Single-particle Correlation Research Articles

The infrared spectrum of the protic ionic liquid 1-methylimidazolium nitrate: An ab initio molecular dynamics simulation study

Complex features observed in the infrared (IR) spectrum of the protic ionic liquid 1-methylimidazolium nitrate, [C1im][NO3], are assigned using ab initio molecular dynamics (AIMD) simulation. AIMD is used at the same level of theory to simulate the known X-ray crystal structure of [C1im][NO3] and a cluster of ionic pairs representing the liquid phase. The calculation of several single particle and collective time correlation functions of velocity forms the basis for the AIMD simulation assignment of the infrared spectra. The AIMD simulation demonstrates that the lift of the degeneracy of the anion asymmetric stretching mode, νas(NO3), due to symmetry breaking and coupling to external modes result in multiple band splitting in the crystal spectrum in the region of the νas(NO3) mode. Owing of the intrinsic anharmonic characteristic of the AIMD simulation, the calculation accounts for the broad band in the high-frequency range of the IR spectrum caused by the cation ν(NH) stretching mode in strong cation–anion hydrogen bond. The AIMD simulation of the liquid captures spectral changes upon melting of [C1im][NO3] due to loosening of the NH···O hydrogen bond and changes in the [NO3]- interaction with other hydrogen atoms of the imidazolium ring. The AIMD simulation assigns the intermolecular stretching mode of the hydrogen bond, ν(NH…O), as the band at 183 cm−1 in the far infrared spectrum of the [C1im][NO3] crystal.

Complexity of fermionic states

How much information does a fermionic state contain? To address this fundamental question, we define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution, minimized over all Fock representations. The complexity characterizes the minimum computational and physical resources required to represent the state and store the information obtained from it by measurements. Alternatively, the complexity can be regarded as a Fock space entanglement measure describing the intrinsic many-particle entanglement in the state. We establish a universal lower bound for the complexity in terms of the single-particle correlation matrix eigenvalues and formulate a finite-size complexity scaling hypothesis. Remarkably, numerical studies on interacting lattice models suggest a general model-independent complexity hierarchy: ground states are exponentially less complex than average excited states, which, in turn, are exponentially less complex than generic states in the Fock space. Our work has fundamental implications on how much information is encoded in fermionic states. Published by the American Physical Society 2024

Diffusion and Oligomerization States of the Muscarinic M1 Receptor in Live Cells─The Impact of Ligands and Membrane Disruptors.

G protein-coupled receptors (GPCRs) are a major gateway to cellular signaling, which respond to ligands binding at extracellular sites through allosteric conformational changes that modulate their interactions with G proteins and arrestins at intracellular sites. High-resolution structures in different ligand states, together with spectroscopic studies and molecular dynamics simulations, have revealed a rich conformational landscape of GPCRs. However, their supramolecular structure and spatiotemporal distribution is also thought to play a significant role in receptor activation and signaling bias within the native cell membrane environment. Here, we applied single-molecule fluorescence techniques, including single-particle tracking, single-molecule photobleaching, and fluorescence correlation spectroscopy, to characterize the diffusion and oligomerization behavior of the muscarinic M1 receptor (M1R) in live cells. Control samples included the monomeric protein CD86 and fixed cells, and experiments performed in the presence of different orthosteric M1R ligands and of several compounds known to change the fluidity and organization of the lipid bilayer. M1 receptors exhibit Brownian diffusion characterized by three diffusion constants: confined/immobile (∼0.01 μm2/s), slow (∼0.04 μm2/s), and fast (∼0.14 μm2/s), whose populations were found to be modulated by both orthosteric ligands and membrane disruptors. The lipid raft disruptor C6 ceramide led to significant changes for CD86, while the diffusion of M1R remained unchanged, indicating that M1 receptors do not partition in lipid rafts. The extent of receptor oligomerization was found to be promoted by increasing the level of expression and the binding of orthosteric ligands; in particular, the agonist carbachol elicited a large increase in the fraction of M1R oligomers. This study provides new insights into the balance between conformational and environmental factors that define the movement and oligomerization states of GPCRs in live cells under close-to-native conditions.

Mass transport and thermal properties of liquid (melting to boiling point) tungsten: a molecular dynamics simulations

We present molecular dynamics simulation to obtain melting point, structural and atomic transport properties of liquid tungsten. We considered the second-neighbor extended Finnis-Sinclair (EFS) potential as an effective interaction. We find melting temperature (T M) and density in agreement with the reported values. EFS potential gives accurate information for structure factor S(q), pair correlation function g(r), and transport coefficients like self-diffusion coefficient and viscosity upto ∼1.5T M. Large viscosity proposes the rheological nature of liquid W. The self-diffusion coefficient follows the Arrhenius law giving the activation energy 1.22 eV. We find ’shoulder’ in the second peak of S(q), which disappears with temperatures. This characteristic is attributed to the high density and clustering of W-atoms at the near-neighbor distance. The asymmetric first peak in g(r) and shoulder in S(q) proposes that the liquid W exhibits non-normal metallic behaviour. Discrepancy observed in caloric properties for temperature >6000 K is also discussed. We propose that the ’softness’ and broad dip in EFS potential are responsible for these discrepancies, and necessitate the inclusion of angular forces. The single particle correlation is discussed in terms of the velocity autocorrelation function and the long-wavelength limit of S(q) is utilized to derive adiabatic sound velocity in confirmation with reported results.

ACFlow: An open source toolkit for analytic continuation of quantum Monte Carlo data

The purpose of analytic continuation is to establish a real frequency spectral representation of single-particle or two-particle correlation function (such as Green's function, self-energy function, spin and charge susceptibilities) from noisy data generated in finite temperature quantum Monte Carlo simulations. It requires numerical solutions of a family of Fredholm integral equations of the first kind, which is indeed a challenging task. In this paper, an open source toolkit (dubbed ACFlow) for analytic continuation of quantum Monte Carlo data is presented. We first give a short introduction to the analytic continuation problem. Next, three popular analytic continuation algorithms, including the maximum entropy method, the stochastic analytic continuation, and the stochastic optimization method, as implemented in this toolkit are reviewed. And then we elaborate on the major features, implementation details, basic usage, inputs, and outputs of this toolkit. Finally, four representative examples, including analytic continuations of Matsubara self-energy function, Matsubara and imaginary time Green's functions, and current-current correlation function, are shown to demonstrate the usefulness and flexibility of the ACFlow toolkit. Program summaryProgram Title: ACFlowCPC Library link to program files:https://doi.org/10.17632/th6w74gwjm.1Developer's repository link:https://github.com/huangli712/ACFlowLicensing provisions: GNU General Public License Version 3Programming language: JuliaNature of problem: Most of the quantum Monte Carlo methods work on imaginary axis. In order to extract physical observables and compare them with the experimental results, analytic continuation must be done in the post-processing stage to convert the quantum Monte Carlo simulated data from imaginary axis to real axis.Solution method: Three well-established analytic continuation methods, including the maximum entropy method, the stochastic analytic continuation (both A. W. Sandvik's and K. S. D. Beach's algorithms), and the stochastic optimization method, have been implemented in the ACFlow toolkit.Additional comments including restrictions and unusual features: The ACFlow toolkit is written in pure Julia language. It is highly optimized and parallelized. It can be executed interactively in a Jupyter notebook environment.

Engineering an imaginary Stark ladder in a dissipative lattice: Passive PT symmetry, K symmetry, and localized damping

We study an imaginary stark ladder model and propose a realization of the model in a dissipative chain with linearly increasing site-dependent dissipation strength. Due to the existence of a $K$-symmetry and passive $\mathcal{PT}$ symmetry, the model exhibits quite different feature from its Hermitian counterpart. With the increase of dissipation strength, the system first undergoes a passive $\mathcal{PT}$-symmetry breaking transition, with the shifted eigenvalues changing from real to complex, and then a $K$-symmetry restoring transition, characterized by the emergence of pure imaginary spectrum with equal spacing. Accordingly, the eigenstates change from $\mathcal{PT}$-unbroken extended states to the $\mathcal{PT}$-broken states, and finally to stark localized states. In the framework of the quantum open system governed by Lindblad equation with linearly increasing site-dependent dissipation, we unveil that the dynamical evolution of single particle correlation function is governed by the Hamiltonian of the imaginary stark ladder model. By studying the dynamical evolution of the density distribution under various initial states, we demonstrate that the damping dynamics displays distinct behaviors in different regions. A localized damping is observed in the strong dissipation limit.

Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to the superfluid phase in the two-dimensional Bose-Hubbard model

Quantum simulations of the Bose-Hubbard model (BHM) at commensurate filling can follow spreading of correlations after a sudden quench for times long enough to estimate their propagation velocities. In this work we perform tensor network simulation of the quantum Kibble-Zurek (KZ) ramp from the Mott towards the superfluid phase in the square lattice BHM and demonstrate that even relatively short ramp/quench times allow one to test the power laws predicted by the KZ mechanism (KZM). They can be verified for the correlation length and the excitation energy but the most reliable test is based on the KZM scaling hypothesis for the single-particle correlation function: scaled correlation functions for different quench times evaluated at the same scaled time collapse to the same scaling function of the scaled distance. The scaling of the space and time variables is done according to the KZ power laws.

Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system

We investigate the time-dependent R\'{e}nyi entanglement entropy after a quantum quench starting from the Mott-insulating and charge-density-wave states in a one-dimensional free boson system. The second R\'{e}nyi entanglement entropy is found to be the negative of the logarithm of the permanent of a matrix consisting of time-dependent single-particle correlation functions. From this relation and a permanent inequality, we obtain rigorous conditions for satisfying the volume-law entanglement growth. We also succeed in calculating the time evolution of the R\'{e}nyi entanglement entropy in unprecedentedly large systems by brute-force computations of the permanent. We discuss possible applications of our findings to the real-time dynamics of noninteracting bosonic systems.

Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions

The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, t-distributed stochastic neighbor embedding and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.

Single-particle space-momentum angle distribution effect on two-pion HBT correlation with Coulomb interaction

We calculate the HBT radius for with Coulomb interaction using the string melting version of a multiphase transport (AMPT) model. We study the relationship between the single-particle space-momentum angle and the particle sources and discuss HBT radii without single-particle space-momentum correlation. Additionally, we study the Coulomb interaction effect on the numerical connection between the single-particle space-momentum angle distribution and the transverse momentum dependence of .

Study of superconducting gap in presence of antiferromagnetism in iron pnictide superconductors

A Hamiltonian model of the pnictide composite superconductors is presented to study the Superconducting(SC) gap. The total Hamiltonian has been solved by writing equations of motion for single particle Greens function of Zubarev type. Equations for appropriate single particle correlation functions are derived and the order parameters corresponding to superconductivity and antiferromagnetism are determined. The equations for superconducting gap and antiferromagnetic gap are solved self-consistently and numerically. The multi-gap superconductivity is studied for different values of interlayer coupling constant parameters and Debye frequencies.

Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model

Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly challenging for dynamics of systems with more than one spatial dimension. Here we demonstrate that a tensor-network method running on classical computers is useful for this purpose. We specifically analyze real-time dynamics of the two-dimensional Bose-Hubbard model after a sudden quench starting from the Mott insulator by means of the tensor-network method based on infinite projected entangled pair states. Calculated single-particle correlation functions are found to be in good agreement with a recent experiment. By estimating the phase and group velocities from the single-particle and density-density correlation functions, we predict how these velocities vary in the moderate interaction region, which serves as a quantitative benchmark for future experiments and numerical simulations.

Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach

We develop a hierarchical equations of motion (HEOM) approach to compute real-time single-particle correlation functions and thermodynamic properties of the Holstein model at finite temperature. We exploit the conservation of the total momentum of the system to formulate the momentum-space HEOM whose dynamical variables explicitly keep track of momentum exchanges between the electron and phonons. Our symmetry-adapted HEOM enable us to overcome the numerical instabilities inherent to the commonly used real-space HEOM. The HEOM method is then used to study the spectral function and thermodynamic quantities of chains containing up to ten sites. The HEOM results compare favorably to existing literature. To provide an independent assessment of the HEOM approach and to gain insight into the importance of finite-size effects, we devise a quantum Monte Carlo (QMC) procedure to evaluate finite-temperature single-particle correlation functions in imaginary time and apply it to chains containing up to twenty sites. QMC results reveal that finite-size effects are quite weak, so that the results on 5 to 10-site chains, depending on the parameter regime, are representative of larger systems. A detailed comparison between the HEOM and QMC data place our HEOM method among reliable methods to compute real-time finite-temperature correlation functions in parameter regimes ranging from low- to high-temperature, and weak- to strong-coupling regime.

Damping transition in an open generalized Aubry-André-Harper model

We study the damping dynamics of the single-particle correlation for an open system under periodic and aperiodic order, which is dominated by the Lindblad master equation. In the absence of the aperiodic order, the Liouvillian superoperator exhibits the non-Hermitian skin effect, which leads to unidirectional damping dynamics, dubbed as "chiral damping". Due to the non-Hermitian skin effect, the damping dynamics is boundary sensitive: The long-time damping of such open systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. We reveal the phase transition with the inclusion of the hopping amplitude modulation. By using the spectral topology and a finite-size scaling analysis in the commensurate case, we show there exists a phase transition of the skin effect with non-Bloch anti-parity-time symmetry breaking. For the incommensurate case, we find richer phases with the coexistence of the non-Hermitian skin effect and the Anderson localization, which are separated by a generalized mobility edge. We reveal the transition of the damping dynamics as a consequence of the phase transition. Furthermore, we propose a possible scheme with ultracold atoms in a dissipative momentum lattice to realize and detect the damping dynamics.

Consistent description for cluster dynamics and single-particle correlation

Cluster dynamics and single-particle correlation are simultaneously treated for the description of the ground state of $^{12}\mathrm{C}$. The recent development of the antisymmetrized quasicluster model (AQCM) makes it possible to generate $jj$-coupling shell-model wave functions from $\ensuremath{\alpha}$ cluster models. The cluster dynamics and the competition with the $jj$-coupling shell-model structure can be estimated rather easily. In the present study, we further include the effect of single-particle excitation; the mixing of the two-particle--two-hole excited states is considered. The single-particle excitation is not always taken into account in the standard cluster model analyses, and the two-particle--two-hole states are found to strongly contribute to the lowering of the ground state owing to the pairing-like correlations. By extending AQCM, all of the basis states are prepared on the same footing, and they are superposed based on the framework of the generator coordinate method (GCM).

Microscopic Study of Two Band Superconductivity in Magnesium Diboride Superconductor (MgB<sub>2</sub>)

We formulate a Model Hamiltonian of two band superconductivity for Magnesium Diboride superconductors (MgB₂). It is a conventional BCS type metallic superconductor which has the highest critical temperature T_c=39K. It is assumed that the superconductivity in MgB₂ arises due to metallic nature of the 2D sheets. From band structure calculations, it is observed that two types of bands i.e. σ and π bands are located at Fermi surface. Here, we consider phonon mediated superconductivity in which σ band is dominant over π band i.e. σ band is more coupled to a superconductor with much higher coupling. We consider a model Hamiltonian with mean field approach and solve this by calculating equations of motion of Green functions for a single particle. We determine the quasi-particle energy from the poles of the Green functions. We derive the single particle correlation functions and determine the two SC order parameters for both σ and π band. Here, the two SC order parameters for the bands are solved self- consistently and numerically. The conduction bandwidth (W) is considered as W=8t₀, where t₀ is the hopping integral. To make all the physical quantities dimensionless, we divide 2t₀ in each of the physical quantities. We then calculate the gap ratio 2∆(0)/K<SUB>B</SUB>T_c for both the bands. It is seen form our theoretical model that the two bands of MgB₂ superconductors have two different SC gaps with the same critical temperature. We also observe the variation of dispersion curves of quasi-particles for different temperature parameters for both σ and π band.

Single gold nanostars with multiple branches as multispectral orientation probes in single-particle rotational tracking.

Herein, we performed a single-particle correlation study to characterize the optical properties of gold nanostars (AuNSs) with multiple sharp branches under dark-field (DF) and differential interference contrast (DIC) microscopy, and to examine their use as multispectral orientation probes. We presented the polarization-dependent, periodic DIC images and intensities of single AuNSs at their localized surface plasmon resonance (LSPR) wavelengths with high sensitivity. Furthermore, we demonstrated that single AuNSs protrude multiple branches that can be used as individual sensors with DIC polarization anisotropy. Thus, unlike conventional Au nanorod (AuNR) probes, single AuNSs were presented as multispectral optical sensors that can provide detailed information such as rotational motions and rotational speeds at different branches of their star-like structure in dynamic environments.

Helical damping and dynamical critical skin effect in open quantum systems

Non-Hermitian skin effect and critical skin effect are unique features of non-Hermitian systems. In this Letter, we study an open system with its dynamics of single-particle correlation function effectively dominated by a non-Hermitian damping matrix, which exhibits $\mathbb{Z}_2$ skin effect, and uncover the existence of a novel phenomenon of helical damping. When adding perturbations that break anomalous time reversal symmetry to the system, the critical skin effect occurs, which causes the disappearance of the helical damping in the thermodynamic limit although it can exist in small size systems. We also demonstrate the existence of anomalous critical skin effect when we couple two identical systems with $\mathbb{Z}_2$ skin effect. With the help of non-Bloch band theory, we unveil that the change of generalized Brillouin zone equation is the necessary condition of critical skin effect.

Imaging Switchable Protein Interactions with an Active Porous Polymer Support.

Mechanistic details about how local physicochemistry of porous interfaces drives protein transport mechanisms are necessary to optimize biomaterial applications. Cross-linked hydrogels made of stimuli-responsive polymers have potential for active protein capture and release through tunable steric and chemical transformations. Simultaneous monitoring of dynamic changes in both protein transport and interfacial polymer structure is an experimental challenge. We use single-particle tracking (SPT) and fluorescence correlation spectroscopy Super-resolution Optical Fluctuation Imaging (fcsSOFI) to relate the switchable changes in size and structure of a pH-responsive hydrogel to the interfacial transport properties of a model protein, lysozyme. SPT analysis reveals the reversible switching of protein transport dynamics in and at the hydrogel polymer in response to pH changes. fcsSOFI allows us to relate tunable heterogeneity of the hydrogels and pores to reversible changes in the distribution of confined diffusion and adsorption/desorption. We find that physicochemical heterogeneity of the hydrogels dictates protein confinement and desorption dynamics, particularly at pH conditions in which the hydrogels are swollen.

Imaging Switchable Protein Interactions With an Active Porous Polymer Support.

Mechanistic details about how local physicochemistry of porous interfaces drive protein transport mechanisms are necessary to optimize biomaterials applications. Cross-linked hydrogels made of stimuli-responsive polymers have potential for active protein capture and release through tunable steric and chemical transformations. Simultaneous monitoring of dynamic changes in both protein transport and interfacial polymer structure is an experimental challenge. We use single-particle tracking (SPT) and fluorescence correlation spectroscopy Super-resolution Optical Fluctuation Imaging (fcsSOFI) to relate the switchable changes in size and structure of a pH-responsive hydrogel to the interfacial transport properties of a model protein, lysozyme. SPT analysis reveals the reversible switching of protein transport dynamics in and at the hydrogel polymer in response to pH changes. fcsSOFI allows us to relate tunable heterogeneity of the hydrogels and pores to reversible changes in the distribution of confined diffusion and adsorption/desorption. We find that physicochemical heterogeneity of the hydrogels dictates protein confinement and desorption dynamics, particularly at pH conditions in which the hydrogels are swollen.