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Articles by Roderich Moessner
Condensed Matter > Strongly Correlated Electrons
Landau Fermi-liquid theory characterizes interacting metals through quasiparticles and their residual interactions. It is a challenge to incorporate non-trivial quantum geometry -- as encoded by Berry phases and the quantum metric -- as a fundamental ingredient. We formulate a Berry-Landau Fermi-liquid theory for spinless fermions within an isolated band crossing the Fermi surface and derive the Landau functional through the Nozières--Luttinger construction.
Πώς τα σμήνη πουλιών «αψηφούν» έναν από τους θεμελιώδεις νόμους της Φυσικής
Τα σμήνη των πουλιών, οι αποικίες των βακτηρίων, ακόμη και τα ανθρώπινα πλήθη κινούνται σύμφωνα με κανόνες αλληλεπίδρασης που φαίνεται να παραβιάζουν μια από τις πιο θεμελιώδεις αρχές της φυσικής: τον νόμο του Νεύτωνα για τη δράση και την αντίδραση. Τα πουλιά μπορούν να δουν ένα μεγάλο μέρος του τι συμβαίνει γύρω τους, αλλά όταν πετούν σε σμήνος, ανταποκρίνονται μόνο στα πουλιά που βρίσκονται δίπλα ή μπροστά τους. Δεν προσαρμόζουν την κίνησή τους με βάση τα πουλιά που ακολουθούν από πίσω.
Hamiltonian description of non-reciprocal interactions
Abstract In many systems, including sedimenting particles and bird flocks, interactions do not derive from a potential and are generally non-reciprocal, meaning that they do not obey the action–reaction principle. As a result, one cannot define a conventional energy function or use analytical and numerical tools that rely on it. Here we address this limitation by constructing a Hamiltonian with auxiliary degrees of freedom that, under a constraint, generates the original non-reciprocal dynamics.
Research Portal of the TU Dresden
Antiferromagnetic Ising models on frustrated lattices can realize classical spin liquids, with highly degenerate ground states and, possibly, fractionalized excitations and emergent gauge fields. Motivated by the recent interest in many-body systems in negatively curved space, we study hyperbolic frustrated Ising models. Specifically, we consider nearest-neighbor Ising models on tesselations with odd-length loops in two-dimensional hyperbolic space.
Density-and-phase domain walls in a condensate with dynamical gauge potential
It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties.
Monopole magnetohydrodynamics on a plane: Magnetosonic waves and dynamo instability
Condensed matter systems can host emergent "vacua"with particles, fields, and dimension different from that of the universe we inhabit. Motivated by the appearance of emergent gauge fields with both electric and magnetic charges, we consider the fate of electromagnetism in two dimensions in the presence of magnetic monopoles. We find that generically electromagnetic fields are damped due to resistive effects. However, we can still identify a magnetohydrodynamic regime.
Monopole magnetohydrodynamics on a plane: Magnetosonic waves and dynamo instability
Condensed matter systems can host emergent “vacua” with particles, fields, and dimension different from that of the universe we inhabit. Motivated by the appearance of emergent gauge fields with both electric and magnetic charges, we consider the fate of electromagnetism in two dimensions in the presence of magnetic monopoles. We find that generically electromagnetic fields are damped due to resistive effects. However, we can still identify a magnetohydrodynamic regime.
Irrational Moments and Signatures of Higher-Rank Gauge Theories in Diluted Classical Spin Liquids
Classical spin liquids (CSLs) have proved to be a fruitful setting for the emergence of exotic gauge theories. Vacancy clusters in CSLs can introduce gauge charges into the system, and the resulting behavior in turn reveals the nature of the underlying theory. We study these effects for a series of CSLs on the honeycomb lattice. We find that dilution leads to the emergence of effective free spins with tuneable, and generally irrational, size.
Classification of classical spin liquids: Typology and resulting landscape
Classical spin liquids (CSL) lack long-range magnetic order and are characterized by an extensive ground-state degeneracy. We propose a classification scheme of CSLs based on the structure of the flat bands of their Hamiltonians. Depending on absence or presence of the gap from the flat band, the CSL are classified as algebraic or fragile topological, respectively.
Adaptive Trotterization for Time-Dependent Hamiltonian Quantum Dynamics Using Piecewise Conservation Laws
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical trade-off between improved accuracy for finer time steps, and increased error rate on account of the larger circuit depth.
Ising fracton spin liquid on the honeycomb lattice
We study a classical Ising model on the honeycomb lattice with local two-body interactions and present strong evidence that at low temperature it realizes a higher-rank Coulomb liquid with fracton excitations. We show that the excitations are (type-I) fractons, appearing at the corners of membranes of spin flips.
Classification of classical spin liquids: Detailed formalism and suite of examples
The hallmark of highly frustrated systems is the presence of many states close in energy to the ground state. Fluctuations between these states can preclude the emergence of any form of order and lead to the appearance of spin liquids. Even on the classical level, spin liquids are not all alike: they may have algebraic or exponential correlation decay, and various forms of long wavelength description, including vector or tensor gauge theories.
Exploiting polarization dependence in two-dimensional coherent spectroscopy: Examples of ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Nd}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$
Two-dimensional coherent spectroscopy (2DCS) probes the nonlinear optical response of correlated systems. An interesting application is the study of fractionalized excitations, which are challenging to distinguish unambiguously in linear response.
Prethermalization in aperiodically kicked many-body dynamics
Driven many-body systems typically experience heating due to the lack of energy conservation. Heating may be suppressed for time-periodic drives, but little is known for less regular drive protocols. In this paper, we investigate the heating dynamics in aperiodically kicked systems, specifically those driven by quasiperiodic Thue-Morse or a family of random sequences with n-multipolar temporal correlations.
Thermodynamics and fractal dynamics of a nematic spin ice: A doubly frustrated pyrochlore Ising magnet
The Ising antiferromagnets on the triangular and on the pyrochlore lattices are two of the most iconic examples of magnetic frustration, paradigmatically illustrating many exotic properties such as emergent gauge fields, fractionalization, and topological order. In this paper, we show that the two instances of frustration can, remarkably, be combined in a single system, where they coexist without inducing conventional long-range ordering.
Hybrid dyons, inverted Lorentz force, and magnetic Nernst effect in quantum spin ice
Topological magnets host two sets of gauge fields: that of native Maxwell electromagnetism, owing to the magnetic dipole moment of its constituent microscopic moments, and that of the emergent gauge theory describing the topological phase. Here, we show that in quantum spin ice, the emergent magnetic charges of the latter carry native electric charge of the former.
Dynamical signatures of symmetry-broken and liquid phases in an $S$ = $\frac{1}{2}$ Heisenberg antiferromagnet on the triangular lattice
We present the dynamical spin structure factor of the antiferromagnetic spin-12 J1−J2 Heisenberg model on a triangular lattice obtained from large-scale matrix-product state simulations. The high frustration due to the combination of antiferromagnetic nearest- and next-nearest-neighbor interactions yields a rich phase diagram. We resolve the low-energy excitations both in the 120∘ ordered phase and in the putative spin-liquid phase at J2/J1=0.125.
Spectral Response of Disorder-Free Localized Lattice Gauge Theories
We show that certain lattice gauge theories exhibiting disorder-free localization have a characteristic response in spatially averaged spectral functions: a few sharp peaks combined with vanishing response in the zero frequency limit. This reflects the discrete spectra of small clusters of kinetically active regions formed in such gauge theories when they fragment into spatially finite clusters in the localized phase due to the presence of static charges.
Spurious Symmetry Enhancement in Linear Spin Wave Theory and Interaction-Induced Topology in Magnons
Linear spin wave theory (LSWT) is the standard technique to compute the spectra of magnetic excitations in quantum materials. In this Letter, we show that LSWT, even under ordinary circumstances, may fail to implement the symmetries of the underlying ordered magnetic Hamiltonian leading to spurious degeneracies. In common with pseudo-Goldstone modes in cases of quantum order by disorder these degeneracies tend to be lifted by magnon-magnon interactions.
Prethermalization in periodically driven nonreciprocal many-body spin systems
We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the dynamics of the system cannot be derived from any time-dependent Hamiltonian. In the high-frequency limit, we find that the magnetization dynamics features a long-lived metastable plateau, whose duration is controlled by the fourth power of the drive frequency.
Time-reversal invariant finite-size topology
We report finite-size topology in the quintessential time-reversal (TR) invariant systems, the quantum spin Hall insulator (QSHI) and the three-dimensional, strong topological insulator (STI)—previously-identified helical or Dirac cone boundary states of these phases hybridize in wire or slab geometries with one open boundary condition for finite system size, and additional, topologically protected, lower-dimensional boundary modes appear for open boundary conditions in two or more directions...
Subdiffusive spin transport in disordered classical Heisenberg chains
We study the transport and equilibration properties of a classical Heisenberg chain, whose couplings are random variables drawn from a one-parameter family of power-law distributions. The absence of a scale in the couplings makes the system deviate substantially from the usual paradigm of diffusive spin hydrodynamics and exhibit a regime of subdiffusive transport with an exponent changing continuously with the parameter of the distribution.
Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
We analyze the near-adiabatic dynamics in a ramp through the critical point (CP) of the classical transverse field Ising chain. This is motivated, conceptually, by the fact that this CP—unlike its quantum counterpart—experiences no thermal or quantum fluctuations, and technically by the tractability of its effective model.
Mobility edges through inverted quantum many-body scarring
Abstract We show that the rainbow state, which has volume-law entanglement entropy for most choices of bipartitions, can be embedded in a many-body localized spectrum. For a broad range of disorder strengths in the resulting model, we numerically find a narrow window of highly entangled states in the spectrum, embedded in a sea of area law entangled states. The construction hence embeds mobility edges in many-body localized systems.
Magnon scattering off quantum Hall skyrmion crystals probes interplay of topology and symmetry breaking
We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets, which act as the source of magnons. Thanks to recent experimental advances, such a set-up can be realised in quantum Hall heterojunctions, and it is interesting as skyrmions are topological objects while the skyrmion crystals break internal and translational symmetries, thus allowing to study the interplay of topological and symmetry breaking physics.
Abundance of Hard-Hexagon Crystals in the Quantum Pyrochlore Antiferromagnet
We propose a simple family of valence-bond crystals as potential ground states of the S=1/2 and S=1 Heisenberg antiferromagnet on the pyrochlore lattice. Exponentially numerous in the linear size of the system, these can be visualized as hard-hexagon coverings, with each hexagon representing a resonating valence-bond ring. This ensemble spontaneously breaks rotation, inversion, and translation symmetries.
Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid
Abstract We study the phase diagram of a bilayer quantum spin liquid model with Kitaev-type interactions on a square lattice. We show that the low energy limit is described by a π-flux Hubbard model with an enhanced SO(4) symmetry. The antiferromagnetic Mott transition of the Hubbard model signals a magnetic fragmentation transition for the spin and orbital degrees of freedom of the bilayer.
Identifying and Constructing Complex Magnon Band Topology
Abstract Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials.
Arresting dynamics in hardcore spin models
Abstract We study the dynamics of hardcore spin models on the square and triangular lattice, constructed by analogy to hard spheres, where the translational degrees of freedom of the spheres are replaced by orientational degrees of freedom of spins on a lattice and the packing fraction as a control parameter is replaced by an exclusion angle. In equilibrium, models on both lattices exhibit a Kosterlitz-Thouless transition at an exclusion angle ΔKT.
From Dual Unitarity to Generic Quantum Operator Spreading
Abstract Dual-unitary circuits are paradigmatic examples of exactly solvable yet chaotic quantum many-body systems, but solvability naturally goes along with a degree of nongeneric behavior. By investigating the effect of weakly broken dual unitarity on the spreading of local operators, we study whether, and how, small deviations from dual unitarity recover fully generic many-body dynamics.
Intermediate-scale theory for electrons coupled to frustrated local moments
Abstract A classic route for destroying long-lived electronic quasiparticles in a weakly interacting Fermi liquid is to couple them to other low-energy degrees of freedom that effectively act as a bath. We consider here the problem of electrons scattering off the spin fluctuations of a geometrically frustrated antiferromagnet, whose nonlinear Landau-Lifshitz dynamics, which remains nontrivial at all temperatures, we model in detail.
Order by disorder in classical kagome antiferromagnets with chiral interactions
Abstract The Heisenberg antiferromagnet on the kagome lattice is an archetypal instance of how large ground-state degeneracies arise, and how they may get resolved by thermal and quantum fluctuations. Augmenting the Heisenberg model by chiral spin interactions has proved to be of particular interest in the discovery of certain chiral quantum spin liquids.
Avoided quasiparticle decay from strong quantum interactions
Abstract Quantum states of matter—such as solids, magnets and topological phases—typically exhibit collective excitations (for example, phonons, magnons and anyons)1. These involve the motion of many particles in the system, yet, remarkably, act like a single emergent entity—a quasiparticle.
Quantum oscillations in nodal line systems
We study signatures of magnetic quantum oscillations in three-dimensional nodal line semimetals at zero temperature. The extended nature of the degenerate bands can result in a Fermi surface geometry with topological genus one, as well as a Fermi surface of electron and hole pockets encapsulating the nodal line.
Phase Structure of Driven Quantum Systems
Abstract Clean and interacting periodically driven systems are believed to exhibit a single, trivial “infinite-temperature” Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions.
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