Title:	Many-body Localization and Local information
DNr:	NAISS 2026/3-334
Project Type:	NAISS Medium
Principal Investigator:	Jens Bardarson <bardarson@kth.se>
Affiliation:	Kungliga Tekniska högskolan
Duration:	2026-04-28 – 2027-05-01
Classification:	10304
Homepage:	https://github.com/DavidAce/DMRG
Keywords:

Abstract

Static and dynamic properties of many-body quantum systems are inherently difficult to study. Quantum entanglement generated by many interacting degrees of freedom generally demands computational resources that grow exponentially with system size. This makes exact classical simulations infeasible for large systems and at intermediate and long times. As a result, many questions in many-body quantum physics remain open. To overcome this entanglement barrier, we have developed several approximate algorithms based on different ideas but sharing a common principle: to discard unimportant, typically non-local entanglement information and thereby obtain a sub-exponential representation of the quantum state. Our projects broadly encompass two approaches to the quantum many-body problem. (i) Tensor Networks. Disorder can exponentially suppress long-range entanglement, giving rise to a Many-Body Localized (MBL) phase whose states admit efficient tensor-network representations. We develop tensor-network algorithms for classical computers to study MBL phenomenology and quantum matter more broadly. Our fLBIT algorithm uses a random-circuit model of emergent MBL quasiparticles to simulate the dynamics of large systems over long times with high precision. We also developed GDMRG, an extension of the widely used Density Matrix Renormalization Group (DMRG) algorithm, to obtain mid-spectrum eigenstates with unprecedented performance and precision. In addition, we developed efficient methods for computing local information from tensor-network states. (ii) Information lattice. A central theme of our work is the information lattice, which decomposes the quantum information in a given state into spatially local components known as local information. Based on this framework, we developed the Local-Information Time Evolution algorithm (LITE) to study dynamics in effectively infinite interacting quantum systems by systematically discarding correlations above a chosen length scale. We use this to investigate open and closed quantum systems. In another direction, we use the information lattice to investigate and characterize various non-interacting and many-body systems as well as disordered and topological systems from the quantum information perspective. Although the information lattice is a decomposition of von Neumann correlation, it also provides a witness to nonstabilizerness, another quantum resource quantifying how efficiently a quantum state can be represented on a classical computer. Our recent work uses the information lattice to characterize quantum states through their scale of nonstabilizerness. Our ongoing work in this direction involve investigating quantum critical states in both two and three dimensions, developing time evolution algorithm for higher dimensional systems, identifying signatures of quantum thermalization in many-body systems. Both (i) and (ii) rely heavily on numerical linear algebra for large dense and sparse matrices, including iterative eigensolvers, diagonalization, singular-value decomposition, and tensor contraction, and our codes parallelize over shared and distributed memory as needed.