Other Drives/Programmes

TSU COLLOQUIUM

Abstract

Density functional theory (DFT) and time-dependent density functional theory (TDDFT), owing to their great balance of speed and accuracy, have remained essential tools to understand all manners of nanoscale processes and materials behavior. Although, in principle, an exact theory, in practice, DFT (TDDFT) requires approximations to the exact exchange-correlation (XC) functionals to encapsulate the quantum many-electron interactions into a mean-field of the electron density. The existing XC approximations, despite their successes, exhibit several notable deficiencies—inaccurate band-gaps, bond-dissociation curves, reaction barriers, to name a few. These deficiencies of the existing XC approximations severely limit the reliability of DFT (TDDFT) in predictions of material properties. Additionally, the high computational demands of DFT (TDDFT) limits their routine usage to length-scales of few hundred atoms and timescales of few tens of picoseconds for ab initio molecular dynamics (AIMD) (few tens of femtoseconds for TDDFT). This, in turn, renders a wide array of problems—energetics of dislocation in crystalline materials, dynamics of water splitting, surface plasmons in metal nanoclusters, to name a few—inaccessible to DFT (TDDFT). In this talk, I will present different strategies to address the above accuracy and efficiency challenges in DFT/TDDFT. First, I will introduce a data-driven approach to model the XC approximation. In particular, I will present an accurate and robust solution to the inverse DFT problem that connects DFT to the wavefunction based methods (e.g., configuration interaction, quantum Monte Carlo), and hence, is crucial to the generation of training data needed to model the XC approximation. Subsequently, I will discuss various machine-learning approaches to construct the XC approximation, using the training data from inverse DFT. Lastly, I will present various efficient spatial and temporal discretization schemes, ranging from mixed basis formulation to exponential time-integrators, that can enable large-scale DFT/TDDFT calculations than possible, heretofore.

TSU COLLOQUIUM

Abstract

Fluctuation-driven heterogeneous cooperative dynamics and self-organization are signatures of a diverse class of physical systems, from polymer (and colloidal) glasses to biopolymers. In this presentation, I will talk about two such systems where either fluctuation-controlled dynamics or the effect of fluctuations around the mean-field state of the system are crucial.

Firstly, I will discuss the formulation of a microscopic liquid state theory of how attractive functionalities between sticky groups regularly co-polymerized in a chain backbone affect local structure and segmental dynamics of unentangled polymer liquids. Based on the bare attractive interaction and single-chain structure as input, integral equation theory is combined with activated dynamics approaches that capture caging and physical bond formation to study emergent high-frequency elasticity and local relaxation processes. The dynamic free energies and corresponding sticker and non-sticker barrier hopping timescales that define the coupled bond breakage and cage escape processes are predicted within a two-step dynamical scenario that applies in the strong attraction regime. The first step involves non-sticker hopping (alpha relaxation), which is perturbed due to physical bonds between sticky segments that act as pinning constraints. This theoretical development will be supplemented by a discussion comparing the theory predictions for alpha relaxation time and the glass transition temperature of associating polymers with experimental results.

Secondly, building on the exact single-chain statistics of semiflexible polymers and mean-field solutions for both isotropic and nematic states, I will discuss extending a theory for the free energy functional of semiflexible polymer solutions with alignment interaction up to quadratic order to specifically understand the three Frank elastic (FE) constants of long-wavelength splay, bend, and twist modes of deformation. Enhanced alignment of polymers in their nematic state is responsible for crucial mechanical and material properties of fibers found in both biological systems and chemical physics. These deformations characterize the normal modes of the deviation of the local nematic director field of liquid crystalline behavior. The theoretical picture suggests that the three FE constants can be exactly mapped to correlation functions involving real spherical harmonics. Numerical simulations supplementing the theoretical discussion suggest excellent agreement, and the presented theory serves as a basis for understanding protein-brush-induced membrane deformations important for membrane tethering and fusion.

TSU COLLOQUIUM

Abstract

In this seminar, I will present the “link representation formalism” that we introduced in our recent works [1-2], where we assume entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry associated with the entanglement structure of a quantum many-body state, which may occasionally differ from the one suggested by the Hamiltonian of the system.

In the cases where the representation is exact, the elements of the link matrix coincide with the mutual information between pairs of sites. In others, it provides a very good approximation, and in all cases, it yields a natural entanglement contour that is similar to earlier proposals [3]. We will present examples where the representation is exact and then discuss several non-exact cases where we can apply certain approximation techniques, including matrix product states, free fermionic states, or cases in which contiguous blocks are especially relevant. The accuracy of the representation for different types of states and partitions will also be discussed.

Finally, we show that the representation helps us extend the application of the quasi-particle picture, useful in explaining the growth of entanglement entropy of short-range initial states when quenched under a critical Hamiltonian, to the initial states presenting long-range correlations [4-5].

References

[1] Sudipto Singha Roy, Silvia N. Santalla, Javier Rodríguez-Laguna, and Germán Sierra, “Entanglement as geometry and flow”, Physical Review B101, 195134 (2020).
[2] Sudipto Singha Roy, Silvia N. Santalla, Germán Sierra, and Javier Rodríguez-Laguna, “Link representation of the entanglement entropies for all bipartitions”, Journal of Physics A: Mathematical and Theoretical 54, 305301 (2021).
[3] Y. Chen and G. Vidal, “Entanglement contour”, J. Stat. Mech. P10011 (2014).
[4] Sudipto Singha Roy, Giovanni Ramírez, Silvia N. Santalla, Germán Sierra, and Javier Rodríguez-Laguna, “Exotic correlation spread in free-fermionic states with initial patterns”, Physical Review B105, 214306 (2022).
[5] Silvia N. Santalla, Giovanni Ramírez, Sudipto Singha Roy, Germán Sierra, and Javier Rodríguez-Laguna, “Entanglement links and the quasiparticle picture”, arXiv:2208.03766 [quant-ph] (2022).