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Topics in current chemistry

Probing Strongly Correlated Materials in Non-equilibrium: Basic Concepts and Possible Future Trends in First Principle Approaches

Miroslav Hopjan, Claudio Verdozzi

Published Jan 1, 2014• 5 citations
Publisher
DOI
10.1007/128_2014_528

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Correlated systems are a wide class of materials in which the strong electron-electron repulsion is the origin of very fascinating and unusual properties, among which metal-to-insulator transitions and high temperature superconductivity are the most striking examples. In the recent years, the fast development of non-adiabatic probing techniques opened new interesting perspectives for the investigation of such materials in non-equilibrium conditions. In this thesis, we discuss the theoretical description of few relevant cases which represent different examples of non-equilibrium phenomena in correlated materials. In particular, we will focus on the dynamics following a sudden excitation and the coupling to an external driving field. As a first example we consider the dynamics across a phase transition, namely we explore the possibility of driving a phase transition as the result of a sudden excitation, as e.g. the coupling with a short light pulse. We consider systems showing different equilibrium phases and study the conditions under which the off-equilibrium dynamics may lead to non-trivial dynamical phase transitions. A different case is represented by the dynamics induced by a driving electric field. This problem is particularly relevant for the possible applications of correlated materials in electronic devices. Here we consider the paradigmatic case of a correlated material coupled to external sources which impose a finite bias across the system. We analyze the formation and the properties of the non-equilibrium stationary states in which a finite current flows through the system. This allows us to study the non-linear response properties of a correlated system. In this context, a particularly relevant aspect is the problem of the dielectric breakdown of a Mott insulator, namely the formation of conducting states in the Mott insulating phase. In this thesis we explore different mechanisms leading to such possibility. First we discuss a quantum tunneling mechanism of carriers driven across the insulating gap by the effect of strong electric-fields. Eventually, we discuss the possibility of a resistive transition from an insulating to a metallic state induced by the application of an external electric-field.

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Simulating Condensed Matter Physics on Quantum Hardware

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Quantum hardware platforms are getting increasingly sophisticated in their ability to simulate condensed matter, including but not limited to strongly-correlated, topological, and non-equilibrium phenomena. This review surveys recent progress in quantum-hardware-based simulations of condensed matter, primarily emphasizing gate-based digital quantum computer simulation, with analog experiments discussed as complementary benchmarks. We first review major hardware platforms, including superconducting qubits, trapped-ions, ultracold atoms, Rydberg arrays, photonic systems, and moire quantum materials. We then introduce the basic ingredients of digital quantum simulation. Building on this foundation, we discuss representative applications to condensed-matter physics, spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations. Finally, we summarize key methodological tools used in state-of-the-art quantum-simulation workflows. We emphasize that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation.

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First-principles study of ultrafast quasiparticle dynamics in typical quantum materials

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Quasiparticles are fundamental in describing the complex many-body interactions underlying single-particle excitations, playing a key role in understanding the macroscopic properties of quantum materials. Recent advancements in ultrafast laser technology, combined with various detection methods, have enabled precise monitoring and manipulation of quantum states and their dynamic processes. These developments not only enhance our comprehension of quasiparticle excitation mechanisms but also facilitate driving materials into non-equilibrium states, uncovering novel physical phenomena and advancing the design and application of innovative functional materials. The computational approach based on real-time time-dependent density functional theory (rt-TDDFT) transcends the limitations of linear response theory, enabling first-principles simulations of the dynamic response of strongly coupled quasiparticles under non-equilibrium conditions. The proposed method provides accurate predictions of highly nonlinear phenomena induced by strong laser fields, offering deeper insights into the underlying physical mechanisms. These theoretical insights are crucial for optimizing the performance of optoelectronic devices. This paper introduces the theoretical foundations of Ehrenfest dynamics within the framework of rt-TDDFT and presents case studies on the evolution of various quasiparticles under laser excitation. The results demonstrate the significant potential of ultrafast lasers for probing and controlling the properties of quantum materials, while also underscoring the vital role of dynamic simulations for studying non-equilibrium states and their time-domain characteristics.

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Correlated systems are a wide class of materials in which the strong electron-electron repulsion is the origin of very fascinating and unusual properties, among which metal-to-insulator transitions and high temperature superconductivity are the most striking examples. In the recent years, the fast development of non-adiabatic probing techniques opened new interesting perspectives for the investigation of such materials in non-equilibrium conditions. In this thesis, we discuss the theoretical description of few relevant cases which represent different examples of non-equilibrium phenomena in correlated materials. In particular, we will focus on the dynamics following a sudden excitation and the coupling to an external driving field. As a first example we consider the dynamics across a phase transition, namely we explore the possibility of driving a phase transition as the result of a sudden excitation, as e.g. the coupling with a short light pulse. We consider systems showing different equilibrium phases and study the conditions under which the off-equilibrium dynamics may lead to non-trivial dynamical phase transitions. A different case is represented by the dynamics induced by a driving electric field. This problem is particularly relevant for the possible applications of correlated materials in electronic devices. Here we consider the paradigmatic case of a correlated material coupled to external sources which impose a finite bias across the system. We analyze the formation and the properties of the non-equilibrium stationary states in which a finite current flows through the system. This allows us to study the non-linear response properties of a correlated system. In this context, a particularly relevant aspect is the problem of the dielectric breakdown of a Mott insulator, namely the formation of conducting states in the Mott insulating phase. In this thesis we explore different mechanisms leading to such possibility. First we discuss a quantum tunneling mechanism of carriers driven across the insulating gap by the effect of strong electric-fields. Eventually, we discuss the possibility of a resistive transition from an insulating to a metallic state induced by the application of an external electric-field.
Quantum hardware platforms are getting increasingly sophisticated in their ability to simulate condensed matter, including but not limited to strongly-correlated, topological, and non-equilibrium phenomena. This review surveys recent progress in quantum-hardware-based simulations of condensed matter, primarily emphasizing gate-based digital quantum computer simulation, with analog experiments discussed as complementary benchmarks. We first review major hardware platforms, including superconducting qubits, trapped-ions, ultracold atoms, Rydberg arrays, photonic systems, and moire quantum materials. We then introduce the basic ingredients of digital quantum simulation. Building on this foundation, we discuss representative applications to condensed-matter physics, spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations. Finally, we summarize key methodological tools used in state-of-the-art quantum-simulation workflows. We emphasize that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation.
Quasiparticles are fundamental in describing the complex many-body interactions underlying single-particle excitations, playing a key role in understanding the macroscopic properties of quantum materials. Recent advancements in ultrafast laser technology, combined with various detection methods, have enabled precise monitoring and manipulation of quantum states and their dynamic processes. These developments not only enhance our comprehension of quasiparticle excitation mechanisms but also facilitate driving materials into non-equilibrium states, uncovering novel physical phenomena and advancing the design and application of innovative functional materials. The computational approach based on real-time time-dependent density functional theory (rt-TDDFT) transcends the limitations of linear response theory, enabling first-principles simulations of the dynamic response of strongly coupled quasiparticles under non-equilibrium conditions. The proposed method provides accurate predictions of highly nonlinear phenomena induced by strong laser fields, offering deeper insights into the underlying physical mechanisms. These theoretical insights are crucial for optimizing the performance of optoelectronic devices. This paper introduces the theoretical foundations of Ehrenfest dynamics within the framework of rt-TDDFT and presents case studies on the evolution of various quasiparticles under laser excitation. The results demonstrate the significant potential of ultrafast lasers for probing and controlling the properties of quantum materials, while also underscoring the vital role of dynamic simulations for studying non-equilibrium states and their time-domain characteristics.