arXiv subjects

Robert Peters

Publications and source records attributed to Robert Peters.

At least 19 recordsLinked to original sources

arXiv2026

Correlation-Driven Nonlinear Magnetoelectric Response in an Altermagnet: A Dynamical Mean-Field Study

We investigate the optical nonlinear magnetoelectric effect (NMEE) in a strongly correlated altermagnet using dynamical mean-field theory. Unlike effective band descriptions with an imposed spin splitting, our approach determines the altermagnetic order, electronic spectrum, and optical nonlinear response self-consistently. We find that the NMEE is finite in the altermagnetic phase and vanishes in the paramagnetic phase. Its frequency dependence reflects the spin-resolved spectral structure and provides an estimate of the characteristic altermagnetic spin-splitting scale. Interaction and temperature tuning produce qualitatively different behavior: at low temperature, reducing the interaction strength toward the interaction-driven magnetic phase boundary enhances the response, whereas increasing the temperature suppresses it and drives it to zero above the critical temperature. These results establish the optical NMEE as a probe of correlated altermagnetic order and suggest that tuning parameters such as pressure, strain, or chemical substitution toward an interaction-driven phase boundary may provide a promising route to maximizing the response.

cond-mat.str-el↗

arXiv2026

The toric code under antiferromagnetic isotropic Heisenberg interactions

We investigate the impact of an isotropic antiferromagnetic Heisenberg perturbation on the toric code, focusing on the resulting quantum phase transition and the nature of the phase that emerges beyond topological order. Using neural-network quantum states (NQS), we compute ground states over a wide range of Heisenberg couplings while fully respecting the exact symmetries of the model. In the weak-coupling regime, the numerical results are in excellent agreement with an effective low-energy description derived from a Schrieffer-Wolff (SW) transformation, providing analytic control over the perturbative breakdown of topological order. We show that the Heisenberg perturbation only renormalizes local operators at low orders, whereas mixing between topological sectors occurs only at a perturbative order proportional to the system size. At intermediate values of the Heisenberg interaction, the topological phase breaks down. We estimate the critical point through a combination of the fidelity susceptibility and the logarithmic susceptibility of non-contractible Wilson loops for various system sizes. Furthermore, we utilize the topological entanglement entropy to provide a comprehensive characterization of the phase transition. Beyond the transition, an antiferromagnetic $\pm X/\pm Z$ N\'eel phase emerges, characterized by a fourfold-degenerate symmetry-broken manifold, which is explicitly probed using staggered-magnetization-based diagnostics. Our results show how local two-spin interactions, which naturally arise in realistic implementations of the toric code, drive the breakdown of topological order. Moreover, we establish the SW approach as a systematic framework for analyzing such perturbations in combination with variational many-body methods.

cond-mat.str-el↗

arXiv2025

Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems

The non-Hermitian skin effect (NHSE), characterized by the extensive localization of bulk modes at the boundaries, has attracted significant attention as a hallmark feature of non-Hermitian topology. This localization invalidates the conventional Bloch band theory, necessitating an analysis under open boundary conditions even in the thermodynamic limit. The Amoeba formulation addresses this challenge by computing the spectral potential rather than the spectrum itself. Based on the (strong) Szeg\"o limit theorem and its topological generalization, this approach reduces the evaluation of the potential to an optimization problem involving the Ronkin function. However, while the generalized Szeg\"o limit theorem is formally applicable in arbitrary dimensions, its implementation is limited to single-band systems, and its applicability to multiband systems remains unclear even in one-dimensional systems. In this paper, we establish the Wiener-Hopf factorization (WHF) of the non-Bloch Hamiltonian as a powerful framework, providing a unified and rigorous foundation for Amoeba analysis in one-dimensional multiband systems. By combining the WHF with Hermitian doubling, we first elucidate the applicability criteria for the generalized Szeg\"o limit theorem in multiband systems. We then show that the WHF provides the natural mathematical origin for the symmetry-decomposed Ronkin function in symmetry class AII$^\dagger$, leading to a rigorous proof of the generalized Szeg\"o limit theorem for these systems and opening a path toward systematic generalizations to other symmetry classes.

cond-mat.mes-hall↗

arXiv2025

Thermodynamic formulation of the spin magnetic octupole moment in bulk crystals

The discovery of unconventional antiferromagnets, such as altermagnets, has drawn significant attention to higher-rank magnetic multipoles, particularly magnetic octupoles. Despite the advances in research, attempts to understand their microscopic properties remain limited due to the unbounded nature of the position operator in bulk crystals. In this paper, we address this problem by using a well-known thermodynamic approach and derive a formula for the spin magnetic octupole moment (SMOM) that can be used in bulk crystals. The resulting formula is gauge invariant and satisfies St\v{r}eda formulas that relate the SMOM to the spin magnetoelectric dipole-quadrupole susceptibilities. Furthermore, we apply this formula to several models and examine the fundamental properties of the SMOM. For example, in $d$-wave altermagnets, the nonrelativistic component of the SMOM, which is independent of spin-orbit coupling, is larger than the relativistic component, which is induced by spin-orbit coupling. These nonrelativistic SMOMs have the same microscopic origin as the nonrelativistic spin splitting that characterizes $d$-wave altermagnetism. Moreover, they exhibit a N\'{e}el vector dependence consistent with Landau theory for $d$-wave altermagnetism [Phys. Rev. Lett. $\textbf{132}$, 176702 (2024)].

cond-mat.mtrl-sci↗

arXiv2025

Symplectic-Amoeba formulation of the non-Bloch band theory for one-dimensional two-band systems

The non-Hermitian skin effect is a topological phenomenon, resulting in the condensation of bulk modes near the boundaries. Due to the localization of bulk modes at the edges, boundary effects remain significant even in the thermodynamic limit. This makes conventional Bloch band theory inapplicable and hinders the accurate computation of the spectrum. The Amoeba formulation addresses this problem by determining the potential from which the spectrum can be derived using the generalized Szeg\"o's limit theorem, reducing the problem to an optimization of the Ronkin function. While this theory provides novel insights into non-Hermitian physics, challenges arise from the multiband nature and symmetry-protected degeneracies, even in one-dimensional cases. In this work, we investigate one-dimensional two-band class AII$^\dagger$ systems, where Kramers pairs invalidate the conventional Amoeba formalism. We find that these challenges can be overcome by optimizing the band-resolved Ronkin functions, which is achieved by extrapolating the total Ronkin function. Finally, we propose a generalized Szeg\"o's limit theorem for class AII$^\dagger$ and numerically demonstrate that our approach correctly computes the potential and localization length.

cond-mat.mes-hall↗

arXiv2024

Thermodynamic relations for the Cooper pair's momentum in helical superconductors

Two thermodynamic relations are proposed for the exact measurement of the center-of-mass (COM) momentum of the Cooper pairs in helical superconductors. The first relation concerns the constraint on the change in the COM momentum in response to the variation in the magnetic field, which is linked to the superconducting Edelstein effect. The second relation is related to a first-order phase transition, showing that the jump of the COM momentum can be measured from the slope of the transition line on the phase diagram, where the supercurrent is used as a control parameter. These relations solve the difficulty of detecting the momentum, enabling broader and more precise exploration of noncentrosymmetric superconductors.

cond-mat.supr-con↗

arXiv2024

Nonlinear Magnetoelectric Effect under Magnetic Octupole Order: Its Application to a $d$-Wave Altermagnet and a Pyrochlore Lattice with All-In/All-Out Magnetic Order

Extensive investigation has recently been conducted into a new class of antiferromagnetic order known as magnetic octupole order. However, the high rank of octupoles makes it difficult to detect and manipulate them by using conventional methods such as the anomalous Hall effect. In this paper, we propose the nonlinear magnetoelectric effect (NMEE), a second-order response to an electric field that induces a spontaneous magnetization, as a finite response under magnetic octupole order. First, we classify the magnetic point groups to identify antiferromagnets with such order, and derive the NMEE tensor using quantum kinetic theory. Then, we confirm the effectiveness of the NMEE through model calculations for two specific examples: a $d$-wave altermagnet and a pyrochlore lattice with all-in/all-out magnetic order. In particular, the intrinsic NMEE exhibits a large response in a magnetic Weyl semimetal phase of the pyrochlore lattice. This enhanced response is explained by the fact that the response tensor involves the quantum metric, which is enhanced near Weyl points. Furthermore, our results show that the NMEE has a sizeable value that can be detected by the magneto-optical Kerr effect.

cond-mat.mtrl-sci↗

arXiv2024

Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system

Non-Hermitian systems exhibit novel phenomena without Hermitian counterparts, such as exceptional points and the non-Hermitian skin effect. These non-Hermitian topological phenomena are observable in single-particle excitations of correlated systems in equilibrium, which are described by Green's functions. In this paper, we demonstrate the appearance of the hinge non-Hermitian skin effect in the effective Hamiltonian that describes the single-particle properties of an $f$-electron system. Skin effects result in a strong sensitivity to boundary conditions, and a large number of eigenstates localize at one boundary when open boundary conditions are applied. Our system exhibits such sensitivity and hosts skin modes localized around hinges. This hinge skin effect is induced by a non-Hermitian topology of the surface Brillouin zone. The hinge skin modes are observed for one-dimensional subsystems located between one pair of exceptional points in the surface Brillouin zone. This paper highlights that correlated materials are an exciting platform for analyzing non-Hermitian phenomena.

cond-mat.str-el↗

arXiv2024

Nonlinear Edelstein Effect in Strongly Correlated Electron Systems

Nonlinear spintronics, which combines nonlinear dynamics and spintronics, opens a new route for controlling spins and spin dynamics beyond conventional spintronics based on linear responses. Strongly correlated electron systems, which can have large nonlinear responses, are promising candidates for nonlinear spintronics. In this paper, we focus on the nonlinear Edelstein effect (NEE), a generalization of the Edelstein effect, and study the impact of electron correlations on the NEE by performing numerical calculations on a Hubbard model. We find that correlation effects can either enhance or suppress the nonlinear response. We show that the enhancement and suppression of the response are due to the real and imaginary components of the self-energy, respectively. Additionally, we have explored the relationship between the NEE and photomagnetic or optomagnetic effects. Our findings demonstrate that electron correlations can either enhance or suppress the optical spin injection, depending on the light frequency, while always strengthening the inverse Faraday effect.

cond-mat.str-el↗

arXiv2024

Quantum skyrmion dynamics studied by neural network quantum states

We study the dynamics of quantum skyrmions under a magnetic field gradient using neural network quantum states. First, we obtain a quantum skyrmion lattice ground state using variational Monte Carlo with a restricted Boltzmann machine as the variational ansatz for a quantum Heisenberg model with Dzyaloshinskii-Moriya interaction. Then, using the time-dependent variational principle, we study the real-time evolution of quantum skyrmions after a Hamiltonian quench with an inhomogeneous external magnetic field. We show that field gradients are an effective way of manipulating and moving quantum skyrmions. Furthermore, we demonstrate that quantum skyrmions can decay when interacting with each other. This work shows that neural network quantum states offer a promising way of studying the real-time evolution of quantum magnetic systems that are outside the realm of exact diagonalization.

cond-mat.dis-nn↗

arXiv2024

Orbital optical activity in noncentrosymmetric metals and superconductors

We present the optical activity induced by the orbital magnetic moment in metals and superconductors using Green's function formalization. We show that an apparent singularity of the optical activity vanishes in the normal state; however, it remains finite in the superconducting state and is related to the superconducting Edelstein effect, ensuring the missing area measurement. Finally, we calculate the optical activity in a model Hamiltonian mimicking doped transition metal dichalcogenides to investigate its characteristic spectrum, and we analyze the Kerr effect to discuss a possibility to observe the optical activity in experiments.

cond-mat.mtrl-sci↗

arXiv2023

Two-particle correlation effects on nonlinear optical responses in the 1d interacting Rice-Mele model

Nonlinear responses in crystalline solids are attracting a great deal of attention because of exciting phenomena, such as the bulk photovoltaic effect in noncentrosymmetric crystals and the third harmonic generation related to Higgs modes in superconductors, and their potential applicability to electronic devices. Recently, nonlinear responses have also been studied in strongly correlated electron systems. Experimental evidence has revealed that correlations play a significant role in nonlinear responses. However, most theoretical calculations only consider excitonic effects or involve numerically demanding approaches, making interpreting the results challenging. In this paper, we adopt another approach, which is based on real-time evolution using the correlation expansion method. Particularly, we focus on the 1d interacting Rice-Mele model. We analyze the impact of the density-density interaction on the linear and nonlinear conductivities and demonstrate that two-particle correlations beyond the mean-field level enhance second-order nonlinear responses, especially the second harmonic generation, while the linear response is not strongly affected. Furthermore, by decomposing the current into a one-particle contribution and six two-particle contributions, we show that the ``biexciton transition" term and its nonlinear oscillations is the most dominant two-particle contribution to the nonlinear response. In addition, we also show that the intercell charge-charge correlation is strongly enhanced when the system is driven with the frequency corresponding to the excitonic peak and can even exceed the intracell correlation. This implies the possibility of manipulating two-particle correlations with external fields.

cond-mat.str-el↗

arXiv2023

Unique properties of the optical activity in noncentrosymmetric superconductors: sum rule, missing area, and relation with the superconducting Edelstein effect

We present general properties of the optical activity in noncentrosymmetric materials, including superconductors. We derive a sum rule of the optical activity in general electric states and show that the summation of the spectrum is zero, which is independent of the details of electric states. The optical activity has a $\delta$-function singularity that vanishes in normal phases. However, the singularity emerges in superconducting phases, corresponding to the Meissner effect in the optical conductivity. The spectrum decreases by the superconducting gap and has a missing area compared to the normal phase. This area is exactly equivalent to the coefficient of the $\delta$-function singularity due to the universal sum rule. Furthermore, the coefficient is exactly equivalent to the superconducting Edelstein effect, which has not yet been observed in experiments. Thus, this measurement of the missing area offers an alternative way to observe the superconducting Edelstein effect.

cond-mat.mtrl-sci↗

arXiv2023

Unconventional gap dependence of high harmonic generation in the extremely strong light-matter coupling regime

High harmonic generation(HHG) is one of the most commonly studied nonlinear optical phenomena, originating in the ultrafast dynamics of electrons in atomic gasses and semiconductors. It has attracted much attention because of its non-perturbative nature and potential for future attosecond laser pulse sources. On the theory side, a semi-classical picture based on tunneling ionization of electrons is successfully used in explaining key characteristics of the HHG. This model assumes that electric fields non-perturbatively excite electrons beyond the ionization potential or band gap. Thus, intuitively, a larger gap should lead to an exponentially smaller HHG emission. Despite this intuition, the HHG in the Mott insulator Ca2RuO4 has shown an unconventional exponential increase with respect to the gap width. This experiment implies effects beyond the semi-classical theory. However, most theoretical works have focused on the dependence of the HHG on external control parameters, and the gap dependence of the HHG is poorly understood even in non interacting systems. Thus, it is essential to clarify the gap dependence of the HHG in a fully quantum mechanical approach. Here, we analyze numerically exactly the gap dependence of the HHG in two-level systems. We find an increase in the strength of the HHG when the Rabi frequency is large compared to the gap width. Furthermore, the relaxation and scattering of electrons increase the visibility of this gap dependence. Finally, we find that the enhancement rate follows a universal scaling law regardless of the driving frequency. The existence of this gap dependence in two-level systems suggests that this unconventional gap dependence is a universal behavior that can be found not only in Mott insulators but also in atomic gasses and semiconductors.

physics.optics↗

arXiv2023

Ground State Properties of Quantum Skyrmions described by Neural Network Quantum States

We investigate the ground state properties of quantum skyrmions in a ferromagnet using variational Monte Carlo with the neural network quantum state as variational ansatz. We study the ground states of a two-dimensional quantum Heisenberg model in the presence of the Dzyaloshinskii-Moriya interaction (DMI). We show that the ground state accommodates a quantum skyrmion for a large range of parameters, especially at large DMI. The spins in these quantum skyrmions are weakly entangled, and the entanglement increases with decreasing DMI. We also find that the central spin is completely disentangled from the rest of the lattice, establishing a non-destructive way of detecting this type of skyrmion by local magnetization measurements. While neural networks are well suited to detect weakly entangled skyrmions with large DMI, they struggle to describe skyrmions in the small DMI regime due to nearly degenerate ground states and strong entanglement. In this paper, we propose a method to identify this regime and a technique to alleviate the problem. Finally, we analyze the workings of the neural network and explore its limits by pruning. Our work shows that neural network quantum states can be efficiently used to describe the quantum magnetism of large systems exceeding the size manageable in exact diagonalization by far.

cond-mat.mes-hall↗

arXiv2023

The quantum skyrmion Hall effect in f electron systems

The flow of electric current through a two-dimensional material in a magnetic field gives rise to the family of Hall effects. The quantum versions of these effects accommodate robust electronic edge channels and fractional charges. Recently, the Hall effect of skyrmions, classical magnetic quasiparticles with a quantized topological charge, has been theoretically and experimentally reported, igniting ideas on a quantum version of this effect. To this end, we perform dynamical mean field theory calculations on localized $f$ electrons coupled to itinerant $c$ electrons in the presence of spin-orbit interaction and a magnetic field. Our calculations reveal localized nano quantum skyrmions that start moving transversally when a charge current in the itinerant electrons is applied. The results show the time-transient build-up of the quantum skyrmion Hall effect, accompanied by an Edelstein effect and a magnetoelectric effect that rotate the spins. This work motivates studies about the steady state of the quantum skyrmion Hall effect, looking for eventual quantum skyrmion edge channels and their transport properties.

cond-mat.str-el↗

arXiv2023

$\mathbb{Z}_2$ Non-Hermitian skin effect in equilibrium heavy-fermions

We demonstrate that a correlated equilibrium $f$-electron system with time-reversal symmetry can exhibit a $\mathbb{Z}_2$ non-Hermitian skin effect of quasi-particles. In particular, we analyze a two-dimensional periodic Anderson model with spin-orbit coupling by combining the dynamical mean-field theory (DMFT) and the numerical renormalization group. We prove the existence of the $\mathbb{Z}_2$ skin effect by explicitly calculating the topological invariant and show that spin-orbit interaction is essential to this effect. Our DMFT analysis demonstrates that the $\mathbb{Z}_2$ skin effect of quasi-particles is reflected on the pseudo-spectrum. Furthermore, we analyze temperature effects on this skin effect using the generalized Brillouin zone technique, which clarifies that the skin modes are strongly localized above the Kondo temperature.

cond-mat.str-el↗

arXiv2023

Quantum theory of the Intrinsic Orbital Magnetoelectric Effect in itinerant electron systems at finite temperatures

Magnetization can be induced by an electric field in systems without inversion symmetry $\mathcal{P}$ and time-reversal symmetry $\mathcal{T}$. This phenomenon is called the magnetoelectric (ME) effect. The spin ME effect has been actively studied in multiferroics. The orbital ME effect also exists and has been mainly discussed in topological insulators at zero temperature. In this paper, we study the intrinsic orbital ME response in metals at finite temperature using the Kubo formula. The intrinsic response originates from the Fermi sea and does not depend on the dissipation. Especially in systems with $\mathcal{PT}$-symmetry, the extrinsic orbital ME effect becomes zero, and the intrinsic ME effect is dominant. We apply the response tensor obtained in this work to a $\mathcal{PT}$-symmetric model Hamiltonian with antiferromagnetic loop current order demonstrating that the intrinsic ME effect is enhanced around the Dirac points.

cond-mat.mtrl-sci↗