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Natural Sciences

Disclosed: Quasiparticle properties and dynamics in real and momentum space

Ursula Wurstbauer

Published Jun 1, 2021• 1 citation
Publisher

Abstract

Physical properties of solid-state materials and other systems are determined by manifold interactions.While for weakly interacting systems their description in a single-particle picture is often sufficient, this approach fails when the interactions become stronger and many particles are involved.The quantum-mechanical problem of describing elementary excitations and collective behavior in many-body systems is often solved by introducing quasiparticles, thereby transforming the problem of strongly interacting particles to that of weakly interacting quasiparticles.

DOI
10.1002/ntls.10017

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Physical properties of solid-state materials and other systems are determined by manifold interactions.While for weakly interacting systems their description in a single-particle picture is often sufficient, this approach fails when the interactions become stronger and many particles are involved.The quantum-mechanical problem of describing elementary excitations and collective behavior in many-body systems is often solved by introducing quasiparticles, thereby transforming the problem of strongly interacting particles to that of weakly interacting quasiparticles.
Condensed matter physics is a rich field with a wide variety of phenomena. In condensed matter, we consider systems composed of many electrons and nuclei, with the only fundamental interaction being electromagnetism. Nuclei of a given charge and mass are considered as point particles. The relevant fundamental physics that we use as our foundations is the quantum many-body problem. That is, just standard many-body quantum mechanics, but formulated in terms of a useful second quantized field theory, which can deal with an arbitrary number of particles within a single Hilbert space. In general, this many-body problem is essentially intractable for numbers of particles as large as those we must consider for materials. Thus we must look for simplifications and look at easily measurable aspects which allow us to make predictions still. We employ the trick of phrasing the questions differently. Rather than look at the time evolution of an arbitrary many-body wavefunction for the fundamental degrees of freedom, we look at transport in scenarios where the starting point is a relatively simple assumed equilibrium state of the material, consisting of a ground state with postulated quasiparticle excitations.
Solid state physics, a very broad field in natural science, aims to explain physical properties of materials modeled as a many-body ensemble of the order of ∼ 10^23 interacting particles. For interacting metallic systems, one of the most powerful tools for unraveling the consequences of the collective interaction is the Fermi liquid theory. While still being an approximation, it excellently models many materials especially in the low-temperature and low-energy regime by treating themany-body problem as being equivalent to effectively non-interacting ”particles”, which is done by introducing the concept of quasiparticles. During the last few decades, several exotic phases of matter have been discovered, which originate from strong Coulomb interactions between the electrons, whose description is beyond the Fermi liquid theory. This thesis addresses the question of the validity of Fermi liquid theory once a single hole is introduced into an antiferromagnet with completely localized spins due to the strong interactions. Here, the most-studied case concerns the so-called 2D t − J model, which hosts a well-defined quasiparticle, the spin polaron. Focusing on a more tractable case, the t − Jz model without quantum spin fluctuations, we study the stability of the spin polaron solution once the nextnearest neighbor hopping t′ is introduced into the system. We focus on observations at the Γ-point and the X-point of systems with fixed Jz = 0.4t and varying t′ ∈ [−0.5t, 0.5t]. The model is numerically solved using exact diagonalization on finite-size lattices of up to 32 sites. A study of the quasiparticle weight under finite-size scaling reveals an “anomalous” regime at the Γ-point fort′ ≤ −0.3t, indicated by a vanishing quasiparticle weight. In order to characterize the low-energy dynamics within this “anomalous” regime, we investigated the spin correlation centered around the hole, as well as the magnon number distribution of a single-doped 20-site system. Based on the results, we present a preliminary picture of the antiferromagnetic ground state doped with one hole within that “anomalous” regime (t′ ≤ −0.3t) that deviates from the standard spin polaron as the cloud of magnetic fluctuations, typically localized around the hole, delocalizes over the whole finite-size lattice. Consequently, such systems show a weakly suppressed antiferromagnetic configuration under single-hole doping.
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.
This chapter presents field-theoretic methods and discusses three well-known "pictures" or representations used in discussing quantum mechanical problems. It explores how to build up the true one-electron and one-phonon Green's functions as a perturbation series involving the corresponding functions for the non-interacting system. In elementary discussions of quantum mechanics one usually works in the "Schrodinger picture" in which the dynamical variables are taken to be time independent so that the wave function contains the time dependence of the problem. The one-electron Green's function gives information about the spin and charge densities and the momentum distribution of the electrons as well as information about the excitation spectrum of the system. When the system consists only of fermions interacting via an instantaneous two-body potential, the one-particle Green's function also suffices to determine the ground-state energy of the system. The electrical conductivity, magnetic susceptibility, and many other non-equilibrium properties can be obtained from the two-particle Green's function.