Many-body effects in altermagnets and electron–phonon systems

Abstract

In this dissertation, which is situated in the field of theoretical condensed matter physics, we investigate many-body effects in altermagnets and electron–phonon systems. Specifically, we study a Heisenberg model for two-dimensional altermagnets, a dissipative variant of the Yukawa–Sachdev–Ye–Kitaev (YSYK) model, and the Holstein model. In all of these systems, the presence or absence of quasiparticles plays a central role. Consequently, the description of these quasiparticles and their influence on the state of the system constitute the primary focus of this work. Since the Heisenberg model can be bosonized using the Holstein–Primakoff transformation, all systems considered in this dissertation can be analyzed using many-body methods, in particular within the framework of Green's function techniques. Altermagnets constitute a recently identified class of magnetic materials characterized by their distinct symmetry properties. They combine properties of both ferromagnets and antiferromagnets, thereby offering promising opportunities for future applications, for example in spintronics. Consequently, they have become the subject of intense current research, and new candidate altermagnetic materials are continuously being proposed. The central question addressed in this part of the dissertation is, using nonlinear spin-wave theory, whether the collective magnetic excitations, namely magnons, are stable at zero temperature or undergo spontaneous decay driven exclusively by quantum-mechanical effects. The dissipative YSYK model belongs to the class of SYK models, which describe strongly coupled chaotic systems with Gaussian-distributed interactions. In the limit of an infinite number of particles, these models can be solved exactly at the level of the self-energy. They do not possess quasiparticles, exhibit a non-Fermi-liquid (NFL) phase associated with strange-metal behavior and high-temperature superconductivity, and display several additional remarkable properties that have also attracted considerable interest in gravitational physics. The primary objective of this part of the dissertation is to explain the self-tuning criticality of the NFL phase in the dissipative YSYK model. Although this phenomenon had previously been found by solving the exact Dyson–Schwinger equations (DSEs) in the infinite-particle limit, its origin has remained unexplained. To this end, we develop a functional renormalization group (FRG) approach for the dissipative YSYK model. Although the influence of lattice vibrations on electronic systems has been investigated for decades using well-established many-body and kinetic-theory methods, the behavior of strongly coupled electron–phonon systems remains incompletely understood. To address this problem, we study the microscopic Holstein model with dispersionless Einstein phonons at zero temperature. By combining the Dyson–Schwinger equations of the Holstein model with the exact FRG flow equations formulated within the chemical-potential cutoff scheme, we derive a Ward identity relating the electronic compressibility to the renormalized phonon frequency. This identity implies that the compressibility diverges when the renormalized phonon frequency vanishes, leading to a Pomeranchuk instability in the density channel with zero angular momentum. Using the nonperturbative FRG, we investigate the presence of this instability and propose a phase diagram of the Holstein model in arbitrary dimensions.