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Quantum many-body systems display rich phase structure in their low-temperature equilibrium states 1 . However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases 2 – 8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC) 7 , 9 – 15 . Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order 7 , 16 , 17 . In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states 7 , 9 , 10 . Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors. A study establishes a scalable approach to engineer and characterize a many-body-localized discrete time crystal phase on a superconducting quantum processor.

Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among which is the well known Anderson localization 1 , where increasing the randomness induces a metal–insulator transition. The introduction of topology in condensed-matter physics 2 – 4 lead to the discovery of topological phase transitions and materials as topological insulators 5 . Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy 6 and new topological phases 7 – 9 . Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition 10 . Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal–insulator), a topological and parity–time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops 11 . Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled.  A triple phase transition, where changing a single parameter simultaneously gives rise to metal–insulator, topological and a parity–time symmetry-breaking phase transitions, is observed in non-Hermitian Floquet quasicrystals.

Biomolecular condensation via liquid–liquid phase separation of intrinsically disordered proteins/regions (IDPs/IDRs) along with other biomolecules is proposed to control critical cellular functions, whereas aberrant phase transitions are associated with a range of neurodegenerative diseases. Here, we show that a disease-associated stop codon mutation of the prion protein (PrP) at tyrosine 145 (Y145Stop), resulting in a truncated, highly disordered, N-terminal IDR, spontaneously phase-separates into dynamic liquid-like droplets. Phase separation of this highly positively charged N-terminal segment is promoted by the electrostatic screening and a multitude of weak, transient, multivalent, intermolecular interactions. Single-droplet Raman measurements, in conjunction with an array of bioinformatic, spectroscopic, microscopic, and mutagenesis studies, revealed a highly mobile internal organization within the liquid-like condensates. The phase behavior of Y145Stop is modulated by RNA. Lower RNA:protein ratios promote condensation at a low micromolar protein concentration under physiological conditions. At higher concentrations of RNA, phase separation is abolished. Upon aging, these highly dynamic liquid-like droplets gradually transform into ordered, β-rich, amyloid-like aggregates. These aggregates formed via phase transitions display an autocatalytic self-templating characteristic involving the recruitment and binding-induced conformational conversion of monomeric Y145Stop into amyloid fibrils. In contrast to this intrinsically disordered truncated variant, the wild-type full-length PrP exhibits a much lower propensity for both condensation and maturation into amyloids, hinting at a possible protective role of the C-terminal domain. Such an interplay of molecular factors in modulating the protein phase behavior might have much broader implications in cell physiology and disease.

Liquid–liquid phase separation and related phase transitions have emerged as generic mechanisms in living cells for the formation of membraneless compartments or biomolecular condensates. The surface between two immiscible phases has an interfacial tension, generating capillary forces that can perform work on the surrounding environment. Here we present the physical principles of capillarity, including examples of how capillary forces structure multiphase condensates and remodel biological substrates. As with other mechanisms of intracellular force generation, for example, molecular motors, capillary forces can influence biological processes. Identifying the biomolecular determinants of condensate capillarity represents an exciting frontier, bridging soft matter physics and cell biology. The physical principles of capillarity, including how capillary forces can influence biological processes, are discussed.

We reconstitute a phosphotyrosine-mediated protein condensation phase transition of the ∼200 residue cytoplasmic tail of the epidermal growth factor receptor (EGFR) and the adaptor protein, Grb2, on a membrane surface. The phase transition depends on phosphorylation of the EGFR tail, which recruits Grb2, and crosslinking through a Grb2-Grb2 binding interface. The Grb2 Y160 residue plays a structurally critical role in the Grb2-Grb2 interaction, and phosphorylation or mutation of Y160 prevents EGFR:Grb2 condensation. By extending the reconstitution experiment to include the guanine nucleotide exchange factor, SOS, and its substrate Ras, we further find that the condensation state of the EGFR tail controls the ability of SOS, recruited via Grb2, to activate Ras. These results identify an EGFR:Grb2 protein condensation phase transition as a regulator of signal propagation from EGFR to the MAPK pathway.

Spontaneous partitioning of a homogeneous solution of molecules, or liquid-phase separation, underlies the formation of cellular bodies from P granules to nucleoli. Essentially, dense-phase liquid droplets act like cellular compartments. Du and Chen show that DNA binding to its cytoplasmic sensor, cyclic GMP–AMP synthase (cGAS), results in liquid droplets containing activated cGAS (see the Perspective by Ablasser). This phenomenon occurs through multivalent interactions, augmented by zinc, between DNA binding domains on cGAS and DNA in a length-dependent manner. Binding triggers a switchlike reaction that concentrates the enzyme and reactants to enhance STING-dependent interferon responses. Science , this issue p. 704 ; see also p. 646 DNA sensor cGAS forms liquid droplets that stimulate innate immune responses. The binding of DNA to cyclic GMP–AMP synthase (cGAS) leads to the production of the secondary messenger cyclic GMP–AMP (cGAMP), which activates innate immune responses. We have shown that DNA binding to cGAS robustly induced the formation of liquidlike droplets in which cGAS was activated. The disordered and positively charged cGAS N terminus enhanced cGAS-DNA phase separation by increasing the valencies of DNA binding. Long DNA was more efficient in promoting cGAS liquid phase separation and cGAS enzyme activity than short DNA. Moreover, free zinc ions enhanced cGAS enzyme activity both in vitro and in cells by promoting cGAS-DNA phase separation. These results demonstrated that the DNA-induced phase transition of cGAS promotes cGAMP production and innate immune signaling.

Biomolecular condensates form via coupled associative and segregative phase transitions of multivalent associative macromolecules. Phase separation coupled to percolation is one example of such transitions. Here, we characterize molecular and mesoscale structural descriptions of condensates formed by intrinsically disordered prion-like low complexity domains (PLCDs). These systems conform to sticker-and-spacers architectures. Stickers are cohesive motifs that drive associative interactions through reversible crosslinking and spacers affect the cooperativity of crosslinking and overall macromolecular solubility. Our computations reproduce experimentally measured sequence-specific phase behaviors of PLCDs. Within simulated condensates, networks of reversible inter-sticker crosslinks organize PLCDs into small-world topologies. The overall dimensions of PLCDs vary with spatial location, being most expanded at and preferring to be oriented perpendicular to the interface. Our results demonstrate that even simple condensates with one type of macromolecule feature inhomogeneous spatial organizations of molecules and interfacial features that likely prime them for biochemical activity. The authors provide a physical description for condensates as complex fluids defined by small-world network structures for their interiors, and of interfaces featuring a preference of locally and globally expanded conformations.

Membraneless compartments can form in cells through liquidliquid phase separation (see the Perspective by Polymenidou). But what prevents these cellular condensates from randomly fusing together? Using the RNA-binding protein (RBP) Whi3, Langdon et al. demonstrated that the secondary structure of different RNA components determines the distinct biophysical and biological properties of the two types of condensates that Whi3 forms. Several RBPs, such as FUS and TDP43, contain prion-like domains and are linked to neurodegenerative diseases. These RBPs are usually soluble in the nucleus but can form pathological aggregates in the cytoplasm. Maharana et al. showed that local RNA concentrations determine distinct phase separation behaviors in different subcellular locations. The higher RNA concentrations in the nucleus act as a buffer to prevent phase separation of RBPs; when mislocalized to the cytoplasm, lower RNA concentrations trigger aggregation. Science , this issue p. 922 , p. 918 ; see also p. 859 High concentrations of RNA prevent pathological aggregation of RNA binding proteins in the nucleus. Prion-like RNA binding proteins (RBPs) such as TDP43 and FUS are largely soluble in the nucleus but form solid pathological aggregates when mislocalized to the cytoplasm. What keeps these proteins soluble in the nucleus and promotes aggregation in the cytoplasm is still unknown. We report here that RNA critically regulates the phase behavior of prion-like RBPs. Low RNA/protein ratios promote phase separation into liquid droplets, whereas high ratios prevent droplet formation in vitro. Reduction of nuclear RNA levels or genetic ablation of RNA binding causes excessive phase separation and the formation of cytotoxic solid-like assemblies in cells. We propose that the nucleus is a buffered system in which high RNA concentrations keep RBPs soluble. Changes in RNA levels or RNA binding abilities of RBPs cause aberrant phase transitions.

When aged below the glass transition temperature, Tg , the density of a glass cannot exceed that of the metastable super-cooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL ) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

Adding a nonadsorbing polymer to passive colloids induces an attraction between the particles via the \"depletion\" mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory, and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger interparticle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower interparticle attraction show unidirectional rotation. These micro-rotors demonstrate the self-assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self-assembly of rotors are generic features of aggregating swimmers and should therefore occur in a variety of biological and synthetic active particle systems.