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H. -J. Schmidt

Publications and source records attributed to H. -J. Schmidt.

At least 19 recordsLinked to original sources
arXiv2021

Observation of phase synchronization and alignment during free induction decay of quantum spins with Heisenberg interactions

Equilibration of observables in closed quantum systems that are described by a unitary time evolution is a meanwhile well-established phenomenon apart from a few equally well-established exceptions. Here we report the surprising theoretical observation that integrable as well as non-integrable spin rings with nearest-neighbor or long-range isotropic Heisenberg interaction not only equilibrate but moreover also synchronize the directions of the expectation values of the individual spins. We highlight that this differs from spontaneous synchronization in quantum dissipative systems. Here, we observe mutual synchronization of local spin directions in closed systems under unitary time evolution. Contrary to dissipative systems, this synchronization is independent of whether the interaction is ferro- or antiferromagnetic. In our numerical simulations, we investigate the free induction decay (FID) of an ensemble of up to $N = 25$ quantum spins with $s = 1/2$ each by solving the time-dependent Schrödinger equation numerically exactly. Our findings are related to, but not fully explained by conservation laws of the system. The synchronization is very robust against for instance random fluctuations of the Heisenberg couplings and inhomogeneous magnetic fields. Synchronization is not observed with strong enough symmetry-breaking interactions such as the dipolar interaction. We also compare our results to closed-system classical spin dynamics which does not exhibit phase synchronization due to the lack of entanglement. For classical spin systems the fixed magnitude of individual spins effectively acts like additional $N$ conservation laws.

cond-mat.str-el↗
arXiv2021

Accuracy of the typicality approach using Chebyshev polynomials

Trace estimators allow to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures that can be traced back to an improper behavior of the approximated density of states with and without smoothing kernel. Applications to archetypical quantum spin systems are discussed as examples.

cond-mat.str-el↗
arXiv2020

Supersymmetric spin-phonon coupling prevents odd integer spins from quantum tunneling

Quantum tunneling of the magnetization is a phenomenon that impedes the use of small anisotropic spin systems for storage purposes even at the lowest temperatures. Phonons, usually considered for temperature dependent relaxation of magnetization over the anisotropy barrier, also contribute to magnetization tunneling for integer spin quantum numbers. Here we demonstrate that certain spin-phonon Hamiltonians are unexpectedly robust against the opening of a tunneling gap, even for strong spin-phonon coupling. The key to understanding this phenomenon is provided by an underlying supersymmetry that involves both spin and phonon degrees of freedom.

cond-mat.str-el↗
arXiv2016

Spin waves in rings of classical magnetic dipoles

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system's ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with $N\longrightarrow \infty$ is investigated and completely solved.

cond-mat.other↗
arXiv2014

Motion of a thin spherically symmetric Shell of Dust in the Schwarzschild field

The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general equation of motion and solve it in closed form for the case of parabolic motion. Especially the motion near the horizon and near the singularity are examined.

gr-qc↗
arXiv2014

Magnetic susceptibility of frustrated spin-s J1-J2 quantum Heisenberg magnets: High-temperature expansion and exact diagonalization data

Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J1 and next nearest-neighbor exchange coupling J2 we investigate the magnetic susceptibility of two-dimensional J1-J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and high-temperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on the ratio J2/J1 by comparing with susceptibility measurements on corresponding magnetic compounds.

cond-mat.str-el↗
arXiv2013

Isotropic universe with almost scale-invariant fourth-order gravity

We study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we discuss is the case of a very small negative value of the parameter b in the Lagrangian L = R^2 + b G ln G which leads to the replacement of the exact de Sitter solution from L = R^2 (being a local attractor) to a power-law inflation exact solution also representing a local attractor. This shows how one can modify the dynamics from de Sitter to power-law inflation by the addition of the G ln G-term.

gr-qc↗
arXiv2013

Exact radial solution in 2+1 gravity with a real scalar field

In this paper we give some general considerations about circularly symmetric, static space-times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of 2+1 dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to 2+1 dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions.

gr-qc↗
arXiv2011

Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole

We deduce a new formula for the perihelion advance of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole.

gr-qc↗
arXiv2011

Gauss-Bonnet lagrangian G ln G and cosmological exact solutions

For the lagrangian L = G ln G where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedman models using a statefinder parametrization. Further we show, that among all lagrangians F(G) this L is the only one not having the form G^r with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R)-theories in 2-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n=4.

gr-qc↗
arXiv2008

Perihelion precession for modified Newtonian gravity

We calculate the perihelion precession delta for nearly circular orbits in a central potential V(r). Differently from other approaches to this problem, we do not assume that the potential is close to the Newtonian one. The main idea in the deduction is to apply the underlying symmetries of the system to show that delta must be a function of r V''(r)/V'(r), and to use the transformation behaviour of delta in a rotating system of reference. This is equivalent to say, that the effective potential can be written in a one-parameter set of possibilities as sum of centrifugal potential and potential of the central force. We get a universal formula for delta. It has to be read as follows: a circular orbit at this value r exists and is stable if and only if this delta is a well-defined real; and if this is the case, then the angular difference from one perihelion to the next one for nearly circular orbits at this r is exactly 2 pi + delta. Then we show how to apply this result to examples of recent interest like modified Newtonian gravity and linearized fourth-order gravity. In the second part of the paper, we generalize this universal formula to static spherically symmetric space-times. For the Schwarzschild black hole with mass parameter m > 0 it leads to a surprisingly unknown formula. It represents a strict result and is applicable for all values r > 6m and is in good agreement with the fact that stable circular orbits exist for r > 6m only.

gr-qc↗
arXiv2007

Optimized implementation of the Lanczos method for magnetic systems

Numerically exact investigations of interacting spin systems provide a major tool for an understanding of their magnetic properties. For medium size systems the approximate Lanczos diagonalization is the most common method. In this article we suggest two improvements: efficient basis coding in subspaces and simple restructuring for openMP parallelization.

cond-mat.str-el↗
arXiv2006

Exact eigenstates of highly frustrated spin lattices probed in high fields

Strongly frustrated antiferromagnets such as the magnetic molecule {Mo72Fe30}, the kagome, or the pyrochlore lattice exhibit a variety of fascinating properties like low-lying singlets, magnetization plateaus as well as magnetization jumps. During recent years exact many-body eigenstates could be constructed for several of these spin systems. These states become ground states in high magnetic fields, and they also lead to exotic behavior. A key concept to an understanding of these properties is provided by independent localized magnons. The energy eigenvalue of these n-magnon states scales linearly with the number n of independent magnons and thus with the total magnetic quantum number M=Ns-n. In an applied field this results in a giant magnetization jump which constitutes a new macroscopic quantum effect. It will be demonstrated that this behavior is accompanied by a massive degeneracy, an extensive (T=0)-entropy, and thus a large magnetocaloric effect at the saturation field. The connection to flat band ferromagnetism will be outlined.

cond-mat.str-el↗
arXiv2006

Fourth order gravity: equations, history, and applications to cosmology

The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented.

gr-qc↗
arXiv2005

Einsteins Arbeiten in Bezug auf die moderne Kosmologie

We comment on the paper [1] by Albert Einstein from 1918 to Willem De Sitter's solution [2] of the Einstein field equation from today's point of view. To this end, we start by describing the geometry of the De Sitter space-time and present its importance for the inflationary cosmological model.

gr-qc↗
arXiv2004

Schwarzschild and Synge once again

We complete the historical overview about the geometry of a Schwarzschild black hole at its horizon by emphasizing the contribution made by J. L. Synge in 1950 to its clarification.

gr-qc↗