Two-dimensional Optical Su-Schrieffer-Heeger Model Reveals Valence Bond Solid Phases at Significantly Higher Critical Temperatures

The interplay between electrons and vibrations, known as electron-phonon coupling, drives fascinating behaviour in materials, and scientists are now exploring how this interaction manifests in lower-dimensional systems. Jadson L. Portela e Silva, from the Universidade Federal do Rio de Janeiro, Gabriel Rein from the Universität Würzburg, and Sebastião dos A. Sousa-Júnior from the University of Houston, alongside colleagues, investigate this phenomenon within a two-dimensional model inspired by the Su-Schrieffer-Heeger framework. Their work reveals the emergence of distinct ordered phases, including valence bond solids and antiferromagnetic states, as they vary the strength of the electron-phonon interaction and the vibrational frequency. Importantly, the team demonstrates that these phases appear at higher temperatures than predicted by simpler models, suggesting a novel mechanism for polaron formation and opening new avenues for understanding and potentially controlling electronic properties in advanced materials.

Researchers investigate the two-dimensional optical Su-Schrieffer-Heeger (SSH) model, where electron movement is linked to vibrations within the material’s structure. Employing sign-problem-free auxiliary-field quantum Monte Carlo simulations, complemented by mean-field analysis, they determine the long-range ordered phases as a function of electron-phonon coupling and phonon frequency. By examining both adiabatic and anti-adiabatic regimes, the team reveals the emergence of staggered and armchair valence bond solid (VBS) phases, as well as the O(4) antiferromagnetic phase. These findings contribute to a deeper understanding of correlated electron systems and their complex ordering behaviour.

Electron-Phonon Coupling and Correlated Electron Systems

This body of research focuses on strongly correlated electron systems, particularly the interplay between electron-phonon interactions, charge density waves, superconductivity, and various quantum phases. The central theme explores how electrons interact with lattice vibrations, driving many interesting phenomena. Researchers investigate the formation of charge density waves, the emergence of superconductivity, and a range of quantum phases including topological phases, spin liquids, valence bond solids, and nematic phases. Quantum Monte Carlo (QMC) methods are the primary computational tools, with auxiliary-field QMC, determinant QMC, and Langevin Monte Carlo employed.

Finite-size scaling and critical exponent analysis are used to extrapolate results and characterize phase transitions. Research focuses on polaron formation, the stability and mobility of these electron-vibration coupled quasi-particles, and the formation of bipolarons. The nature of charge density wave transitions, the role of dimensionality and interactions, and the potential for electron-phonon interactions to drive superconductivity are also key areas of investigation. Scientists explore the interplay between competing ordered phases, the impact of disorder on electronic and phononic properties, and the behaviour of frustrated systems. They investigate topological phases arising from electron-phonon interactions, quantum criticality near phase transitions, and specific valence bond orderings like Kekulé order. This research represents a significant effort to understand the complex interplay between electrons and phonons in materials, and how these interactions give rise to fascinating quantum phenomena, with implications for developing new materials with tailored electronic and optical properties.

SSH Model Reveals Valence Bond Solid Phases

Scientists have achieved a comprehensive understanding of the two-dimensional optical Su-Schrieffer-Heeger (SSH) model, detailing its ground-state and finite-temperature phase diagrams through advanced computational methods. The research reveals the existence of staggered and armchair valence bond solid (VBS) phases, alongside transitions to an antiferromagnetic (AFM) phase, across both adiabatic and anti-adiabatic regimes. Experiments demonstrate that a nonzero critical electron-phonon coupling is required to stabilize the staggered VBS phase, unlike related models. Data show weak, short-range AFM correlations for coupling strengths below this threshold, indicating metallic behaviour.

The team’s investigations reveal a rich phase diagram encompassing these VBS regions and transitions to the AFM phase, providing a detailed picture of the model’s behaviour. Measurements confirm that the VBS transition occurs at critical temperatures significantly higher than those observed in models where phonons couple to charge density, such as the Holstein model. This difference arises from the presence of lighter polarons in the metallic regime, enhancing the stability of the VBS phase at elevated temperatures. The finite-temperature phase diagram, therefore, expands the understanding of this model and its potential applications. The research establishes a numerical benchmark for the optical SSH model, clarifying recent discussions in the literature and providing a foundation for future investigations into electron-phonon interactions and correlated electron systems.

Optical SSH Model Reveals Novel Ground States

This research establishes a comprehensive understanding of the optical Su-Schrieffer-Heeger model, a system where electron movement is linked to vibrations within the material’s structure. Through advanced computational methods, scientists have mapped the ground-state phases of this model, revealing the emergence of distinct ordered states, including staggered and armchair valence bond solid phases, alongside an antiferromagnetic phase. These findings demonstrate that the optical SSH model, unlike its bond-based counterpart, exhibits a unique wavevector dependence in its electron-phonon coupling, significantly influencing the resulting phases. The study clarifies the behaviour of polarons, electrons coupled to vibrations, within the model, showing that they are lighter and contribute to higher critical temperatures for the observed valence bond solid transitions compared to systems with local electron-phonon interactions. Importantly, the team demonstrated the model’s symmetries using a Majorana fermion formulation, providing a deeper insight into its underlying physics. Future work could also investigate the model’s behaviour at finite temperatures and explore its potential relevance to real materials exhibiting similar electron-phonon interactions, potentially guiding the design of novel electronic devices.