arXiv subjects

J. Richter

Publications and source records attributed to J. Richter.

At least 19 recordsLinked to original sources

arXiv2024

Nonlinear calcium King plot constrains new bosons and nuclear properties

Nonlinearities in King plots (KP) of isotope shifts (IS) can reveal the existence of beyond-Standard-Model (BSM) interactions that couple electrons and neutrons. However, it is crucial to distinguish higher-order Standard Model (SM) effects from BSM physics. We measure the IS of the transitions ${{}^{3}P_{0}~\rightarrow~{}^{3}P_{1}}$ in $\mathrm{Ca}^{14+}$ and ${{}^{2}S_{1/2} \rightarrow {}^{2}D_{5/2}}$ in $\mathrm{Ca}^{+}$ with sub-Hz precision as well as the nuclear mass ratios with relative uncertainties below $4\times10^{-11}$ for the five stable, even isotopes of calcium (${}^{40,42,44,46,48}\mathrm{Ca}$). Combined, these measurements yield a calcium KP nonlinearity with a significance of $\sim 900 \sigma$. Precision calculations show that the nonlinearity cannot be fully accounted for by the expected largest higher-order SM effect, the second-order mass shift, and identify the little-studied nuclear polarization as the only remaining SM contribution that may be large enough to explain it. Despite the observed nonlinearity, we improve existing KP-based constraints on a hypothetical Yukawa interaction for most of the new boson masses between $10~\mathrm{eV/c^2}$ and $10^7~\mathrm{eV/c^2}$.

physics.atom-ph↗

arXiv2023

Magneto- and barocaloric properties of the ferro-antiferromagnetic sawtooth chain

Materials that are susceptible to pressure and external magnetic fields allow the combined use of both for caloric processes. Here we report investigations of the ferromagnetic-antiferromagnetic sawtooth chain that due to its critical behavior not only allows for both barocaloric as well as magnetocaloric processes but also features very large cooling rates in the vicinity of the quantum critical point.

cond-mat.str-el↗

arXiv2022

Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets

Unconventional features of the magnetization curve at zero temperature such as plateaus or jumps are a hallmark of frustrated spin systems. Very little is known about their behavior at non-zero temperatures. Here we investigate the temperature dependence of the magnetization curve of the kagome lattice antiferromagnet in particular at 1/3 of the saturation magnetization for large lattice sizes of up to N=48 spins. We discuss the phenomenon of asymmetric melting and trace it back to a combined effect of unbalanced magnetization steps on either side of the investigated plateau as well as on the behavior of the density of states across the plateau. We compare our findings to the square-kagome lattice that behaves similarly at low temperatures at zero field, but as we will demonstrate differently at 1/3 of the saturation magnetization. Both systems possess a flat one-magnon band and therefore share with the class of flat-band systems the general property that the plateau that precedes the jump to saturation melts asymmetrically but now with a minimal susceptibility that bends towards lower fields with increasing temperature.

cond-mat.str-el↗

arXiv2022

Ground state selection by magnon interactions in the fcc antiferromagnet

We study the nearest-neighbor Heisenberg antiferromagnet on a face-centered cubic lattice with arbitrary spin S. The model exhibits degenerate classical ground states including two collinear structures AF1 and AF3 described by different propagation vectors that are prime candidates for the quantum ground state. We compute the energy for each of the two states as a function of S using the spin-wave theory that includes magnon-magnon interaction in a self-consistent way and the numerical coupled cluster method. Our results unambiguously demonstrate that quantum fluctuations stabilize the AF1 state for realistic values of spin. Transition to the harmonic spin-wave result, which predicts the AF3 state, takes place only for S > 10. We also study quantum renormalization of the magnon spectra for both states as a function of spin.

cond-mat.str-el↗

arXiv2021

Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem

It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-1/2 Heisenberg diamond and octahedral chains. Besides monomeric particles assigned within the localized-magnon theory to bound one- and two-magnon eigenstates, the effective monomer-dimer lattice-gas model additionally includes dimeric particles assigned to a singlet-tetramer (singlet-hexamer) state as a cornerstone of dimer-tetramer (tetramer-hexamer) ground state of a spin-1/2 Heisenberg diamond (octahedral) chain. A feasibility of the effective description is confirmed through the exact diagonalization and finite-temperature Lanczos methods. Both quantum spin chains display rich ground-state phase diagrams including discontinuous as well as continuous field-driven phase transitions, whereby the specific heat shows in vicinity of the former phase transitions an extraordinary low-temperature peak coming from a highly-degenerate manifold of low-lying excitations.

cond-mat.stat-mech↗

arXiv2021

Anomalous thermodynamics of a quantum spin system with large residual entropy

In contrast to strongly frustrated classical systems, their quantum counterparts typically have a non-degenerate ground state. A counterexample is the celebrated Heisenberg sawtooth spin chain with ferromagnetic zigzag bonds $J_1$ and competing antiferromagnetic basal bonds $J_2$. At a quantum phase transition point $|J_2/J_1|=1/2$, this model exhibits a flat one-magnon excitation band leading to a massively degenerate ground-state manifold which results in a large residual entropy. Thus, for the spin-half model, the residual entropy amounts to exactly one half of its maximum value $\lim_{T\to\infty} S(T)/N = \ln2$. In the present paper we study in detail the role of the spin quantum number $s$ and the magnetic field $H$ in the parameter region around the transition (flat-band) point. For that we use full exact diagonalization up to $N=20$ lattice sites and the finite-temperature Lanczos method up to $N=36$ sites to calculate the density of states as well as the temperature dependence of the specific heat, the entropy and the susceptibility. The study of chain lengths up to $N=36$ allows a careful finite-size analysis. At the flat-band point we find extremely small finite-size effects for spin $s=1/2$, i.e., the numerical data virtually correspond to the thermodynamic limit. In all other cases the finite-size effects are still small and become visible at very low temperatures. In a sizeable parameter region around the flat-band point the former massively degenerate ground-state manifold acts as a large manifold of low-lying excitations leading to extraordinary thermodynamic properties at the transition point as well as in its vicinity such as an additional low-temperature maximum in the specific heat. Moreover, there is a very strong influence of the magnetic field on the low-temperature thermodynamics including an enhanced magnetocaloric effect.

cond-mat.str-el↗

arXiv2020

Magnon crystallization in the kagome lattice antiferromagnet

We present numerical evidence for the crystallization of magnons below the saturation field at non-zero temperatures for the highly frustrated spin-half kagome Heisenberg antiferromagnet. This phenomenon can be traced back to the existence of independent localized magnons or equivalently flat-band multi-magnon states. We present a loop-gas description of these localized magnons and a phase diagram of this transition, thus providing information for which magnetic fields and temperatures magnon crystallization can be observed experimentally. The emergence of a finite-temperature continuous transition to a magnon-crystal is expected to be generic for spin models in dimension $D>1$ where flat-band multi-magnon ground states break translational symmetry.

cond-mat.str-el↗

arXiv2020

Finite-size scaling of typicality-based estimates

According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation, or trace estimator, provides a powerful approach to, e.g., thermodynamic quantities for systems with large Hilbert-space sizes, which usually cannot be treated exactly, analytically or numerically. Here, we discuss the finite-size scaling of the accuracy of such trace estimators from two perspectives. First, we study the full probability distribution of random-vector expectation values and, second, the full temperature dependence of the standard deviation. With the help of numerical examples, we find pronounced Gaussian probability distributions and the expected decrease of the standard deviation with system size, at least above certain system-specific temperatures. Below and in particular for temperatures smaller than the excitation gap, simple rules are not available.

cond-mat.stat-mech↗

arXiv2020

Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates

We study trace estimators for equilibrium thermodynamic observables that rely on the idea of typicality and derivatives thereof such as the finite-temperature Lanczos method (FTLM). As numerical examples quantum spin systems are studied. Our initial aim was to identify pathological examples or circumstances, such as strong frustration or unusual densities of states, where these methods could fail. Instead we failed with the attempt. All investigated systems allow such approximations, only at temperatures of the order of the lowest energy gap the convergence is somewhat slower in the number of random vectors over which observables are averaged.

cond-mat.str-el↗

arXiv2019

The delta-chain with ferro- and antiferromagnetic interactions in applied magnetic field

We study the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions in an external magnetic field which generalizes the field-free case studied previously. This model plays an important role for the recently synthesized compound Fe$_{10}$Gd$_{10}$ which is nearly quantum critical. The classical version of the model is solved exactly and explicit analytical results for the low-temperature thermodynamics are obtained. The spin-$s$ quantum model is studied using exact diagonalization and finite-temperature Lanzos techniques. Particular attention is focused on the magnetization and the susceptibility. The magnetization of the classical model in the ferromagnetic part of the phase diagram defines the universal scaling function which is valid for the quantum model. The dependence of the susceptibility on the spin quantum number $s$ at the critical point between the ferro- and ferrimagnetic phases is studied and the relation to Fe$_{10}$Gd$_{10}$ is discussed.

cond-mat.str-el↗

arXiv2019

Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model

The zero-temperature phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths $J_{1}>0$ and $J_{2} \equiv κJ_{1}>0$, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength $J_{1}^{\perp} \equiv δJ_{1}$. The magnetic order parameter $M$ (viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the Néel or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when $δ< 0$) or antiparallel (when $δ> 0$) to one another. Calculations are performed at $n$th order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked cluster theorem and the Hellmann-Feynman theorem, with $n \leq 10$. The sole approximation made is to extrapolate such sequences of $n$th-order results for $M$ to the exact limit, $n \to \infty$. By thus locating the points where $M$ vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the $κ$--$δ$ half-plane with $κ> 0$. In particular, we provide the accurate estimate, ($κ\approx 0.547,δ\approx -0.45$), for the position of the quantum triple point (QTP) in the region $δ< 0$. We also show that there is no counterpart of such a QTP in the region $δ> 0$, where the two quasiclassical phase boundaries show instead an ``avoided crossing'' behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected.

cond-mat.str-el↗

arXiv2019

Dynamical typicality for initial states with a preset measurement statistics of several commuting observables

We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schrödinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This so-called dynamical typicality property thus corroborates the widespread observation that a few macroscopic features are sufficient to ensure the reproducibility of experimental measurements despite many unknown and uncontrollable microscopic details of the system. We also discuss and exemplify the usefulness of our general analytical result as a powerful numerical tool.

cond-mat.stat-mech↗

arXiv2019

Thermal DMRG for highly frustrated quantum spin chains: a user perspective

Thermal DMRG is investigated with emphasis of employability in molecular magnetism studies. To this end magnetic observables at finite temperature are evaluated for two one-dimensional quantum spin systems: a Heisenberg chain with nearest-neighbor antiferromagnetic interaction and a frustrated sawtooth (delta) chain. It is found that thermal DMRG indeed accurately approximates magnetic observables for the chain as well as for the sawtooth chain, but in the latter case only for sufficiently high temperatures. We speculate that the reason is due to the peculiar structure of the low-energy spectrum of the sawtooth chain induced by frustration.

cond-mat.str-el↗

arXiv2018

Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions

Motivated by a novel cyclic compound $Fe_{10}Gd_{10}$ with record ground state spin in which the arrangement of magnetic ions with $s=\frac{5}{2}$ and $s=\frac{7}{2}$ corresponds to a saw-tooth chain we investigate the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions. We study both classical and quantum versions of the model. The classical model is exactly solved and quantum effects are studied using full diagonalization and a finite temperature Lanczos technique for finite delta-chains as well as modified spin wave theory. It is shown that the main features of the magnetic susceptibility of the quantum spin delta chain are correctly described by the classical spin model, while quantum effects significantly change the low-temperature behavior of the specific heat. The relation of the obtained results to the $Fe_{10}Gd_{10}$ system is discussed.

cond-mat.str-el↗

arXiv2018

Non-Coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method

Coplanar model states for applications of the coupled cluster method (CCM) to problems in quantum magnetism are those in which all spins lie in a plane, whereas three-dimensional (3D) model states are, by contrast, non-coplanar ones in which all the spins do not lie in any single plane. Here we extend the CCM to non-coplanar / 3D model states and we present results for three cases: (a) the spin-half one-dimensional Ising ferromagnet in an applied transverse magnetic field (as an exactly solvable test model to use as a yardstick for the viability and accuracy of our new methodology); (b) the spin-half triangular-lattice Heisenberg antiferromagnet in the presence of an external magnetic field; and (c) the spin-$S$ triangular-lattice {\it XXZ} antiferromagnet in the presence of an external magnetic field, for the cases $\frac{1}{2} \leq S \leq5 $. For 3D model states the sets of algebraic CCM equations for the ket- and bra-state correlation coefficients become complex-valued, but ground-state expectation values of all physical observables are manifestly real numbers, as required. Excellent correspondence is seen with the results of other methods, where they exist, for these systems. CCM results demonstrate explicitly that coplanar ordering is favoured over non-coplanar ordering for the triangular-lattice spin-half Heisenberg antiferromagnet at all values of the applied external magnetic field, whereas for the anisotropic {\it XXZ} model non-coplanar ordering can be favoured in some regions of the parameter space. Specifically, we present a precise determination of the boundary (i.e., the critical value of the {\it XXZ} anisotropy parameter $Δ$) between a 3D ground state and a coplanar ground state for the {\it XXZ} model for values for the external magnetic field near to saturation, for values of the spin quantum number $S \leq 5$.

cond-mat.str-el↗

arXiv2018

The spin-$\frac{1}{2}$ Heisenberg ferromagnet on the pyrochlore lattice: A Green's function study

We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss the properties of this spin model at arbitrary temperatures. To this end, we use the Green's function technique within the random-phase (or Tyablikov) approximation as well as the linear spin-wave theory and quantum Monte Carlo simulations. We compare our results to the ones obtained recently by other methods to corroborate our findings. Finally, we contrast our results with the ones for the simple-cubic-lattice case: both lattices are identical at the mean-field level. We demonstrate that thermal fluctuations are more efficient in the pyrochlore case (finite-temperature frustration effects). Our results may be of use for interpreting experimental data for ferromagnetic pyrochlore materials.

cond-mat.str-el↗

arXiv2018

Comment on `Oxygen vacancy-induced magnetic moment in edge-sharing CuO$_{2}$ chains of Li$_{2}$CuO$_{2}$'

In a recent work devoted to the magnetism of Li$_{2}$CuO$_{2}$, Shu et al. [New J. Phys. 19 (2017) 023026] have proposed a "simplified" unfrustrated microscopic model that differs considerably from the models refined through decades of prior work. We show that the proposed model is at odds with known experimental data, including the reported magnetic susceptibility $χ(T)$ data up to 550~K. Using an 8$^{\rm th}$ order high-temperature expansion for $χ(T)$, we show that the experimental data for Li$_{2}$CuO$_{2}$ are consistent with the prior model derived from inelastic neutron scattering (INS) studies. We also establish the $T$-range of validity for a Curie-Weiss law for the real frustrated magnetic system. We argue that the knowledge of the long-range ordered magnetic structure for $T<T_N$ and of $χ(T)$ in a restricted $T$-range provides insufficient information to extract all of the relevant couplings in frustrated magnets; the saturation field and INS data must also be used to determine several exchange couplings, including the weak but decisive frustrating antiferromagnetic (AFM) interchain couplings.

cond-mat.str-el↗

arXiv2018

Magnetism of the N=42 kagome lattice antiferromagnet

For the paradigmatic frustrated spin-half Heisenberg antiferromagnet on the kagome lattice we performed large-scale numerical investigation of thermodynamic functions by means of the finite-temperature Lanczos method for system sizes of up to N=42. We present the dependence of magnetization as well as specific heat on temperature and external field and show in particular that a finite-size scaling of specific heat supports the appearance of a low-temperature shoulder below the major maximum. This seems to be the result of a counterintuitive motion of the density of singlet states towards higher energies. Other interesting features that we discuss are the asymmetric melting of the 1/3 magnetization plateau as well the field dependence of the specific heat that exhibits characteristic features caused by the existence of a flat one-magnon band. By comparison with the unfrustrated square-lattice antiferromagnet the tremendous role of frustration in a wide temperature range is illustrated.

cond-mat.str-el↗