New Simulations Model Charge Transfer in Complex Materials with High Accuracy

Hari Kumar Yadalam and Mark T. Mitchison at the Trinity College Dublin present a process-tensor approach, using tensor networks to compute the statistics of charge transfer across an interface within interacting one-dimensional systems. The method accurately simulates non-Markovian correlations, preserving key physical properties and enabling the analysis of transport behaviour in the Heisenberg spin-$1/$2 XXZ brickwork circuit model. The research recovers established transport exponents and reveals anomalous transport characteristics, including a breakdown of Kardar-Parisi-Zhang universality, ultimately offering a pathway to better understand current fluctuations in strongly interacting systems operating far from equilibrium. Process tensor networks model open quantum system dynamics A novel numerical technique, centred around process tensors, mathematical objects representing quantum system influence, was employed. It calculates charge transfer statistics by modelling the interface between quantum systems as an ‘open’ system impacted by its surroundings, extending beyond simple average measurements to capture fluctuations. Process tensors provide a complete description of the influence of the bulk system on the interface degrees of freedom, effectively encoding the system’s memory and allowing for the investigation of non-equilibrium dynamics. To manage computational complexity, matrix-product states, an efficient method for representing complex quantum states on computers, were utilised. Matrix-product states achieve this efficiency by representing the many-body wavefunction as a network of smaller matrices, significantly reducing the computational resources required compared to traditional methods. This is particularly crucial when dealing with the exponential growth of Hilbert space dimensionality in quantum systems. Simulations of magnetization transport within the Heisenberg spin-1/2 XXZ brickwork circuit model, a one-dimensional system with U symmetry, were performed at infinite temperature, simplifying energy state modelling. The XXZ model is a paradigmatic example in condensed matter physics, exhibiting a rich phase diagram and serving as a testbed for various theoretical approaches. Setting the temperature to infinity effectively focuses the analysis on universal features of the transport process, eliminating the need to consider detailed thermal effects. This allowed for the capture of fluctuations in charge transfer, moving beyond average measurements, and addressed current fluctuations in strongly interacting systems where traditional approximations, such as the Landauer-Büttiker formalism, fail. The simulations revealed correct transport exponents for ballistic, superdiffusive, and diffusive behaviours, categorising transport regimes based on system parameters. Specifically, the exponents of $$1, $3/$2, and $$1 were recovered for these respective regimes, validating the method against known theoretical predictions. The ability to distinguish between these regimes is vital for understanding the fundamental mechanisms governing charge transport in various materials. Accurate modelling of quantum transport via process-tensor networks and full counting statistics A tenfold improvement in calculating full counting statistics was achieved, enabling accurate computation of charge transfer statistics across an interface in one-dimensional quantum systems. Full counting statistics provide a more complete picture of charge transfer than simply measuring the average current, as they reveal the probability distribution of all possible current values. This advance, facilitated by a new numerical tensor-network method, accurately models non-Markovian correlations, how a system’s past influences its future, crucial for understanding behaviour far from equilibrium. Markovian approximations, which assume the future depends only on the present, often break down in strongly interacting systems, necessitating the use of non-Markovian approaches like the one presented. Simulations verified the method’s accuracy, demonstrating its superiority over earlier techniques reliant on average measurements. These earlier techniques often miss crucial information about the fluctuations in charge transfer, leading to an incomplete understanding of the system’s behaviour. Anomalous transport, evidenced by a self-similar scaling form of the moment-generating function, a mathematical tool for analysing fluctuations, outside the ballistic regime, was demonstrated, extending beyond simple categorisation. The moment-generating function allows for the systematic calculation of various statistical moments of the charge transfer distribution, providing insights into the nature of the fluctuations. Confirmation of a breakdown of Kardar-Parisi-Zhang universality, a well-established theory predicting behaviour in similar systems, in higher-order transport cumulants at a specific isotropic point suggests the model exhibits behaviour not fully captured by existing theoretical frameworks. The Kardar-Parisi-Zhang theory describes the scaling behaviour of interfaces in random growth processes, and its breakdown in this context indicates that the underlying physics of charge transport in this system is more complex than previously thought. Current simulations remain limited to one-dimensional systems and infinite temperatures, leaving a significant gap before applying this technique to more complex, realistic materials. Extending the method to higher dimensions and finite temperatures represents a significant challenge for future research. Process tensors reveal limits to Kardar-Parisi-Zhang theory in quantum material interfaces Calculating how energy and information flow within quantum materials remains a central challenge in physics. This new technique, employing ‘process tensors’ to map interactions, offers a major leap in accurately modelling charge transfer, the movement of electrical charge, across interfaces within these materials. The ability to accurately model interfacial charge transfer is crucial for understanding the functionality of many quantum devices, including transistors and sensors. The work highlights a potential conflict with the widely accepted Kardar-Parisi-Zhang theory, a framework used to describe seemingly random growth processes, prompting a re-evaluation of established models. The implications of this conflict extend beyond the specific system studied, potentially requiring a revision of our understanding of interfacial phenomena in a broader range of materials. Questioning the universal validity of the Kardar-Parisi-Zhang theory represents valuable work, clarifying where established models may falter when applied to specific quantum systems. Accurately modelling charge transfer, the flow of electrical charge, is key for designing next-generation materials with tailored electronic properties. A new computational method for charting charge transfer within complex quantum systems has been established. Scientists accurately modelled how charge traverses an interface between quantum materials using ‘process tensors’, surpassing previous techniques limited to average measurements. The approach successfully simulates various transport behaviours, including unimpeded, slow, and unusual sc6aling, and reveals a departure from established theoretical predictions concerning Kardar-Parisi-Zhang universality, a concept describing random growth processes. This departure suggests that the assumptions underlying the Kardar-Parisi-Zhang theory may not hold in strongly interacting quantum systems, opening up new avenues for theoretical investigation and potentially leading to the development of more accurate models of quantum transport. Scientists developed a new computational method to model charge transfer across interfaces in one-dimensional quantum materials. This technique, utilising ‘process tensors’, allows for a more accurate representation of how charge moves than previous approaches which were limited to average measurements. Results from simulations of the Heisenberg spin-$1/2$ XXZ brickwork circuit model demonstrate various transport behaviours and indicate a breakdown of the Kardar-Parisi-Zhang theory in higher-order transport cumulants. The research provides a foundation for describing non-Markovian open quantum systems and may necessitate a re-evaluation of existing models of interfacial phenomena. 👉 More information 🗞 Process-tensor approach to full counting statistics of charge transport in quantum many-body circuits 🧠 ArXiv: https://arxiv.org/abs/2603.28894 Tags: