Ab-Initio Approach to Many-Body Quantum Spin Dynamics

TL;DR

This paper introduces ML-MCTDH, a new numerical method for simulating long-time quantum spin dynamics in many-body systems, overcoming challenges posed by entanglement growth and Hilbert space size.

Contribution

The paper demonstrates that ML-MCTDH accurately simulates quantum spin dynamics and outperforms existing methods like DTWA, especially for anisotropic models and two-point observables.

Findings

ML-MCTDH accurately captures time evolution of observables.

ML-MCTDH outperforms DTWA in reliability for two-point correlators.

Entanglement growth rate depends on interaction range and disorder.

Abstract

A fundamental longstanding problem in studying spin models is the efficient and accurate numerical simulation of the long-time behavior of larger systems. The exponential growth of the Hilbert space and the entanglement accumulation at long times pose major challenges for current methods. To address these issues, we employ the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) framework to simulate the many-body spin dynamics of the Heisenberg model in various settings, including the Ising and XYZ limits with different interaction ranges and random couplings. Benchmarks with analytical and exact numerical approaches show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. A comparison with the discrete truncated Wigner approximation (DTWA) highlights that ML-MCTDH is particularly well-suited for handling anisotropic models and provides more reliable results for two-point observables across all tested cases. The behavior of the corresponding entanglement dynamics is analyzed to reveal the complexity of the quantum states. Our findings indicate that the rate of entanglement growth strongly depends on the interaction range and the presence of disorder. This particular relationship is then used to examine the convergence behavior of ML-MCTDH. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems.