Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space

Abstract

Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.

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Plain Language Summary

Understanding the quantum dynamics exhibited by large-spin systems is fundamental for various fields of physics, quantum information science, and biology. However, quantum many-body systems are complex; computing their exact time evolution is, in general, impossible. Numerical approximation methods have been developed but are mostly limited to dealing with low-dimensional systems or weakly interacting regimes. We develop and test a new semiclassical approach for dealing with the time evolution of generic spin-lattice models. Our method substantially improves the accuracy of existing semiclassical methods by accounting for the inherently discrete nature of quantum-mechanical spin.

Our technique, which relies on a Monte Carlo sampling, is able to accurately capture the dynamics of the x , y , and z moments of a single spin and also entanglement and correlations between pairs of spins, regardless of the dimension of the model. We test our method using coupled two-level systems with interactions that decay with increasing distance in different ways and find that our method yields results that are in agreement with analytical and numerically exact calculations.

This method opens up the possibility of studying quantum dynamics in long-range spin models accessible to recent state-of-the-art experiments in regimes where other numerical techniques cannot be applied. We expect that our method will be useful for analyzing the quantum dynamics of polar molecules, Rydberg atoms, and photonic crystals, for instance.