Simulating matrix models with tensor networks

TL;DR

This paper explores the use of tensor network methods, particularly matrix product states, to simulate matrix models relevant to quantum gravity and black hole physics, aiming to understand their entanglement and dynamics.

Contribution

It introduces tensor network techniques for simulating matrix models, focusing on constructing ground states and analyzing their entanglement properties.

Findings

Successful construction of ground states as matrix product states

Analysis of entanglement structure in matrix model ground states

Potential for tensor networks to explore intractable regimes of matrix models

Abstract

Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe quantum black holes via the holographic principle. Simulating these models allows for exploration of their kinematic and dynamic properties, particularly in parameter regimes that are analytically intractable. In this study, we examine the potential of tensor network techniques for such simulations. Specifically, we construct ground states as matrix product states and analyse features such as their entanglement structure.