Speaker
Description
Over the past 30 years, tensor network techniques have been established as powerful tools in computational condensed matter physics. In one-dimensional quantum systems, one usually represents the many-body wave function as a matrix product state (MPS), a tensor network consisting of three-legged tensors, with individual tensors corresponding to the lattice sites in the system. This ansatz enables efficient numerical computations such as ground-state searches and time evolutions.
More recently, the concept of quantics tensor trains emerged, presenting a different perspective on tensor networks that serve as a way to represent (multivariate) continuous functions as tensor trains (cf. Núñez Fernández et al.). Instead of associating tensors with physical lattice sites, tensors encode scales that refine the domain of a function. This perspective has inspired many applications outside of quantum many-body physics, like superfast Fourier transforms.
We study how to effectively utilize the quantics framework to better understand quantum many-body dynamics of time-dependent observables after a quench. As an example, we will discuss the application of quantics tensor cross-interpolation to the quantum Ising model. We examine whether different parameters of the quantics representation or relating physical quantities allow us to reproduce information about the physical system. We find that low-index Rényi entropies exhibit qualitatively different behavior in the integrable and non-integrable regimes of the quantum Ising model, suggesting their potential as a tool for distinguishing between dynamical regimes.
