This paper explores the application of real-time Feynman diagrammatics as a powerful theoretical framework for understanding and predicting emergent topological phenomena in quantum materials under non-equilibrium conditions. Traditional approaches, primarily focused on equilibrium systems, often fall short in describing the rich dynamics and transient phases induced by external drives or sudden quenches. We delve into the intricacies of the Keldysh formalism, a crucial tool for non-equilibrium quantum field theory, and detail how it can be combined with diagrammatic expansions to capture time-dependent correlations and interactions. The methodology presented allows for the analysis of phenomena such as Floquet topological insulators, dynamically induced topological phase transitions, and the evolution of topological invariants in time-dependent settings. Through this framework, we aim to uncover novel topological states that emerge far from equilibrium, offering pathways for their experimental realization and manipulation. The discussion highlights the unique insights provided by a real-time perspective, contrasting it with static descriptions and emphasizing its potential to drive advancements in both fundamental condensed matter physics and the engineering of quantum devices.
This paper explores the application of real-time Feynman diagrammatics as a powerful theoretical framework for understanding and predicting emergent topological phenomena in quantum materials under non-equilibrium conditions. Traditional approaches, primarily focused on equilibrium systems, often fall short in describing the rich dynamics and transient phases induced by external drives or sudden quenches. We delve into the intricacies of the Keldysh formalism, a crucial tool for non-equilibrium quantum field theory, and detail how it can be combined with diagrammatic expansions to capture time-dependent correlations and interactions. The methodology presented allows for the analysis of phenomena such as Floquet topological insulators, dynamically induced topological phase transitions, and the evolution of topological invariants in time-dependent settings. Through this framework, we aim to uncover novel topological states that emerge far from equilibrium, offering pathways for their experimental realization and manipulation. The discussion highlights the unique insights provided by a real-time perspective, contrasting it with static descriptions and emphasizing its potential to drive advancements in both fundamental condensed matter physics and the engineering of quantum devices.
The exploration of topological phases of matter has predominantly focused on equilibrium systems. However, recent advances in experimental techniques allow for precise manipulation and probing of quantum systems far from equilibrium, opening new avenues for discovering and engineering novel topological states. Current theoretical tools, largely categorized into variational and perturbative methods, often struggle to capture the full complexity of these non-equilibrium phenomena. Variational approaches offer broad applicability but can lack microscopic detail, while perturbative methods provide precise insights within specific regimes but are limited by their applicability range. This paper introduces a synergistic variational-perturbative framework designed to overcome these limitations. By integrating the strengths of both methodologies, our framework aims to provide a robust and accurate description of non-equilibrium topological matter, spanning both weakly and strongly driven regimes, and accommodating many-body interactions. We elaborate on the conceptual underpinnings, methodological details, and potential applications of this combined approach, demonstrating its capacity to predict and characterize dynamic topological invariants, non-equilibrium phase transitions, and emergent phenomena in driven quantum systems. This framework promises to be a powerful tool for advancing our understanding and control of topological properties in dynamical settings.
This paper explores topological thermodynamics in driven dissipative quantum materials, a field at the intersection of non-equilibrium statistical mechanics, quantum topology, and condensed matter physics. We review theoretical frameworks and experimental advancements, highlighting how driving forces and dissipative processes influence the formation, stability, and characterization of topological phases. A special focus is placed on Floquet engineering for open quantum systems, where periodic driving and environmental coupling lead to novel non-equilibrium steady states with exotic topological properties. We discuss challenges in defining thermodynamic quantities like temperature and entropy in these far-from-equilibrium settings and examine how topological invariants manifest in dissipative dynamics and transport. The paper uniquely synthesizes advancements in periodically driven, open quantum systems by critically examining how dissipation, often seen as detrimental, can be precisely engineered to reveal or even stabilize topological order. This offers a distinct perspective on designing next-generation quantum technologies. Key theoretical tools, including generalized Floquet theory, Keldysh formalism, and non-Hermitian descriptions, are discussed alongside experimental platforms like photonic quantum gases and cold atomic systems.
We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in many-body Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.
Non-equilibrium quantum phase transitions (NEQPTs) represent a frontier in condensed matter physics and quantum statistical mechanics, characterized by abrupt changes in the steady-state properties of open quantum systems or by critical dynamics in closed systems far from thermal equilibrium. Unlike their equilibrium counterparts, NEQPTs are profoundly influenced by driving forces, dissipation, and the specific dynamics of quantum quenches. Understanding these complex phenomena requires theoretical frameworks that can accurately capture both strong correlations and real-time evolution in the presence of environmental interactions. Traditional theoretical tools, such as purely variational methods or purely perturbative expansions, often fall short when dealing with the intricate interplay of coherent and incoherent processes characteristic of NEQPTs. Variational approaches, while adept at capturing ground state properties and short-time dynamics within a chosen ansatz, struggle with long-time thermalization and the inclusion of subtle quantum and thermal fluctuations beyond the variational manifold. Conversely, perturbative methods, particularly those based on the Keldysh formalism, can systematically include interactions and environmental effects but typically rely on a small expansion parameter, limiting their applicability to weakly interacting or weakly driven regimes. This paper proposes a novel "Variational-Perturbative Unification" framework designed to overcome these limitations. The core idea is to combine the strengths of both approaches: using a variational ansatz to capture the dominant non-equilibrium many-body state or dynamics, and then systematically incorporating quantum and thermal fluctuations, as well as dissipation, through a perturbative expansion around this optimized variational state. This hybrid methodology aims to provide a robust and accurate description of NEQPTs, offering insights into critical exponents, universality classes, and the dynamic pathways to steady states. We explore the theoretical underpinnings of this unified approach, discuss its potential applications to driven-dissipative systems and quantum quenches, and highlight how it can reveal novel non-equilibrium phenomena.
The topology of quantum materials is the frontier research in condensed matter physics. In contrast with the conventional classification of materials by using the local symmetry breaking criterion, the states of quantum systems are classified according to the topology of wave functions. The potential applications of topological states may lead the traditional microelectronics to break through and accelerate the significant improvement in topological electronics. Most of the recent studies focus on the topological states of quantum systems under equilibrium conditions without external perturbations. The topological states of quantum systems far from the equilibrium under time-periodic driving have attracted wide attention. Here we first introduce the framework of Floquet engineering under the frame of the Floquet theorem. The nonequilibrium topological states of massless and massive Dirac fermions are discussed including the mechanism of phase transition. Light field driven electronic transition term in the quantum material gains extra time-dependent phase. Thereby the manipulation of effective transition term of the electron is realized to regulate the non-equilibrium topological states. We also mention how the photoinduced coherent phonon affects the nonequilibrium topological states of quantum systems from the perspective of atom manufacturing. Furthermore, research outlook on the nonequilibrium topological states is given. This review provides some clues to the design of physical properties and transport behaviors of quantum materials out of equilibrium.
The exploration of quantum phases in strongly correlated electron systems represents a frontier in condensed matter physics, offering insights into phenomena such as high-temperature superconductivity, Mott insulation, and quantum spin liquids. Traditional theoretical approaches, relying on perturbative or mean-field approximations, often fall short in capturing the intricate interplay of electron correlations that drive these exotic phases. This paper delves into the critical role of exact and highly accurate diagrammatic expansions as powerful, non-perturbative tools for unraveling the emergence and characterization of quantum phases. We review the theoretical foundations of these methods, including advanced techniques like Dynamical Mean-Field Theory extensions and the Functional Renormalization Group, and discuss their ability to systematically incorporate non-local correlations. By examining their application to canonical models, we illustrate how these expansions provide a robust framework for constructing phase diagrams, predicting novel quantum states, and discerning the mechanisms underlying quantum phase transitions. We highlight the computational advancements, such as diagrammatic Monte Carlo, that enable the practical implementation of these complex theories. Finally, we discuss current challenges and future prospects, emphasizing the potential of exact diagrammatic expansions to deepen our understanding of quantum matter and guide the discovery of new materials with tailored functionalities.