Diagnosis of Mixed-State Topological Phases Via Disorder Parameters Enables Characterization of Strongly Correlated Systems

Identifying the distinct phases of matter in complex, interacting systems presents a significant challenge for physicists, but a new framework developed by Shao-Hang Shi, Xiao-Qi Sun, and Zi-Xiang Li from the Beijing National Laboratory for Condensed Matter Physics offers a powerful solution. The researchers introduce a method that diagnoses these ‘mixed-state’ phases by analysing a property called the ‘disorder parameter’ and observing how it changes with system size. This approach successfully maps the transition between different insulating states in established models, including the shift from a spin Hall insulator to a trivial Mott insulator, and crucially overcomes computational hurdles that previously prevented accurate analysis of the anomalous Hall phase. By providing an efficient and robust tool for exploring these complex systems, this work opens up new avenues for investigating a wide range of previously inaccessible phenomena in materials science and condensed matter physics.

This work introduces a general and numerically efficient framework to diagnose topological phases in strongly interacting systems via the disorder parameter of the U(1) charge operator. Specifically, the researchers introduce the topological scaling indicator, derived from the finite-size scaling of the second derivative of the disorder parameter generating function. This indicator exhibits characteristic linear scaling with the system’s linear dimension for topological phases, a signature that vanishes upon transition into a topologically trivial phase. Crucially, the team develops an efficient determinant Quantum Monte Carlo algorithm to facilitate these calculations.

Detecting Topology in Interacting Mixed States

This research details a new method for detecting topological phases in two-dimensional systems, even those with strong interactions between electrons. The core idea involves calculating a topological indicator based on how the system responds to changes in size, providing a robust way to identify these phases. The method utilizes Quantum Monte Carlo calculations to determine this indicator, demonstrating its applicability to both non-interacting and interacting systems. Topological phases are states of matter characterized by unique properties and robust edge states, while mixed states represent systems that are not in a pure quantum state, reflecting realistic materials subject to disorder or thermal fluctuations. The team employed open boundary conditions, allowing observation of edge states, and carefully considered the characteristic length scale related to their localization. This work provides a powerful tool for characterizing these complex states of matter.

Topological Phases Identified Via Scaling Indicator

Scientists have developed a new method to identify topological phases in materials, even when those materials exhibit strong interactions between electrons. This work introduces a “topological scaling indicator” that characterizes these phases by examining the behaviour of a “disorder parameter” related to the charge of electrons within the material. The team demonstrated that this indicator exhibits a characteristic linear scaling with the system’s size for topological phases, a signature that vanishes when the material transitions to a non-topological state. Crucially, the researchers devised an efficient computational algorithm, a determinant Monte Carlo method, to calculate this scaling indicator in interacting systems, overcoming significant computational challenges. Applying this method to the Kane-Mele-Hubbard model, they successfully mapped the transition from a spin Hall insulator to a trivial Mott insulator, confirming the method’s ability to track phase transitions. The team also circumvented the “sign problem”, a common obstacle in quantum simulations, allowing them to robustly identify the anomalous Hall phase at accessible temperatures.

Scaling Indicator Reveals Complex Quantum Phases

This research introduces a new method for identifying and characterizing phases of strongly interacting quantum systems, specifically those exhibiting “mixed states”, complex arrangements of matter defying simple classification. Scientists developed a “scaling indicator” based on the behaviour of a “disorder parameter”, a mathematical quantity sensitive to the system’s underlying order. By examining how this indicator changes with system size, researchers can reliably distinguish between different phases and detect transitions between them, even in systems where traditional methods fail. The team successfully applied this technique to the Kane-Mele-Hubbard and Haldane-Hubbard models. They accurately mapped the transition from a spin Hall insulator to a trivial Mott insulator in the former, and crucially, overcame a significant computational obstacle, the “sign problem”, to robustly identify the anomalous Hall phase in the latter at accessible temperatures. This achievement opens a pathway to study a wider range of strongly interacting systems previously inaccessible due to computational limitations.