Many-body Localization and Local information
Title: Many-body Localization and Local information
DNr: SNIC 2022/5-558
Project Type: SNIC Medium Compute
Principal Investigator: Jens Bardarson <>
Affiliation: Kungliga Tekniska högskolan
Duration: 2022-12-01 – 2023-12-01
Classification: 10304


Properties in out-of-equilibrium dynamics of many-body quantum systems are intrinsically hard. The reason is that quantum entanglement generally requires resources that grow exponentially with system size. Therefore one is limited to simulating remote systems, and many of the most exciting questions are out of reach. We use various, radically different approaches to address this problem. (i) Tensor Networks: One large class of dynamical systems defy the aforementioned picture: systems exhibiting Many-Body Localization (MBL) admit a compressed representation using tensor networks. We have implemented two algorithms that use tensor networks to study the entanglement statistics of disordered quantum spin chains. Our first code calculates eigenstates of the quantum Ising-Majorana model using the Density Matrix Renormalization Group (DMRG) algorithm. We aim to clarify the nature of the phase transition between the two MBL regimes expected to exist within this model. Our second code simulates the dynamics of MBL systems using Time-Evolving Block Decimation (TEBD). Other studies have claimed that slow particle fluctuations seen over long time scales in simulations challenge the existence of the MBL phase. Our approach can simulate larger systems to longer time scales, and preliminary tests indicate that such particle fluctuations can be consistent with MBL. (ii) Real-time diagrammatic Monte Carlo is a method well suited to study the onset and breakdown of MBL in large or open systems. In particular, we aim to investigate the presence of MBL in phonon-coupled disordered spin systems, where a phonon thermal bath can serve as a mediator of spin-spin interactions leading to an MBL regime in the dynamics of the system. As usual in Monte Carlo approaches, numerical simulations to investigate this problem require significant numerical resources that can be provided only by a sizeable high-performance computing cluster. (iii) Time evolution of local information: Simulating non-localized systems while keeping track of all degrees of freedom is generally not possible. Based on new insights (by members of our group and their collaborators SciPostPhys.13.4.080), we have developed code that systematically discards long-range correlations allowing us to approximate the dynamics in systems with the error controlled by the length scale after which we disregard entanglement. To be more specific, we aim to solve the von-Neumann equation (VNE) describing the time evolution of density matrices by using the locality of the Hamiltonians we investigate. Instead of solving the VNE for the entire system, which is a formidable task even for small system sizes, our methods decompose the whole system into smaller subsystems and solve the corresponding VNE on each subsystem. This newly developed code is the main reason we reapply for more computation time. The code, as written, is excellently suited to be applied on a sizeable high-performance computing cluster since it is parallelizable using MPI and OpenMP. However, in our current SNIC allocation, we do not have enough CPU hours to run simulations based on this method.