Gross-neveu Model Exhibits Phase Transitions to Gapped Anomalous Hall Insulator at Finite Coupling

The behaviour of interacting electrons in materials often leads to surprising new phases, and recent research explores these possibilities within the theoretical framework of the Gross-Neveu model. Gabriel Osiander Rein, Fakher F. Assaad, and Igor F. Herbut, from the Universität Würzburg and Simon Fraser University, investigate how this model predicts transitions between different states of matter, specifically from a metallic phase to one with unusual insulating properties. Their work demonstrates a spontaneous breaking of symmetry, indicating a shift in the fundamental order of the system, and reveals a weakly first-order transition relevant to materials like graphene. Importantly, the team’s simulations, employing a sophisticated computational technique, confirm theoretical predictions and uncover a novel pathway to superconductivity when a chemical potential is introduced, offering new insights into the behaviour of strongly interacting electron systems.

Topology, Interactions, and Disorder in 2D Materials

This research investigates strongly correlated electron systems, focusing on topological phases of matter and novel phenomena in two-dimensional materials like graphene. Scientists explore how topology, interactions between electrons, and disorder within the material influence its electronic properties. The study employs theoretical techniques, including renormalization group analysis and numerical simulations, connecting to experimental observations in moiré materials, structures formed by twisting layers of 2D materials. These materials offer a platform for observing exotic quantum behavior. The research centers on understanding topological and Chern insulators, materials exhibiting unusual electronic properties protected by their topology.

These properties lead to robust edge states, potentially useful in spintronics and quantum computing. Scientists also investigate quantum criticality, the behavior of materials at extremely low temperatures as parameters are adjusted, leading to non-trivial behavior and potentially new phases of matter. A key focus is the behavior of electrons that strongly interact with each other, a complex scenario that gives rise to emergent phenomena difficult to predict using simpler models. The study suggests that moiré materials can host a variety of novel phases, including correlated insulators, superconductors, and topological states.

The interplay between electron-electron interactions and disorder is crucial in determining these properties; disorder can either disrupt topological order or, surprisingly, enhance it. Researchers identify potential quantum critical points within these systems and investigate their characteristics, emphasizing the importance of topological protection in stabilizing certain phases and preventing their destruction by imperfections. The theoretical predictions are motivated by and intended to explain recent experimental observations in moiré materials and other 2D systems. This research is significant because it advances our understanding of strongly correlated electron systems and topological phases of matter. The findings could contribute to the design of new materials with tailored electronic properties, the development of robust quantum devices based on topological states, and a deeper understanding of quantum many-body physics. Scientists developed a lattice model based on a honeycomb structure, employing a Hamiltonian that combines hopping terms with a novel interaction term. This Hamiltonian, expressed in terms of Majorana lattice fermions, ensures an inherent O(2N) symmetry, crucial for understanding the model’s behavior. This allowed them to explore previously uncharted territory within the Gross-Neveu theory. This approach enabled the team to analyze the model’s behavior and identify the emergence of symmetry breaking and phase transitions.

The study also involved a careful examination of various order parameters, which describe how the system organizes itself. By analyzing the representations of the O(4) symmetry group, researchers determined that the ground state of the model belongs to a specific irreducible representation, indicating a particular ordering of the fermions. This finding provides insights into the nature of the phase transition and the properties of the resulting state. The team’s innovative approach, combining lattice simulations with symmetry analysis, provides a powerful tool for investigating strongly correlated fermion systems and exploring novel quantum phases of matter.

Dirac Semimetal to Quantum Hall Transition

Scientists have achieved a detailed understanding of symmetry breaking in a model of interacting electrons, revealing a transition from a Dirac semimetal to a quantum anomalous Hall (QAH) insulator. This work utilizes a lattice-based computational approach to study the Gross-Neveu model, a theoretical framework describing interacting fermions, and demonstrates a spontaneous breaking of both inversion and time-reversal symmetry at a specific attractive coupling strength. The research confirms the preservation of flavor O(4N) symmetry throughout this transition, aligning with theoretical predictions. The team employed a fermionic auxiliary-field Monte Carlo algorithm to investigate the model in a repulsive interaction regime, successfully circumventing the computational challenges posed by the “sign problem” often encountered in such simulations.

Results demonstrate an O(4N) symmetry breaking transition occurring out of the Dirac semimetal state for N equals 2, a value particularly relevant to graphene. The magnitude of the discontinuity and the critical coupling strength both increase with N, indicating a scaling relationship between system size and transition characteristics. The lattice model exhibits an exact O(2N) symmetry, a subgroup of the low-energy O(4N) symmetry, and the ordered ground state corresponds to an order parameter belonging to its N(2N-1)-dimensional representation. Detailed analysis of other order parameters reveals a distinct hierarchy among those belonging to different representations of the exact O(2N) symmetry. These findings provide valuable insights into the behavior of interacting electron systems and pave the way for exploring novel quantum phases of matter.

Gross-Neveu Model Predicts Quantum Hall Transition

This research establishes a strong connection between the Gross-Neveu model, a theoretical framework in particle physics, and the emergence of exotic quantum states in condensed matter systems. Specifically, scientists demonstrate how this model predicts a transition from a gapless Dirac semimetal, a material with unique electronic properties, to a quantum anomalous Hall (QAH) insulator, a state where electrons flow along the edges without resistance. This transition occurs at a specific attractive coupling strength and is accompanied by the spontaneous breaking of inversion and time-reversal symmetry, while preserving flavor symmetry. The team employed a sophisticated computational technique, a fermionic auxiliary-field Monte Carlo algorithm, to study a lattice version of the Gross-Neveu model in the repulsive regime, a challenging area due to computational complexities.

Their calculations confirm the prediction of symmetry breaking and the emergence of this novel phase transition, particularly relevant to materials like graphene. The addition of a finite chemical potential was found to induce superconductivity, highlighting the rich phase diagram of the model. The authors acknowledge that the observed transition is weakly first-order, meaning the change between phases is not perfectly abrupt, and the size of the discontinuity grows with system parameters.