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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Dynamic compression of Ce and Pr with millisecond time-resolved X-ray diffraction

Abstract Both cerium (Ce) and praseodymium (Pr) undergo a volume collapse transition under compression that originate from similar electronic mechanisms. Yet the outcome could not be more different. In the case of Ce with one affected 4f electron the volume collapse leaves the crystal symmetry intact, whereas for Pr with two 4f electrons the crystal symmetry changes from a distorted face centered cubic structure to a lower symmetry orthorhombic structure. In this paper, we present a study of the effect of strain/compression rate spanning nearly 4 orders of magnitude on the volume collapse phase transitions in Ce and Pr. These dynamic compression experiments in a diamond anvil cell also reveal kinetic differences between the phase transformations observed in these two materials. The transition cannot be overdriven in pressure in Ce, which indicates a fast kinetic process, whereas fast compression rates in Pr lead to a shift of the phase boundary to higher pressures, pointing to slower kinetics possibly due to the realization of a new crystal structure.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Interface-Driven Phenomena in Solids: Thermodynamics, Kinetics and Chemistry

The study of materials interfaces dates back over a century. In solid systems and from an engineering perspective, free surfaces and internal (grain and/or phase) boundaries influence a wide range of properties, such as thermal, electrical and optical transport, and mechanical ones. The properties and the role of interfaces has been discussed extensively in various reviews such as by Sutton and Balluffi. As the characteristic feature size of a materials system (i.e., grain size) is decreased to the nanometer scale, interface-driven physics is expected to dominate due to the increased density of such planar defects. Moreover, interfacial attributes, thermodynamics, and mobility play a key role in phase transformations, such as solidification dynamics and structural transitions in solids, and in homogenization and microstructural evolution processes, such as grain growth, coarsening, and recrystallization. In summary, the set of articles published in this special topic titled: “Interface-Driven Phenomena in Solids: Thermodynamics, Kinetics and Chemistry” covers topics related to microstructure evolution, segregation/adsorption phenomena and interface interactions with other materials defects.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

CFD Modeling of Tank Pressurization and Axial Jet Mixing Experiments with and without Non-Condensable Gas in the Ullage

A two-phase CFD model for tank pressurization and following jet mixing of a cryogenic storage tank is presented using VOF approach for representing the phase boundary and the associated interfacial heat, mass and momentum transfer between the liquid and vapor regions. The CFD model was validated against pressurization and liquid jet mixing data for a 110-inch diameter tank provided by Bullard1. Cases with like-gas and non-condensable gas pressurization are studied. The results of the cases with like-gas pressurization and following mixing are presented first, focusing on the effects of turbulence at the vapor-liquid interface on the tank pressure and phase change rates predictions. The second part of this paper is devoted to testing and validating the CFD model against non-condensable gas pressurization and following mixing. Tank pressures predicted in both cases are compared with each other and with the experimental data.

Computational Fluid Dynamics↗
NASA NTRSDate not supplied

CFD Modeling of Tank Pressurization and Axial Jet Mixing Experiments with and without Non-Condensable Gas in the Ullage

A two-phase CFD model for tank pressurization and following jet mixing of a cryogenic storage tank is presented using VOF approach for representing the phase boundary and the associated interfacial heat, mass and momentum transfer between the liquid and vapor regions. The CFD model was validated against pressurization and liquid jet mixing data for a 110-inch diameter tank provided by Bullard. Cases with like-gas and non-condensable gas pressurization are studied. The results of the cases with like-gas pressurization and following mixing are presented first, focusing on the effects of turbulence at the vapor-liquid interface on the tank pressure and phase change rates predictions. The second part of this paper is devoted to testing and validating the CFD model against non-condensable gas pressurization and following mixing. Tank pressures predicted in both cases are compared with each other and with the experimental data.

Computational Fluid Dynamics↗
NASA NTRS2015

Investigations of Physical Processes in Microgravity Relevant to Space Electrochemical Power Systems

NASA has performed physical science microgravity flight experiments in the areas of combustion science, fluid physics, material science and fundamental physics research on the International Space Station (ISS) since 2001. The orbital conditions on the ISS provide an environment where gravity driven phenomena, such as buoyant convection, are nearly negligible. Gravity strongly affects fluid behavior by creating forces that drive motion, shape phase boundaries and compress gases. The need for a better understanding of fluid physics has created a vigorous, multidisciplinary research community whose ongoing vitality is marked by the continuous emergence of new fields in both basic and applied science. In particular, the low-gravity environment offers a unique opportunity for the study of fluid physics and transport phenomena that are very relevant to management of fluid - gas separations in fuel cell and electrolysis systems. Experiments conducted in space have yielded rich results. These results provided valuable insights into fundamental fluid and gas phase behavior that apply to space environments and could not be observed in Earth-based labs. As an example, recent capillary flow results have discovered both an unexpected sensitivity to symmetric geometries associated with fluid container shape, and identified key regime maps for design of corner or wedge-shaped passive gas-liquid phase separators. In this presentation we will also briefly review some of physical science related to flight experiments, such as boiling, that have applicability to electrochemical systems, along with ground-based (drop tower, low gravity aircraft) microgravity electrochemical research. These same buoyancy and interfacial phenomena effects will apply to electrochemical power and energy storage systems that perform two-phase separation, such as water-oxygen separation in life support electrolysis, and primary space power generation devices such as passive primary fuel cell.

energy storage↗
DOE OSTI2021

Tuning the Double Gyroid Phase Window in Block Copolymers via Polymer Chain Conformation Near the Interface

Block copolymer network morphologies have been proven interesting for applications ranging from mechanical to transport and optical properties. The shape of the polymer chain and its ability to stretch across an interface can be used as handles to target these network morphologies. Here, we show that the double gyroid phase window is broadened when there is a flexible segment near the interface and narrowed when a more constrained segment is placed there by using a series of poly(styrene-b-peptoid) block copolymers in which the polypeptoid block chain conformation can be tuned to adopt either a helical or a coil conformation (NRpe 6 vs Npe 6 ). The double gyroid phase is accessed in both block copolymer series, while the phase boundaries are shifted toward larger polypeptoid volume fractions in the helix-forming PS–(NRpe 6 Nmey) series, due to the more compact helix segment (i.e., the helix segment has the same chain volume as its random coil counterpart but occupies less space). The space-filling difference between the helix and coil segment is further confirmed by the smaller domain spacing of PS–(NRpe 6 Nme 39 ) compared to PS–(Npe 6 Nme 36 ) (13.9 nm vs 14.3 nm) despite the former having a longer polypeptoid block. Furthermore, a broadened double gyroid phase window is accessed in the PS–(Npe 6 Nme y ) series that has a flexible coil segment near the interface. These results demonstrate the possibility of tuning the double gyroid phase in linear block copolymers by chain conformation near the interface alone, highlighting chain conformation as a versatile handle in block copolymer design.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of a micro-scale dislocation pileup on the atomic-scale multi-variant phase transformation and twinning

In this paper, we perform concurrent atomistic–continuum (CAC) simulations to assess the contribution of the internal stress induced by the microscale dislocation pileup at an atomically structured interface to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) the pileup-induced internal stress concentration profile follows neither the classical Eshelby model nor the super-dislocation model alone, but a combination of them; (c) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape. The two variants of the hexagonal phases form a twin with respect to each other; (d) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (e) the microscale dislocation pileup-induced internal shear stress and the structural change at the atomic-scale interface reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface. In conclusion, the gained knowledge will advance our understanding of how the multi-phase material behaves in many complex physical processes, such as the synthesis of multi-phase high-entropy alloys or superhard ceramics under high-pressure torsion, deep mantle earthquakes in geophysics, and so on, which all involve dislocation slip, PTs, twinning, and their interactions across from the atomistic to the microscale and beyond.

36 MATERIALS SCIENCE↗
DOE OSTI2011

Asymmetric cation nonstoichiometry in spinels: Site occupancy in Co{sub 2}ZnO{sub 4} and Rh{sub 2}ZnO{sub 4}

Two cations A and B in A{sub 2}BO{sub 4} spinels appear in precise 2:1 Daltonian ratio ('line compounds') only at very low temperature. More typically, at finite temperature, they tend to become either A rich or B rich. Here we survey the experimentally observed stoichiometry asymmetries and describe the first-principles framework for calculating these. Defect calculations based on first principles are used to calculate the enthalpies of substitution of A atom {Delta}H(A{sub T{sub d}}) and B atom {Delta}H(B{sub O{sub h}}) and determine their site occupancies leading to (non)-stoichiometry. In Co{sub 2}ZnO{sub 4}, the result of the calculation for site occupancy compares well with that measured via anomalous x-ray diffraction. Further, the calculated phase boundary also compares well with that measured via Rietveld refinement of x-ray diffraction data on bulk ceramic sintered samples of Co{sub 2}ZnO{sub 4} and Rh{sub 2}ZnO{sub 4}. These results show that Co{sub 2}ZnO{sub 4} is heavily Co nonstoichiometric above 500 deg. C, whereas Rh{sub 2}ZnO{sub 4} is slightly Zn nonstoichiometric. We found that, in general, the calculated {Delta}H(A{sub T{sub d}}) is smaller than {Delta}H(B{sub O{sub h}}), if the A-rich competing phase is isostructural with the A{sub 2}BO{sub 4} host, for example, A{sub 2}AO{sub 4}, whereas B-rich competing phase is not, for example, BO. This observation is used to qualitatively explain nonstoichiometry and solid solutions observed in other spinels.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Nucleation of metastable bcc intermediates

Here it is shown, via simple arguments, that any material which posseses an (equilibrium) body-centered cubic(bcc) structure in it’s phase diagram has the capacity to preferentially nucleate a non-equilibrium bcc structure upon solidification, even at pressures outside of the range of bcc field of stability. For example, Mishin EAM Cu contains a liquid-fcc-bcc triple point at high pressure (Bendict, 2016); counter-intuitively, the system will solidify via a bcc-intermediate even at pressures lower than the triple point. Further, we point out that, without this understanding of the kinetics, the phase boundary of fcc-bcc would be determined inconsistently from experiments that quench a liquid vs. the pathway of solid-solid transformation. While the phenomena of bcc-mediated nucleation has been studied theoretically in the Lennard-Jones system at ambient pressure(P.R. ten Wolde and Frenkel, 1995), and the general case for bcc predominance below melting has been made(Alexander and McTague, 1978), here we investigate the bcc formation behavior near a liquid-fcc-bcc triple point (which requires non-ambient pressure) and ask “how far away from the bcc phase of stability can bcc still nucleate?”

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Dynamical Slowing-Down in an Ultrafast Photoinduced Phase Transition

Complex systems, which consist of a large number of interacting constituents, often exhibit universal behavior near a phase transition. A slowdown of certain dynamical observables is one such recurring feature found in a vast array of contexts. This phenomenon, known as critical slowing-down, is well studied mostly in thermodynamic phase transitions. However, it is less understood in highly nonequilibrium settings, where the time it takes to traverse the phase boundary becomes comparable to the timescale of dynamical fluctuations. Using transient optical spectroscopy and femtosecond electron diffraction, we studied a photoinduced transition of a model charge-density-wave (CDW) compound LaTe 3 . We observed that it takes the longest time to suppress the order parameter at the threshold photoexcitation density, where the CDW transiently vanishes. Here, this finding can be captured by generalizing the time-dependent Landau theory to a system far from equilibrium. The experimental observation and theoretical understanding of dynamical slowing-down may offer insight into other general principles behind nonequilibrium phase transitions in many-body systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Multidimensional dynamic piezoresponse measurements. Unraveling local relaxation behavior in relaxor-ferroelectrics via big data

Compositional and charge disorder in ferroelectric relaxors lies at the heart of the unusual properties of these systems, such as aging and non-ergodicity, polarization rotations, and a host of temperature and field-driven phase transitions. However, much information about the field-dynamics of the polarization in the prototypical ferroelectric relaxor (1-x)Pb(Mg 1/3 Nb 2/3 )O 3-x PbTiO 3 (PMN-xPT) remains unprobed at the mesoscopic level. We use a piezoresponse force microscopy-based dynamic multimodal relaxation spectroscopy technique, enabling the study of ferroelectric switching and polarization relaxation at mesoscopic length scales, and carry out measurements on a PMN-0.28PT sample with minimal polishing. Results indicate that beyond a threshold DC bias the average relaxation increases as the system attempts to relax to the previous state. Phenomenological fitting reveals the presence of mesoscale heterogeneity in relaxation amplitudes and clearly suggests the presence of two distinct amplitudes. Independent component analysis reveals the presence of a disorder component of the relaxation, which is found to be strongly anti-correlated with the maximum piezoresponse at that location, suggesting smaller disorder effects where the polarization reversal is large and vice versa. The disorder in the relaxation amplitudes is postulated to arise from rhombohedral and field-induced tetragonal phase in the crystal, with each phase associated with its own relaxation amplitude. As a result, these studies highlight the crucial importance of the mixture of ferroelectric phases in the compositions in proximity of the morphotropic phase boundary in governing the local response and further highlight the ability of PFM voltage and time spectroscopies, in conjunction with big-data multivariate analyses, to locally map disorder and correlate it with parameters governing the dynamic behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Phase stabilities of pyrite-related MTCh compounds (M=Ni, Pd, Pt; T=Si, Ge, Sn, Pb; Ch=S, Se, Te): A systematic DFT study

Pyrite-type and related systems appear for a wide range of binary and ternary combinations of transition metals and main group elements that form Zintl type dumbbell anion units. Those representatives with 20 valence electrons exhibit an extraordinary structural flexibility and interesting properties as low-gap semiconductors or thermoelectric and electrode materials. This work is devoted to the systematic exploration of novel compounds within the class of MTCh compounds (M=Ni, Pd, Pt; T=Si, Ge, Sn, Pb; Ch=S, Se, Te) by means of density functional calculations. Their preferred structures are predicted from an extended scheme of colored pyrites and marcasites. To determine their stabilities, competing binary MT{sub 2} and MCh{sub 2} boundary phases are taken into account as well as ternary M{sub 3}T{sub 2}Ch{sub 2} and M{sub 2}T{sub 3}Ch{sub 3} systems. Recently established stability diagrams are presented to account for MTCh ordering phenomena with a focus on a not-yet-reported ordering variant of the NiAs{sub 2} type. Due to the good agreement with experimental data available for several PtTCh systems, the predictions for the residual systems are considered sufficiently accurate. - Graphical abstract: Compositional and structural stability of MTCh compounds is investigated from first principle calculations. A conceptional approach is presented to study and predict novel stable and metastable compounds and structures of low gap semiconductors with TCh dumbbell units that are isoelectronic and structurally related to pyrite (FeS{sub 2}). - Highlights: • Study of compositional stability of MTCh vs. M{sub 3}T{sub 2}Ch{sub 2} and M{sub 2}T{sub 3}Ch{sub 3} compounds. • Study of structural stability of known and novel MTCh compounds. • Prediction of novel stable and metastable structures and compounds isoelectronic to pyrite, FeS{sub 2}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Performance of a Steel/Oxide Composite Waste Form for Combined Waste Steams from Advanced Electrochemical Processes

The results of electrochemical corrosion tests and modeling activities performed collaboratively by researchers at the University of Illinois at Chicago and Argonne National Laboratory as part of workpackage NU-13-IL-UIC-0203-02 are summarized herein. The overall objective of the project was to develop and demonstrate testing and modeling approaches that could be used to evaluate the use of composite alloy/ceramic materials as high-level durable waste forms. Several prototypical composite waste form materials were made from stainless steels representing fuel cladding, reagent metals representing metallic fuel waste streams, and reagent oxides representing oxide fuel waste streams to study the microstructures and corrosion behaviors of the oxide and alloy phases. Microelectrodes fabricated from small specimens of the composite materials were used in a series of electrochemical tests to assess the corrosion behaviors of the constituent phases and phase boundaries in an aggressive acid brine solution at various imposed surface potentials. The microstructures were characterized in detail before and after the electrochemical tests to relate the electrochemical responses to changes in both the electrode surface and the solution composition. The results of microscopic, electrochemical, and solution analyses were used to develop equivalent circuit and physical models representing the measured corrosion behaviors of the different materials pertinent to long-term corrosion behavior. This report provides details regarding (1) the production of the composite materials, (2) the protocol for the electrochemical measurements and interpretations of the responses of multi-phase alloy and oxide composites, (3) relating corrosion behaviors to microstructures of multi-phase alloys based on 316L stainless steel and HT9 (410 stainless steel was used as a substitute) with added Mo, Ni, and/or Mn, and (4) modeling the corrosion behaviors and rates of several alloy/oxide composite materials made with added lanthanide and uranium oxides. These analyses show the corrosion behaviors of the alloy/ceramic composite materials are very similar to the corrosion behaviors of multi-phase alloy waste forms, and that the presence of oxide inclusions does not impact the corrosion behaviors of the alloy phases. Mixing with metallic waste streams is beneficial to lanthanide and uranium oxides in that they react with Zr in the fuel waste to form highly durable zirconates. The measured corrosion behaviors suggest properly formulated composite materials would be suitable waste forms for combined metallic and oxide waste streams generated during electrometallurgical reprocessing of spent nuclear fuel. Electrochemical methods are suitable for evaluating the durability and modeling long-term behavior of composite waste forms: the degradation model developed for metallic waste forms can be applied to the alloy phases formed in the composite and an affinity-based mineral dissolution model can be applied to the ceramic phases.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2011

Quantum entangled ground states of two spinor Bose-Einstein condensates

We revisit in detail the non-mean-field ground-state phase diagram for a binary mixture of spin-1 Bose-Einstein condensates including quantum fluctuations. The noncommuting terms in the spin-dependent Hamiltonian under the single-spatial-mode approximation make it difficult to obtain exact eigenstates. Utilizing spin-z-component conservation and total spin angular momentum conservation, we numerically derive information on the building blocks and evaluate the von Neumann entropy to quantify the ground states. The mean-field phase boundaries are found to remain largely intact, yet the ground states show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Conduction phenomenon of Al{sup 3+} modified lead free (Na{sub 0.5}Bi{sub 0.5}){sub 0.92}Ba{sub 0.08}TiO{sub 3} electroceramics

Choice of proper dopants at A or B-site of ABO{sub 3} perovskite structure can modify the morphotropic phase boundary (MPB), and hence functional properties of polar systems. The chemical nature of donor or acceptor will significantly influence the fundamental properties. Lead-free ferroelectrics have vast potential to replace the lead-based ceramics. The (Na{sub 0.5}Bi{sub 0.5}){sub 1-x}Ba{sub x}TiO{sub 3} (NBT-BT) (at x=0.08) near MPB with small substitution of trivalent cations (Al{sup 3+}) has been synthesized by solid state reaction route. The aim to choose the trivalent cations (Al{sup 3+}) was its relatively smaller radii than that of Bi{sup 3+} cations to develop the antipolar phases in the ferroelectric ceramic. Structural, morphological and elemental compositional analyses were studied by X-ray diffraction (XRD), Secondary electron microscope (SEM) and Energy-dispersive X-ray spectroscopy (EDAX), respectively. Ferroelectric studies were carried out on various compositions of (Na{sub 0.46}Bi{sub 0.46-x}Al{sub x}Ba{sub 0.08})TiO{sub 3} (NBAT-BT) (x=0, 0.05, 0.07, 0.10) electroceramics. It was observed that with increase in concentration of Al the ferroelectricity state changes from soft to hard. Temperature dependent dielectric spectroscopy shows broad dielectric dispersion. The Al doping diminishes the relaxor behavior of NBT-BT ceramics. Impedance spectroscopy shows that electrical resistivity and relaxation frequency decreases with increase in Al-concentration. Modulus spectra indicate that Al significantly change the bulk capacitance of NBT-BT.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Development of ferroelectric correlations in the quantum paraelectric and antiferrodistortive regimes in Ba{sub x}Sr{sub 1-x}TiO{sub 3} (x ≤ 0.10)

The dielectric response ε(T) of Ba{sub x}Sr{sub 1-x}TiO{sub 3} (x ≤ 0.1) for compositions at and below the critical composition for the ferroelectric transition has been studied. With progressive Ba substitution, the growth of ferroelectric correlations and the weakening of the Antiferrodistortive (AFD) and the quantum paraelectric (QPE) effects have been studied by monitoring the changes in both the in and out of phase parts of the dielectric response. For the compositions close to pure SrTiO{sub 3} (x = 0 and x = 0.02), the temperature dependence exhibits a continuous rise in the in-phase part and no ferroelectric peak, consistent with the QPE behavior. With increasing Ba substitution, the low temperature behavior of the in phase part ε{sup ′} progressively changes from a continuous rise to exhibit a weak maximum and finally to a well developed cusp. For higher Ba concentrations, the low temperature peak (T ∼ 50K), which corresponds to ferroelectric correlations, becomes increasingly sharper until at the critical composition, x = 0.10, the system shows a single well defined ferroelectric peak. However, the out of phase response of the x = 0.1 composition exhibited a succession of three BaTiO{sub 3} type ferroelectric transitions. For x≤0.04, the out of phase part shows evidence of an ordering around T ∼ 100K, which is the expected AFD ordering temperature. The deviations of the ε{sup ′}(T) data from the Curie-Weiss law have been analyzed within the frame work of two different theoretical models. It was determined that the dielectric behavior for lower concentrations of Ba (up to x ≤ 0.08) was explainable in terms of a model of non-interacting regions which are themselves homogeneously polarized and undergo a second order phase transition. For the phase boundary composition, i.e., x = 0.1, on the other hand, the data are explainable in terms of the Sherrington and Kirkpatrick model which includes the effects of weak correlations between the polar regions characterized by a glassy order parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Coercivity enhancement in heavy rare earth-free NdFeB magnets by grain boundary diffusion process

Grain boundary diffusion of a Pr 3 (Co,Cu) eutectic alloy has been performed for coercivity enhancement on Nd-lean Nd 10 Fe 84 B 6 nanocrystalline ribbons. The coercivity increases from 0.5 T to 2.5 T after 6 h of infiltration at 600 °C. High resolution electron microscopy and energy dispersive X-ray spectroscopy show that the excess α-Fe present in the initial samples diminishes during infiltration, giving rise to the formation of a Rare Earth-rich RE-Fe inter-boundary phase and a layer of (Nd,Pr) 2 Fe 14 B close to the surface of the hard magnetic grains. Such a microstructure favours the coercivity by increasing the nucleation field for reversal magnetization and providing magnetically isolated/decoupled hard grains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Theory of the phase transition in random unitary circuits with measurements

Here, we present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a nonanalytic change in the amount of information extracted by the measurements about the initial state of the system, quantified by the Fisher information. To compute the von Neumann entanglement entropy $\textit{S}$ and the Fisher information $\mathcal{F}$, we apply a replica method based on a sequence of quantities $\tilde{S}^{(n)}$ and $\mathcal{F}^{(n)}$ that depend on the $\textit{n}$th moments of density matrices and reduce to $\textit{S}$ and $\mathcal{F}$ in the limit $\textit{n}$ → 1. These quantities with $\textit{n}$ ≥ 2 are mapped to free energies of a classical spin model with $\textit{n}$! internal states in two dimensions with specific boundary conditions. In particular, $\tilde{S}^{(n)}$ is the excess free energy of a domain wall terminating on the top boundary, and $\mathcal{F}^{(n)}$ is related to the magnetization on the bottom boundary. Phase transitions occur as the spin models undergo ordering transitions in the bulk. Taking the limit of large local Hilbert space dimension $\textit{q}$ followed by the replica limit $\textit{n}$ → 1, we obtain the critical measurement probability $p_c$ = 1/2 and identify the transition as a bond percolation in the 2D square lattice in this limit. Finally, we show there is no phase transition if the measurements are allowed in an arbitrary nonlocal basis, thereby highlighting the relation between the phase transition and information scrambling. We establish an explicit connection between the entanglement phase transition and the purification dynamics of a mixed state evolution and discuss implications of our results to experimental observations of the transition and simulability of quantum dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗