Majorana String Simulation Advances Real-time Fermion Dynamics in Two-dimensional Lattice Systems

Understanding how electrons behave over time remains a significant challenge in modern physics, with crucial implications for advances in chemistry and materials science. Matteo D’Anna, Jannes Nys from the Institute for Theoretical Physics at ETH Z ̈urich, and Juan Carrasquilla now present a new computational method that overcomes limitations in simulating these dynamic processes. Their approach uses a technique called Majorana strings to track the evolution of electrons in complex materials, achieving accuracy comparable to both cutting-edge theoretical models and real-world experiments. This breakthrough enables scientists to investigate the behaviour of electrons in two dimensions with unprecedented precision, paving the way for the design of novel materials and technologies.

Fermion Dynamics via Heisenberg String Simulation

Researchers introduce a novel method to simulate the behaviour of interacting fermions, a long-standing challenge in understanding quantum systems and materials. This new approach, based on Heisenberg string simulation, accurately models the real-time dynamics of fermions in two-dimensional lattices. By representing fermionic operators using Majorana strings, closed loops of operators obeying specific rules, the team overcomes limitations of traditional quantum Monte Carlo simulations, which often struggle with the ‘sign problem’. This allows for precise calculations of how fermionic systems evolve over time, providing access to crucial information like correlation functions and transport properties. The simulation results demonstrate the feasibility of studying complex quantum phenomena in condensed matter systems and offer a pathway towards understanding strongly correlated materials.

The research team developed an algorithm that propagates observable quantities expressed in a Majorana-string basis. This method employs a carefully designed truncation scheme to preserve accuracy and maintain computational efficiency. The framework remains exact for simplified systems and allows for systematic improvements when applied to more complex, interacting scenarios. The team validated this method by comparing its results to those obtained using established tensor network techniques, including matrix product states and projected entangled pair states, as well as recent experimental data.

Fermionic Quantum System Simulation Advances

This research represents a comprehensive effort to develop and analyse methods for simulating interacting fermionic quantum systems, a crucial problem with applications in materials science, chemistry, and fundamental physics. The overarching goal is to understand the behaviour of these systems, which are notoriously difficult to model due to their complex interactions. The research focuses on both quantum and classical simulation techniques, with a particular emphasis on efficient representations of the quantum state and methods suitable for near-term quantum computers.

Central to this work are tensor networks, powerful tools for representing many-body quantum states efficiently. Matrix product states, a specific type of tensor network, are particularly well-suited for simulating one-dimensional systems and tracking their evolution over time. Researchers also explore Majorana representations, a technique for representing fermions using Majorana operators, which can simplify calculations and potentially improve the efficiency of quantum simulations. Complementary classical simulation techniques, such as Pauli propagation and Lagrangian representations, are used to benchmark quantum simulations and tackle problems currently intractable for quantum computers.

Several software libraries are essential to this research. ITensor provides a powerful framework for tensor network calculations, while Netket serves as a machine learning toolbox for many-body quantum systems. MajoranaPropagation. jl, a Julia library, is specifically designed for simulating fermionic systems using Majorana representations. These tools, along with open-source codebases from SciPost Physics, facilitate the development and dissemination of new simulation techniques.

This research is highly significant because it addresses a critical challenge in modern physics and chemistry: simulating the behaviour of complex quantum systems. The development of efficient simulation algorithms and software tools is essential for materials discovery, drug design, and fundamental understanding of quantum phenomena. The focus on fermionic systems and the development of specialized techniques like Majorana representations are particularly important because fermions are the building blocks of matter and play a crucial role in many physical and chemical processes. The combination of classical and quantum simulation techniques offers a promising approach for tackling the challenges of simulating complex quantum systems.

Majorana Strings Simulate Fermion Dynamics Accurately

This research presents a new algorithm for accurately simulating the real-time dynamics of interacting fermions, a longstanding challenge in physics and materials science. Scientists developed a method based on propagating observable quantities using a Majorana-string basis, combined with a carefully controlled truncation scheme. This approach maintains accuracy while efficiently managing computational complexity, offering a significant advancement over existing techniques. The method proves exact for certain simplified systems and systematically controllable for more complex, interacting scenarios.

The team successfully benchmarked their algorithm against established methods, including tensor networks, and compared results to recent experimental data obtained from ultracold atom experiments. Demonstrations on one- and two-dimensional Fermi-Hubbard quenches show the method achieves high accuracy over timescales comparable to state-of-the-art variational techniques and experiments. Importantly, the simulations reveal finite-size effects and provide qualitative agreement with experimental observations, validating the approach for studying complex fermionic systems.

The authors acknowledge limitations related to the truncation scheme and computational cost, particularly as system size and simulation time increase. Future work will likely focus on extending the method to larger systems and exploring more sophisticated truncation strategies. The researchers also note the potential for combining their approach with variational representations of the initial state, further enhancing its capabilities and broadening its applicability to a wider range of physical problems.