induced phase transitions of lattice fermions in the non-equilibrium steady state (NESS) of an open system with local reservoirs. These systems may become critical in the sense of a diverging correlation length upon changing the reservoir coupling. We here show that the transition to a critical state is associated with a vanishing gap in the damping spectrum. It is shown that although in linear systems there can be a transition to a critical state there is no reservoir-induced quantum phase transition between distinct phases with non-vanishing damping gap. We derive the static and dynamical critical exponents corresponding to the transition to a critical state and show that their possible values, defining universality classes of reservoir-induced phase transitions are determined by the coupling range of the independent local reservoirs. If a reservoir couples to N neighboring lattice sites, the critical exponent can assume all fractions from 1 to 1/(N - 1).

Primitive cooperative particle flow models

Traffic examples from vehicular systems to socio- and micro-biological systems are used to illustrate features relevant for modelling. After some comments on linear flow the emphasis turns to collective traffic flow, as it is captured by driven lattice-based excluding-particle models. An approximate treatment is then given of the most fundamental of these (the one-dimensional “ASEP”), covering its “jamming” steady-state phase transition and its kink dynamics, in both discrete and continuum versions. Necessary generalisations of the process, and of the geometry (to multi-lanes and to higher dimensions), as well as multi-species generalisations, are then briefly discussed, followed by an introduction to exact analytic approaches and recent developments.

Stochastic non-equilibrium systems

Recent advances in the theory of non-equilibrium systems are reviewed. The emphasis is on collective behaviour, particularly non-equilibrium stochastic dynamics and steady state phase transitions. The models discussed are largely lattice-based 'exclusion' models (with hard core interactions) which can include a wide variety of collective stochastic processes and phenomena. The techniques employed range from intuitive reasoning and approximate mean field approaches to scaling and renormalization group methods, and to exact descriptions in terms of operator algebras, where many new results are included. Mappings to quantum systems, particularly lattice spin models, are also exploited, which provide new viewpoints and allow the use of standard techniques including Bethe ansatz and free fermion solutions.

Empirical evidence for a boundary-induced nonequilibrium phase transition

A recently developed theory for boundary-induced phenomena in nonequilibrium systems predicts the existence of various steady-state phase transitions induced by the motion of a shock wave. We provide direct empirical evidence that a phase transition between a free flow and a congested phase occurring in traffic flow on highways in the vicinity of on- and off-ramps can be interpreted as an example of such a boundary-induced phase transition of first order. We analyse the empirical traffic data and give a theoretical interpretation of the transition in terms of the macroscopic current. Additionally we support the theory with computer simulations of the Nagel-Schreckenberg model of vehicular traffic on a road segment which also exhibits the expected second-order transition. Our results suggest ways to predict and to some extent to optimize the capacity of a general traffic network.

Phase transitions and steady-state microstructures in a two-temperature lattice-gas model with mobile active impurities

The nonequilibrium, steady-state phase transitions and the structure of the different phases of a two-dimensional system with two thermodynamic temperatures are studied via a simple lattice-gas model with mobile active impurities ("hot/cold spots") whose activity is controlled by an external drive. The properties of the model are calculated by Monte Carlo computer-simulation techniques. The two temperatures and the external drive on the system lead to a rich phase diagram including regions of microstructured phases in addition to macroscopically ordered (phase-separated) and disordered phases. Depending on the temperatures, microstructured phases of both lamellar and droplet symmetry arise, described by a length scale that is determined by the characteristic temperature controlling the diffusive motion of the active impurities.

Melting of microinclusions close packed in an elastic matrix

A novel representation is proposed of the liquid state in a microcavity, the collective nature of that state being taken into account. In this case a microinclusion undergoing melting is described as a single two-level system. The phase transition of melting in a close-packed system of such inclusions embedded in an elastic medium is described rigorously within the framework of the self-consistent approach. When an additional intermediate premelting state is taken into account, the curve of the steady-state phase transition with a critical point that happens on the phase diagram can be transformed in different ways, depending on the values of the specific parameters. In the simplest case shortening of the straight line takes place; bending is also possible. There is a region of the parameters where the critical line is split. In the latter case the existence of the triple point is also possible. The results obtained are in agreement with the experimental data.

Unsymmetrical and concerted examples of the effect of enzyme--enzyme interactions on steady-state enzyme kinetics.

In previous papers of this series, emphasis has been placed on the steady-state phase transition and critical properties of large lattices of interacting, symmetrical, and identical enzyme molecules. The present paper is concerned with a number of examples of enzyme--enzyme interactions that do not belong to the class of models of the earlier papers. These are more biochemically oriented and include heterologous dimers, a linear chain with unsymmetrical interactions, and concerted isologous dimers (half-the-sites reactivity).

A thermodynamic and stochastic study of fluctuations in non-equilibrium open systems displaying phase transitions in steady states

Landau's theory of fluctuations in second-order phase transitions is generalized for non-equilibrium open systems having one degree of freedom and displaying phase-transition-like phenomena in steady states. Taking diffusion into consideration, the fluctuations induce a spatial correlation function p(r,r') of the form (exp-( mod r-r' mod / xi ))/ mod r-r' mod when the situation is simple enough for a correlation length xi to exist. A general formula for xi is obtained. The stochastic master equation is formulated and solved for such systems in the absence of diffusion. Both thermodynamic and stochastic theories are applied to an intrinsic semiconductor model which shows a recombination-induced non-equilibrium phase transition as the external electric field is increased.