Quantum Critical Crossover Probed Via Impurity Renormalization Group and Fractionalization Effects

Understanding how imperfections within materials influence their quantum properties is a central challenge in condensed matter physics. Tao Yang, Z. Y. Xie, and Rui Wang, from the National Laboratory of Solid State Microstructures and Nanjing University, alongside Baigeng Wang, have developed a novel theoretical approach to investigate this phenomenon. Their research introduces an impurity renormalization group method, combining tensor networks with numerical renormalization group techniques to accurately model the complex interactions between impurities and their surrounding environment. This work is significant because it provides a powerful new tool for probing quantum critical behaviour and reveals previously hidden effects arising from the interplay between material defects and quantum correlations. The team’s findings demonstrate that impurities can induce fractionalisation of magnetic moments and signal transitions into critical regimes, paving the way for a deeper understanding of novel impurity physics in correlated systems.

The research focused on understanding how a system transitions between distinct quantum phases, specifically examining the behaviour near a quantum critical point. Their approach involved analysing the interplay between quantum fluctuations and interactions within the system, employing the IRG technique to effectively renormalise the impurity potential.

This allowed for a detailed exploration of the crossover behaviour and the emergence of novel physical properties. The study aimed to characterise the critical exponents and scaling functions governing the quantum critical crossover, providing insights into the universality classes of these transitions. Researchers developed a theoretical framework to describe the impurity problem within a dynamically fluctuating environment, capturing the essential physics of the quantum critical regime. By systematically integrating out high-energy degrees of freedom, they derived a flow equation for the impurity potential, revealing the evolution of the system towards the fixed point.

This methodology enabled the determination of the critical behaviour and the identification of relevant parameters controlling the crossover. A specific contribution of this work lies in the accurate calculation of the critical exponents associated with the quantum critical crossover, achieving results consistent with established theoretical predictions and experimental observations. The team demonstrated that the IRG method provides a powerful tool for analysing strongly correlated systems near quantum phase transitions. Furthermore, they elucidated the role of quantum fluctuations in driving the crossover and shaping the emergent low-energy physics, advancing the field of quantum criticality and offering a pathway for exploring similar phenomena in diverse physical systems.

Systems can host exotic many-body states that serve as sensitive probes of bath correlations. Quantitative and non-perturbative methods for determining impurity thermodynamics in such settings, however, remain scarce. Researchers have introduced an impurity renormalization group approach which merges the tensor-network representation with the numerical renormalization group cutoff scheme. This method overcomes conventional limitations by treating bath correlations and impurity interactions on an equal footing, allowing for a more holistic analysis. Applying this approach to the finite-temperature quantum critical regime of quantum spin systems, they uncovered striking impurity-induced phenomena, including fractionalization of the local magnetic moment in a coupled Heisenberg ladder.

IRG Validation, Defects in Spin Models Demonstrated

This supplementary material details a novel method, the Impurity Renormalization Group (IRG), for studying quantum spin models with defects. The IRG method is validated by applying it to an incomplete bilayer and a coupled Heisenberg ladder, demonstrating its general applicability. The importance of the impurity ansatz size is highlighted, with larger sizes generally leading to more accurate results, particularly for models with longer-range correlations. The study shows that while quantitative results can shift slightly depending on the shape of the impurity ansatz, the qualitative behaviour and conclusions remain consistent, demonstrating the robustness of the method.

Results are compared to those from other methods, like Quantum Monte Carlo, to confirm accuracy. A detailed convergence test demonstrates how the accuracy of the results depends on the bond dimension used in the tensor network calculations, ensuring reliable results. The specific tensor network ansatz used to calculate the ground state of the coupled Heisenberg ladder is a Projected Entangled Pair State (PEPS) designed to capture the characteristics of the valence bond solid (VBS) phase. Magnetization analysis confirms the expected phase transitions. This material provides a thorough justification for the validity and reliability of the IRG method, demonstrating its potential as a powerful tool for studying quantum systems with defects.

Impurity Renormalisation Reveals Magnetic Fractionalisation

This work introduces an impurity renormalization group (IRG) method, effectively merging tensor-network representations with the numerical renormalization group cutoff scheme. This innovative approach allows for the treatment of both bath correlations and impurity interactions on an equal footing, overcoming limitations present in conventional methods used to study correlated systems with defects. Applying this method to a finite-temperature critical regime within spin systems, researchers have demonstrated the ability to uncover previously inaccessible impurity-induced phenomena. Specifically, investigations into a coupled Heisenberg ladder revealed that an impurity can induce fractionalization of the local magnetic moment, alongside a distinctive evolution of spin correlation functions. The derivative of the impurity susceptibility exhibited cusps, clearly indicating transitions into the critical regime, and a continuous evolution from columnar to pinwheel-like spin-spin correlation textures was observed. While acknowledging that achieving a complete solution for complex systems will require further computational resources, future research directions include applying this IRG method to investigate vacancies in quantum spin liquids, defects in deconfined quantum critical points, and impurities in non-Fermi liquid systems, potentially revealing novel impurity states and furthering our understanding of correlated materials.