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We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy from which one can extract a number of traditional quantities such as entanglement depth and entanglement entropy. Our construction is gauge invariant and goes beyond traditional entanglement measures by visually revealing how quantum information and entanglement is distributed. We use this tool to analyze the internal structures of prototypical stabilizer states (GHZ state, cluster state, stabilizer error correction codes) and are able to contrast the complexity of highly entangled volume law states generated by random unitary operators and random projective measurements., Comment: 9 pages, 7 figures

We construct a sequence of multi-site gates which transform an easily constructed product state into an approximation to the superfluid ground state of the Bose-Hubbard model. The mapping is exact in the one dimensional hard core limit, and for non-interacting particles in both one and two dimensions. The gate sequence has other applications, such as being used as part of a many-body interferometer which probes the existence of doublons., Comment: 12 pages, 10 figures

We numerically calculate the dynamic structure factor of the simplest two dimensional $Z_2$ lattice gauge theory. This provides an important benchmark for future experiments which will explore the dynamics of such models. As would be expected, the spectrum is gapped away from the critical point, and can be understood in terms of the elementary excitations., Comment: 5 pages, 6 figures, journal article

We calculate the properties of a one-dimensional $Z_2$ lattice gauge theory in different Gauss law sectors, corresponding to different configurations of static charges set by the orientations of the gauge spins. Importantly, in quantum simulator experiments these sectors can be accessed without adding any additional physical particles or changing the Hamiltonian: The Gauss law sectors are simply set by the initial conditions. We study the interplay between conservation laws and interactions when the static charges are chosen to form periodic patterns. We classify the different Gauss law sectors and use the density matrix renormalization group to calculate the ground state compressibility, density profiles, charge density wave order parameters, and single particle correlation functions as a function of matter density. We find confined and deconfined phases, charge density waves, correlated insulators, and supersolids., Comment: 11 pages, 11 figures ; Minor revisions in response to referee comments and typo corrections

Many of graphene's remarkable properties are intrinsically linked to its inherent ripples. Defects, whether naturally present or artificially introduced, are known to have a strong impact on the rippling of graphene. However, how defects alter ripple dynamics in two-dimensional (2D) materials in general, and graphene in particular, remains largely unexplored. Here, using machine learning-driven molecular dynamics simulations, we reveal a fundamental connection between defect concentration and ripple dynamics in freestanding graphene sheets. Specifically, we find that at a critical concentration of approximately 0.1%, dynamic rippling undergoes a transition from freely propagating to static ripples. This is in quantitative alignment with the experimentally observed turning point in the non-monotonic scaling of the Young's modulus and emphasises the critical interplay between defects and material dynamics. Our work not only unveils the significant impact of defects on rippling dynamics in graphene but also paves the way to design two-dimensional devices with tailored properties., Comment: 8 pages, 20 pages supplementary information

Motivated by discrepancies between recent cold atom experiments and the associated theory, we explore the effect of immobile holes on the quantum dynamics of $x$-$z$ spin helices in the one-dimensional $XX$ model. We calculate the exact spin dynamics by mapping onto a system of non-interacting fermions, averaging over the distribution of holes. At small hole densities we find that the helical spin pattern decays exponentially, with a pitch dependence that agrees with the experiments. At large hole densities we instead find persistent oscillations. While our analytic approach does not generalize to the $XXZ$ model with arbitrary anisotropies, we validate a matrix product state technique which might be used to model the experiments in those settings., Comment: 10 pages, 8 figures

We study transport in the one-dimensional mass-imbalanced Fermi-Hubbard model at infinite temperature, focusing on the case of strong interactions. Prior theoretical and experimental investigations have revealed unconventionally long transport timescales, with complications due to strong finite size effects. We compute the dynamical current-current correlation function directly in the thermodynamic limit using infinite tensor network techniques. We show that transport in the strong-imbalance limit is dominated by AC resonances, which we compute with an analytic expansion. We study the dephasing of these resonances with mass imbalance, $\eta$. In the small-imbalance limit, the model is nearly integrable. We connect these unusual limits by computing the DC conductivity and transport decay time as a function of $\eta$ and the interaction strength $U/t$. We propose an experimental protocol to measure these correlation functions in cold atom experiments., Comment: 13 pages, 6 figures

Motivated by recent experiments we study the interconversion between ultracold atomic and molecular condensates, quantifying the resulting oscillations and their slow decay. We find that near equilibrium the dominant damping source is the decay of condensed molecules into non-condensed pairs, with a pair kinetic energy that is resonant with the frequency of the oscillating atom-molecule interconversions. The decay, however, is non-exponential, as strong population of the resonant pairs leads to Bose enhancement. Introducing an oscillating magnetic field, which periodically modulates the molecular binding energy, enhances the oscillations at short times. However, the resulting enhancement of the pair-production process results in an accelerated decay which rapidly cuts off the initial oscillation growth., Comment: journal version

We calculate the weak-coupling resistivity of the two-dimensional Bose Hubbard model, comparing with the more familiar fermionic case. At high temperature the resistivity is linear in $T$, while in the low temperature normal state it is exponentially suppressed. We explore the density dependence and calculate the momentum relaxation rate.

We study a 2D measurement-only random circuit motivated by the Bacon-Shor error correcting code. We find a rich phase diagram as one varies the relative probabilities of measuring nearest neighbor Pauli XX and ZZ check operators. In the Bacon-Shor code, these checks commute with a group of stabilizer and logical operators, which therefore represent conserved quantities. Described as a subsystem symmetry, these conservation laws lead to a continuous phase transition between an X-basis and Z-basis spin glass order. The two phases are separated by a critical point where the entanglement entropy between two halves of an L X L system scales as L ln L, a logarithmic violation of the area law. We generalize to a model where the check operators break the subsystem symmetries (and the Bacon-Shor code structure). In tension with established heuristics, we find that the phase transition is replaced by a smooth crossover, and the X- and Z-basis spin glass orders spatially coexist. Additionally, if we approach the line of subsystem symmetries away from the critical point in the phase diagram, some spin glass order parameters jump discontinuously, Comment: 11 pages, 7 figures ; Minor revisions in response to referee comments and corrected typos

By monitoring the quality factor of a quartz tuning fork oscillator we have observed a fluctuation-driven reduction in the viscosity of bulk $^3$He in the normal state near the superfluid transition temperature, $T_c$. These fluctuations, which are only found within $100 \mu$K of $T_c$, play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. They will be of crucial importance for transport probes of the topologically nontrivial features of superfluid $^3$He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, finding data collapse consistent with the predicted theoretical behavior., Comment: 5 figures

Because of the extreme purity, lack of disorder, and complex order parameter, the first-order superfluid $^3$He A-B transition is the leading model system for first order transitions in the early universe. Here we report on the path dependence of the supercooling of the A phase over a wide range of pressures below 29.3 bar at nearly zero magnetic field. The A phase can be cooled significantly below the thermodynamic A-B transition temperature. While the extent of supercooling is highly reproducible, it depends strongly upon the cooling trajectory: The metastability of the A phase is enhanced by transiting through regions where the A phase is more stable. We provide evidence that some of the additional supercooling is due to the elimination of B phase seeds formed upon passage through the superfluid transition. A greater understanding of the physics is essential before the $^3$He can be exploited to model transitions in the early universe., Comment: 6 Figures

We explore matrix product state approximations to wavefunctions which have spontaneously broken symmetries or are critical. We are motivated by the fact that symmetries, and their associated conservation laws, lead to block-sparse matrix product states. Numerical calculations which take advantage of these symmetries run faster and require less memory. However, in symmetry-broken and critical phases the block sparse ansatz yields less accurate energies. We characterize the role of conservation laws in matrix product states and determine when it is beneficial to make use of them., Comment: 10 pages, 6 figures

Motivated by recent experiments, we investigate particle emission from a Bose-Einstein condensate in a one-dimensional lattice, where the interaction strength is periodically modulated. The modulated interactions parametrically excite a collective mode, leading to density oscillations. These collective oscillations in turn drive particle emission. This multistep process amplifies the drive, producing larger particle jets. We find that the amplitude dependence of the emission rate has a characteristic threshold behavior, as seen in experiments., Comment: 5 pages, 6 figures

Quantum information processing relies on precise control of non-classical states in the presence of many uncontrolled environmental degrees of freedom -- requiring careful orchestration of how the relevant degrees of freedom interact with that environment. These interactions are often viewed as detrimental, as they dissipate energy and decohere quantum states. Nonetheless, when controlled, dissipation is an essential tool for manipulating quantum information: Dissipation engineering enables quantum measurement, quantum state preparation, and quantum state stabilization. The progress of quantum device technology, marked by improvements of characteristic coherence times and extensible architectures for quantum control, has coincided with the development of such dissipation engineering tools which interface quantum and classical degrees of freedom. This Review presents dissipation as a fundamental aspect of the measurement and control of quantum devices and highlights the role of dissipation engineering for quantum error correction and quantum simulation that enables quantum information processing on a practical scale., Comment: Review article: 32 pages, 4 figures, 2 boxes

Experimental measurements have reported ultra-fast and radius-dependent water transport in carbon nanotubes which are absent in boron nitride nanotubes. Despite considerable effort, the origin of this contrasting (and fascinating) behaviour is not understood. Here, with the aid of machine learning-based molecular dynamics simulations that deliver first-principles accuracy, we investigate water transport in single-wall carbon and boron nitride nanotubes. Our simulations reveal a large, radius-dependent hydrodynamic slippage on both materials with water experiencing indeed a $\approx 5$ times lower friction on carbon surfaces compared to boron nitride. Analysis of the diffusion mechanisms across the two materials reveals that the fast water transport on carbon is governed by facile oxygen motion, whereas the higher friction on boron nitride arises from specific hydrogen-nitrogen interactions. This work not only delivers a clear reference of unprecedented accuracy for water flow in single-wall nanotubes, but also provides detailed mechanistic insight into its radius and material dependence for future technological application.

We study superfluidity in the 1D Bose-Hubbard model using a variational matrix product state technique. We determine the superfluid density as a function of the Hubbard parameters by calculating the energy cost of phase twists in the thermodynamic limit. As the system is critical, correlation functions decay as power laws and the entanglement entropy grows with the bond dimension of our variational state. We relate the resulting scaling laws to the superfluid density. We compare two different algorithms for optimizing the infinite matrix product state and develop a physical explanation why one of them (VUMPS) is more efficient than the other (iDMRG). Finally, we comment on finite-temperature superfluidity in one dimension and how our results can be realized in cold atom experiments., Comment: 16 pages, 9 figures (some equations use graphicx)

Motivated by recent experiments, we model the dynamics of a condensed Bose gas in a rotating anisotropic trap, where the equations of motion are analogous to those of charged particles in a magnetic field. As the rotation rate is ramped from zero to the trapping frequency, the condensate stretches along one direction and is squeezed along another, becoming long and thin. When the trap anisotropy is slowly switched off on a particular timescale, the condensate is left in the lowest Landau level. We use a time dependent variational approach to quantify these dynamics and give intuitive arguments about the structure of the condensate wavefunction. This preparation of a lowest Landau level condensate can be an important first step in realizing bosonic analogs of quantum Hall states., Comment: 8 pages, 5 figures; Minor revisions in response to referee comments and corrected typos

Motivated by cold-atom experiments and a desire to understand far-from-equilibrium quantum transport, we analytically study the dynamics of spin helices in the one-dimensional $XX$ model. We use a Jordan-Wigner transformation to map the spin chain onto a non-interacting Fermi gas with simple equations of motion. The resulting dynamics are nontrivial, however, as the spin-helix initial condition corresponds to a highly nonequilibrium distribution of the fermions. We find a separation of timescales between the in-plane and out-of-plane spin dynamics. We gain insights from analyzing the case of a uniform spin chain and from a semiclassical model. One of our key findings is that the spin correlation functions decay as $t^{-1/2}$ at long time, in contrast to the experimentally observed exponential decay., Comment: 10 pages, 6 figures

Recent cold atom experiments have observed bad and strange metal behaviors in strongly-interacting Fermi-Hubbard systems. Motivated by these results, we calculate the thermoelectric transport properties of a 2D Fermi-Hubbard system in the weak coupling limit using quantum kinetic theory. We find that many features attributed to strong correlations are also found at weak coupling. In particular, for temperatures $T\gtrsim t$ the electrical resistivity is nearly linear in temperature despite the fact that the quasiparticle scattering rate is non-linear and changes by nearly an order of magnitude. We argue that this asymptotic behavior is a general feature of systems with a finite spectral width, which implies that there is no MIR bound on the resistivity in single-band models. Due to nesting, the $T$-linear resistivity persists down to $T=0$ at half filling. Our work sheds light on the transport regime in ultracold atom experiments, which can differ substantially from that of condensed matter systems. Disentangling these band-structure effects from the physics of strong correlations is a major challenge for future experiments., Comment: 5 pages, 2 figures

We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each segment. By combining this mapping with existing numerical Density-Matrix Renormalization Group routines, we show how one can accurately obtain the ground-state wave function, spatial correlations, and spatial entanglement entropy directly in the continuum. For a prototypical mesoscopic system of strongly-interacting bosons we demonstrate faster convergence than standard grid-based discretization. We illustrate the power of our approach by studying a superfluid-insulator transition in an external potential. We outline how one can directly apply or generalize this technique to a wide variety of experimentally relevant problems across condensed matter physics and quantum field theory., Comment: Main paper: 7 pages, 5 figures; Supplement: 13 pages, 5 figures

We present a driven dissipative protocol for creating an optical analog of the Laughlin state in a system of Rydberg polaritons in a twisted optical cavity. We envision resonantly driving the system into a 4-polariton state by injecting photons in carefully selected modes. The dissipative nature of the polariton-polariton interactions leads to a decay into a two-polariton analog of the Laughlin state. Generalizations of this technique could be used to explore fractional statistics and anyon based quantum information processing. We also model recent experiments that attempt to coherently drive into this same state., Comment: 12 pages, 10 figures

Graphene's intrinsically corrugated and wrinkled topology fundamentally influences its electronic, mechanical, and chemical properties. Experimental techniques allow the manipulation of pristine graphene and the controlled production of defects which allows to control the atomic out-of-plane fluctuations and, thus, tune graphene's properties. Here, we perform large scale machine learning-driven molecular dynamics simulations to understand the impact of defects on the structure of graphene. We find that defects cause significantly higher corrugation leading to a strongly wrinkled surface. The magnitude of this structural transformation strongly depends on the defect concentration and specific type of defect. Analysing the atomic neighborhood of the defects reveals that the extent of these morphological changes depends on the preferred geometrical orientation and the interactions between defects. While our work highlights that defects can strongly affect graphene's morphology, it also emphasises the differences between distinct types by linking the global structure to the local environment of the defects.

Motivated by recent experiments, we calculate particle emission from a Bose-Einstein condensate trapped in a single deep well of a one-dimensional lattice when the interaction strength is modulated. In addition to pair emission, which has been widely studied, we observe single-particle emission. Within linear response, we are able to write closed-form expressions for the single-particle emission rates and reduce the pair emission rates to one-dimensional integrals. The full nonlinear theory of single-particle emission is reduced to a single variable integrodifferential equation, which we numerically solve., Comment: 8 pages, 6 figures

We use quantum kinetic theory to calculate the thermoelectric transport properties of the 2D single band Fermi-Hubbard model in the weak coupling limit. For generic filling, we find that the high-temperature limiting behaviors of the electrical ($\sim T$) and thermal ($\sim T^2$) resistivities persist down to temperatures of order the hopping matrix element $T\sim t$, almost an order of magnitude below the bandwidth. At half filling, perfect nesting leads to anomalous low temperature scattering and nearly $T$-linear electrical resistivity at all temperatures. We hypothesize that the $T$-linear resistivity observed in recent cold atom experiments is continuously connected to this weak coupling physics and suggest avenues for experimental verification. We find a number of other novel thermoelectric results, such as a low-temperature Wiedemann-Franz law with Lorenz coefficient $5\pi^2/36$., Comment: 14 pages, 6 figures

Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex aqueous systems such as solid-liquid interfaces. Here, we present a machine learning framework that enables the efficient development and validation of models for complex aqueous systems. Instead of trying to deliver a globally-optimal machine learning potential, we propose to develop models applicable to specific thermodynamic state points in a simple and user-friendly process. After an initial ab initio simulation, a machine learning potential is constructed with minimum human effort through a data-driven active learning protocol. Such models can afterwards be applied in exhaustive simulations to provide reliable answers for the scientific question at hand. We showcase this methodology on a diverse set of aqueous systems with increasing degrees of complexity. The systems chosen here comprise bulk water with different ions in solution, water on a titanium dioxide surface, as well as water confined in nanotubes and between molybdenum disulfide sheets. Highlighting the accuracy of our approach with respect to the underlying ab initio reference, the resulting models are evaluated in detail with an automated validation protocol that includes structural and dynamical properties and the precision of the force prediction of the models. Finally, we demonstrate the capabilities of our approach for the description of water on the rutile titanium dioxide (110) surface to analyze the structure and mobility of water on this surface. Such machine learning models provide a straightforward and uncomplicated but accurate extension of simulation time and length scales for complex systems.

Motivated by a recent experiment, we study the dynamics of bosons in a disordered optical lattice, interacting with a variably sized bath of disorder free atoms. As the number of particles in the bath is increased, there is a transition between "localized" and "ergodic" behavior, which are characterized by the long-time behavior of an initial density wave. We model the dynamics with a stochastic mean field theory, reproducing the central observations of the experiment. A key conclusion from our study is that particle loss plays an important role., Comment: 7 pages, 4 figures

We present a sequence of driven-dissipative protocols for controlling cold atoms in tilted optical lattices. These experimentally accessible examples are templates that demonstrate how dissipation can be used to manipulate quantum many-body systems. We consider bosonic atoms trapped in a tilted optical lattice, immersed in a superfluid bath, and excited by coherent Raman lasers. With these ingredients, we are able to controllably transport atoms in the lattice and produce self-healing quantum states: a Mott insulator and the topologically ordered spin-1 AKLT state., Comment: Published version after response to referee comments

We examine the discontinuous first-order superfluid $^3$He A to B transition in the vicinity of the polycritical point (2.232 mK and 21.22 bar). We find path-dependent transitions: cooling at fixed pressure yields a well defined transition line in the temperature-pressure plane, but this line can be reliably crossed by depressurizing at nearly constant temperature after transiting $T_{\rm c}$ at a higher pressure. This path dependence is not consistent with any of the standard B-phase nucleation mechanisms in the literature. This symmetry breaking transition is a potential simulator for first order transitions in the early universe.

Experiments on graphene bilayers, where the top layer is rotated with respect to the one below, have displayed insulating behavior when the moir\'e bands are partially filled. We calculate the charge distributions in these phases, and estimate the excitation gaps., Comment: version accepted in PRB

We use kinetic theory to model the dynamics of a small Bose condensed cloud of heavy particles moving through a larger degenerate Fermi gas of light particles. Varying the Bose-Fermi interaction, we find a crossover between bulk and surface dominated regimes -- where scattering occurs throughout the Bose cloud, or solely on the surface. We calculate the damping and frequency shift of the dipole mode in a harmonic trap as a function of the magnetic field controlling an inter-species Feshbach resonance. We find excellent agreement between our stochastic model and the experimental studies of Cs-Li mixtures., Comment: 10 pages, 7 figures

Equations of State (EoS) for fluids have been a staple of engineering design and practice for over a century. Available EoS are based on the fitting of a closed-form analytical expression to suitable experimental data. The underlying mathematical structure and the underlying physical model significantly restrain the applicability and accuracy of the resulting EoS. This contribution explores the issues surrounding the substitution of analytical EoS for machine-learned models, in particular, we describe, as a proof of concept, the effectiveness of a machine-learned model to replicate statistical associating fluid theory (SAFT-VR-Mie) EoS for pure fluids. By utilizing Artificial Neural Network and Gaussian Process Regression, predictions of thermodynamic properties such as critical pressure and temperature, vapor pressures and densities of pure model fluids are performed based on molecular descriptors. To quantify the effectiveness of the Machine Learning techniques, a large data set is constructed using the comparisons between the Machine-Learned EoS and the surrogate data set suggest that the proposed approach shows promise as a viable technique for the correlation, extrapolation and prediction of thermophysical properties of fluids., Comment: Submitted to J. Phys. Chem. B

We introduce an interatomic potential for hexagonal boron nitride (hBN) based on the Gaussian approximation potential (GAP) machine learning methodology. The potential is based on a training set of configurations collected from density functional theory (DFT) simulations and is capable of treating bulk and multilayer hBN as well as nanotubes of arbitrary chirality. The developed force field faithfully reproduces the potential energy surface predicted by DFT while improving the efficiency by several orders of magnitude. We test our potential by comparing formation energies, geometrical properties, phonon dispersion spectra and mechanical properties with respect to benchmark DFT calculations and experiments. In addition, we use our model and a recently developed graphene-GAP to analyse and compare thermally and mechanically induced rippling in large scale two-dimensional (2D) hBN and graphene. Both materials show almost identical scaling behaviour with an exponent of $\eta \approx 0.85$ for the height fluctuations agreeing well with the theory of flexible membranes. Based on its lower resistance to bending, however, hBN experiences slightly larger out-of-plane deviations both at zero and finite applied external strain. Upon compression a phase transition from incoherent ripple motion to soliton-ripples is observed for both materials. Our potential is freely available online at [http://www.libatoms.org]., Comment: This article has been accepted for publication in the Journal of Physical Chemistry C

Motivated by recent experiments, we explore the kinetics of Bose-Einstein condensation in the upper band of a double well optical lattice. These experiments engineer a non-equilibrium situation in which the highest energy state in the band is macroscopically occupied. The system subsequently relaxes and the condensate moves to the lowest energy state. We model this process, finding that the kinetics occurs in three phases: The condensate first evaporates, forming a highly non-equilibrium gas with no phase coherence. Energy is then redistributed among the noncondensed atoms. Finally the atoms recondense. We calculate the time-scales for each of these phases, and explain how this scenario can be verified through future experiments., Comment: 12 Pages, 4 Figures; Revisions in response to referee comments and corrected typographical errors

We construct and characterize tight binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau level wavefunctions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple analytic descriptions. These provide a valuable tool for constructing exactly solvable models. We also implement a numerical algorithm for finding the most local Hamiltonian with a flat Landau level. We find intriguing structures in the spatial dependence of the matrix elements for this optimized model. The models we construct serve as foundations for numerical and experimental studies of topological systems, both non-interacting and interacting., Comment: 6 pages, 4 figures

The surfactant-driven spreading of droplets is an essential process in many applications ranging from coating flow technology to enhanced oil recovery. Despite the significant advancement in describing spreading processes in surfactant-laden droplets, including the exciting phenomena of superspreading, many features of the underlying mechanisms require further understanding. Here, we have carried out molecular dynamics simulations of a coarse-grained model with a force-field obtained from the statistical associating fluid theory to study droplets laden with common and superspreading surfactants. We have confirmed the important elements of the superspreading mechanism, i.e. the adsorption of surfactant at the contact line and the fast replenishment of surfactant from the bulk. Through a detailed comparison of a range of droplets with different surfactants, our analysis has indicated that the ability of surfactant to adsorb at the interfaces is the key feature of the superspreading mechanism. To this end, surfactants that tend to form aggregates and have a strong hydrophobic attraction in the aggregated cores prevent the fast replenishment of the interfaces, resulting in reduced spreading ability. We also show that various surfactant properties, such as diffusion and architecture, play a secondary role in the spreading process. Moreover, we discuss various drop properties such as the height, contact angle, and surfactant surface concentration, highlighting differences between superspreading and common surfactants. We anticipate that our study will provide further insight for applications requiring the control of wetting., Comment: 26 pages, 11 figures

Equilibrium molecular dynamics simulations are used to investigate the effect of phase transitions on the transport properties of highly-confined water between parallel graphene sheets. An abrupt reduction by several orders of magnitude in the mobility of water is observed in strong confinement, as indicated by reduced diffusivity and increased shear viscosity values. The bulk viscosity, which is related to the resistance to expansion and compression of a substance, is also calculated, showing an enhancement compared to the bulk value for all levels of confinement. An investigation into the phase behaviour of confined water reveals a transition from a liquid monolayer to a rhombic frozen monolayer at nanochannel heights between 6.8-7.8 \r{A}; for larger separations, multilayer liquid water is recovered. It is shown how this phase transition is at the root of the impeded transport., Comment: 32 pages, 7 figures. Supplementary information is too large to archive - please request to the main author (EAM)