Project Title: Thermalization of one-dimensional quantum spin systems

We request access to the DLX cluster in order to perform simulations of one-dimensional spin systems.

The project is devoted to the study of thermalization of isolated quantum systems in pure state. Using one-dimensional spin-chains as a theoretical model describing a typical chaotic quantum system we will directly simulate dynamical process of thermalization for various initial states. The goal of the project is to investigate the connection between Eigenstate Thermalization Hypothesis, which provides a microscopic description of the time-averaged state of the quantum system, and time-dependent process of equilibration. In particular we aim to relate typical/characteristic thermalization time to microscopic properties of model Hamiltonians.

The project will require substantial, memory-intensive calculations, both single-node and parallel, for which the DLX cluster is ideally suited. We are planning to model time-dependent processes of equilibration/thermalization by means of full direct diagonalization of the model Hamiltonian. By finding the full set of eigenvalues and eigenvectors in an appropriate basis we will have full control of the system's dynamics. Full diagonalization is implemented in a number ways in different software packages and libraries. Part of the project is to identify computationally preferable methods to deal with large systems with local interactions which result in sparse Hamiltonians.

Personell

UK PI: Al Shapere, shapere@pa.uky.edu

Collaborator

External collaborator:
Anatoly Dymarsky, dymarsky@gmail.com
Maksim Beketov, maksim.beketov@skolkovotech.ru

Software

The software we plan to use includes Matlab and Mathematica (if available) as well as Intel MKL libraries LAPACK and c++ and/or fortran compilers.

Publications

Grants