arXiv subjects

Johannes Richter

Publications and source records attributed to Johannes Richter.

At least 37 records · Page 2Linked to original sources

arXiv2021

Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions

The high-field regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely flat lowest single-magnon band. The corresponding excitations can be localized on loops in real space and have been coined "localized magnons". Thus, the description of the many-body ground states amounts to characterizing the allowed classical loop configurations and eliminating the quantum mechanical linear relations between them. Here, we investigate this loop-gas description on finite kagome lattices with open boundary conditions and compare the results with exact diagonalization for the spin-1/2 XY model on the same lattice. We find that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop configurations. The densest packing of the loops corresponds to a magnon crystal that according to the zero-temperature magnetization curve is a stable ground state of the spin-1/2 XY model in a window of magnetic fields of about 4% of the saturation field just below this saturation field. We also present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM). For a field in the stability range of the magnon crystal, one finds a low-temperature maximum of the specific heat that corresponds to a finite-temperature phase transition into the magnon crystal at low temperatures.

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arXiv2020

Disorder-Free Localization and Many-Body Quantum Scars from Magnetic Frustration

The concept of geometrical frustration has led to rich insights into condensed matter physics, especially as a mechansim to produce exotic low energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high energy states. We consider three classes of non-integrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates that are singlet coverings, and (III) flat band systems hosting magnon crystals. We argue that several 1D and 2D models from class (I) exhibit disorder-free localization in high energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of class (II) and (III) exhibit quantum many-body scars -- eigenstates of non-integrable Hamiltonians with finite energy density and anomalously low entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of non-integrable models exhibiting anomalous thermalization in mid-spectrum states.

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arXiv2020

Investigation of entanglement measures across the magnetization process of a highly frustrated spin-1/2 Heisenberg octahedral chain as a new paradigm of the localized-magnon approach

The bipartite entanglement across the magnetization process of a highly frustrated spin-1/2 Heisenberg octahedral chain is examined within the concept of localized magnons, which enables a simple calculation of the concurrence measuring a strength of the pairwise entanglement between nearest-neighbor and next-nearest-neighbor spins from square plaquettes. A full exact diagonalization of the finite-size Heisenberg octahedral chain with up to 4 unit cells (20 spins) evidences an extraordinary high precision of the localized-magnon theory in predicting measures of the bipartite entanglement at sufficiently low temperatures. While the monomer-tetramer phase emergent at low enough magnetic fields exhibits presence (absence) of the bipartite entanglement between the nearest-neighbor (next-nearest-neighbor) spins, the magnon-crystal phase emergent below the saturation field contrarily displays identical bipartite entanglement between the nearest-neighbor and next-nearest-neighbor spins. The presented results verify a new paradigm of the localized-magnon approach concerned with a simple calculation of entanglement measures.

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arXiv2020

Flat-band physics in the spin-1/2 sawtooth chain

We consider the strongly anisotropic spin-1/2 $XXZ$ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction $J^{zz}=ΔJ$ and aniferromagnetic transversal interaction $J^{xx}=J^{yy}=J>0$. At $Δ=-1/2$ the lowest one-magnon excitation band is dispersionless (flat) leading to a massively degenerate set of ground states. Interestingly, this model admits a three-coloring representation of the ground-state manifold [H.~J.~Changlani et at., Phys. Rev. Lett. {\bf 120}, 117202 (2018)]. We characterize this ground-state manifold and elaborate the low-temperature thermodynamics of the system. We illustrate the manifestation of the flat-band physics of the anisotropic model by comparison with two isotropic flat-band Heisenberg sawtooth chains. Our analytical consideration is complemented by exact diagonalization and finite-temperature Lanczos method calculations.

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arXiv2020

Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet

The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most challenging problems in the field of highly frustrated quantum magnetism. Stimulated by the seminal paper of M.~Planck [M.~Planck, Verhandl. Dtsch. phys. Ges. {\bf 2}, 202-204 (1900)] we calculate thermodynamic properties of this model by interpolating between the low- and high-temperature behavior. For that we follow ideas developed in detail by B.~Bernu and G.~Misguich and use for the interpolation the entropy exploiting sum rules [the ``entropy method'' (EM)]. We complement the EM results for the specific heat, the entropy, and the susceptibility by corresponding results obtained by the finite-temperature Lanczos method (FTLM) for a finite lattice of $N=32$ sites as well as by the high-temperature expansion (HTE) data. We find that due to pronounced finite-size effects the FTLM data for $N=32$ are not representative for the infinite system below $T \approx 0.7$. A similar restriction to $T \gtrsim 0.7$ holds for the HTE designed for the infinite PHAF. By contrast, the EM provides reliable data for the whole temperature region for the infinite PHAF. We find evidence for a gapless spectrum leading to a power-law behavior of the specific heat at low $T$ and for a single maximum in $c(T)$ at $T\approx 0.25$. For the susceptibility $χ(T)$ we find indications of a monotonous increase of $χ$ upon decreasing of $T$ reaching $χ_0 \approx 0.1$ at $T=0$. Moreover, the EM allows to estimate the ground-state energy to $e_0\approx -0.52$.

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arXiv2019

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

We investigate the spin $S=1/2$ Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins ($S=1/2$) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for $S=1$. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data

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arXiv2019

Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the Heisenberg antiferromagnet on the pyrochlore lattice. We discuss the excitation spectra as well as various thermodynamic quantities, such as spin correlations, uniform susceptibility, specific heat and static and dynamical structure factors. For the ground state we present RGM data for arbitrary spin quantum numbers $S$. At finite temperatures we focus on the extreme quantum cases $S=1/2$ and $S=1$. We do not find indications for magnetic long-range order for any value of $S$. We discuss the width of the pinch point in the static structure factor in dependence on temperature and spin quantum number. We compare our data with experimental results for the pyrochlore compound NaCaNi$_2$F$_7$ ($S=1$). Thus, our results for the dynamical structure factor agree well with the experimentally observed features at 3 \ldots 8~meV for NaCaNi$_2$F$_7$. We analyze the static structure factor ${S}_{\bf q}$ to find regions of maximal ${S}_{\bf q}$. The high-temperature series of the ${S}_{\bf q}$ provide a fingerprint of weak {\it order by disorder} selection of a collinear spin structure, where (classically) the total spin vanishes on each tetrahedron and neighboring tetrahedra are dephased by $π$.

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arXiv2017

Thermodynamic properties of Ba$_2$CoSi$_2$O$_6$Cl$_2$ in strong magnetic field: Realization of flat-band physics in a highly frustrated quantum magnet

The search for flat-band solid-state realizations is a crucial issue to verify or to challenge theoretical predictions for quantum many-body flat-band systems. For frustrated quantum magnets flat bands lead to various unconventional properties related to the existence of localized many-magnon states. The recently synthesized magnetic compound Ba$_2$CoSi$_2$O$_6$Cl$_2$ seems to be an almost perfect candidate to observe these features in experiments. We develop a theory for Ba$_2$CoSi$_2$O$_6$Cl$_2$ by adapting the localized-magnon concept to this compound. We first show that our theory describes the known experimental facts and then we propose new experimental studies to detect a field-driven phase transition related to a Wigner-crystal-like ordering of localized magnons at low temperatures.

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arXiv2017

Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the spin-$S$ Heisenberg ferromagnet on the pyrochlore lattice. We examine the excitation spectra as well as various thermodynamic quantities, such as the order parameter (magnetization), the uniform static susceptibility, the correlation length, the spin-spin correlations, and the specific heat, as well as the static and dynamic structure factors. We discuss the influence of the spin quantum number $S$ on the temperature dependence of these quantities. We compare our results for the pyrochlore ferromagnet with the corresponding ones for the simple-cubic lattice both having the same coordination number $z=6$. We find a significant suppression of magnetic ordering for the pyrochlore lattice due to its geometry with corner-sharing tetrahedra.

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arXiv2017

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field

Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-$\frac{1}{2}$ isotropic ($XXX$) Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.

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arXiv2017

Magnetization process and low-temperature thermodynamics of a spin-1/2 Heisenberg octahedral chain

Low-temperature magnetization curves and thermodynamics of a spin-1/2 Heisenberg octahedral chain with the intraplaquette and monomer-plaquette interactions are examined within a two-component lattice-gas model of hard-core monomers, which takes into account all low-lying energy modes in a highly frustrated parameter space involving the monomer-tetramer, localized many-magnon and fully polarized ground states. It is shown that the developed lattice-gas model satisfactorily describes all pronounced features of the low-temperature magnetization process and the magneto-thermodynamics such as abrupt changes of the isothermal magnetization curves, a double-peak structure of the specific heat or a giant magnetocaloric effect.

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arXiv2017

Diversity of quantum ground states and quantum phase transitions of a spin-1/2 Heisenberg octahedral chain

The spin-1/2 Heisenberg octahedral chain with regularly alternating monomeric and square-plaquette sites is investigated using various analytical and numerical methods: variational technique, localized-magnon approach, exact diagonalization (ED) and density-matrix renormalization group (DMRG) method. The model belongs to the class of flat-band systems and it has a rich ground-state phase diagram including phases with spontaneously broken translational symmetry. Moreover, it exhibits an anomalous low-temperature thermodynamics close to continuous or discontinuous field-driven quantum phase transitions between three quantum ferrimagnetic phases, tetramer-hexamer phase, monomer-tetramer phase, localized-magnon phase and two different spin-liquid phases. If the intra-plaquette coupling is at least twice as strong as the monomer-plaquette coupling, the variational method furnishes a rigorous proof of the monomer-tetramer ground state in a low-field region and the localized-magnon approach provides an exact evidence of a single magnon trapped at each square plaquette in a high-field region. In the rest of parameter space we have numerically studied the ground-state phase diagram and magnetization process using DMRG and ED methods. It is shown that the zero-temperature magnetization curve may involve up to four intermediate plateaus at zero, one-fifth, two-fifth and three-fifth of the saturation magnetization, while the specific heat exhibits a striking low-temperature peak in a vicinity of discontinuous quantum phase transitions.

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arXiv2017

Emergence of magnetic long-range order in kagome quantum antiferromagnets

The existence of a spin-liquid ground state of the $s=1/2$ Heisenberg kagome antiferromagnet (KAFM) is well established. Meanwhile, also for the $s=1$ Heisenberg KAFM evidence for the absence of magnetic long-range order (LRO) was found. Magnetic LRO in Heisenberg KAFMs can emerge by increasing the spin quantum number $s$ to $s>1$ and for $s=1$ by an easy-plane anisotropy. In the present paper we discuss the route to magnetic order in $s=1/2$ KAFMs by including an isotropic interlayer coupling (ILC) $J_\perp$ as well as an easy-plane anisotropy in the kagome layers by using the coupled-cluster method to high orders of approximation. We consider ferro- as well as antiferromagnetic $J_\perp$. To discuss the general question for the crossover from a purely two-dimensional (2D) to a quasi-2D and finally to a three-dimensional system we consider the simplest model of stacked (unshifted) kagome layers. Although the ILC of real kagome compounds is often more sophisticated, such a geometry of the ILC can be relevant for barlowite. We find that the spin-liquid ground state present for the strictly 2D $s=1/2$ $XXZ$ KAFM survives a finite ILC, where the spin-liquid region shrinks monotonously with increasing anisotropy. If the ILC becomes large enough (about 15\% of intralayer coupling for the isotropic Heisenberg case and about 4\% for the $XY$ limit) magnetic LRO can be established, where the $q=0$ symmetry is favorable if $J_\perp$ is of moderate strength. If the strength of the ILC further increases, $\sqrt{3}\times \sqrt{3}$ LRO can become favorable against $q=0$ LRO.

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arXiv2017

Interpolation between low and high temperatures of the specific heat for spin systems

The high temperature expansion (HTE) of the specific heat of a spin system fails at low temperatures, even if it is combined with a Padé approximation. On the other hand we often have information about the low temperature asymptotics (LTA) of the system. Interpolation methods combine both kind of information, HTE and LTA, in order to obtain an approximation of the specific heat that holds for the whole temperature range. Here we revisit the entropy method that has been previously published and propose two variants that better cope with problems of the entropy method for gapped systems. We compare all three methods applied to the antiferromagnetic Haldane spin-one chain and especially apply the second variant, called Log Z method, to the cuboctahedron for different spin quantum numbers. In particular, we demonstrate that the interpolation method is able to detect an extra low-temperature maximum in the specific heat that may appear if a separation of two energy scales is present in the considered system. Finally we illustrate how interpolation also works for classical spin systems.

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arXiv2017

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model

We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop like transition in the considered isotropic spin model.

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arXiv2016

Quantum phase transitions: The mean-field perspective

To illustrate a simple mean-field-like approach for examining quantum phase transitions we consider the $J-J^\prime$ quantum Heisenberg antiferromagnet on a square lattice. The exchange couplings $J$ and $J^\prime$ are competing with each other. The ratio $J^\prime/J$ is the control parameter and its change drives the transition. We adopt a variational ansatz, calculate the ground-state energy as well as the order parameter and describe the quantum phase transition inherent in the model. This description corresponds completely to the standard Landau theory of phase transitions. We also discuss how to generalize such an approach for more complicated quantum spin models.

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arXiv2016

High-temperature expansion for frustrated magnets: Application to the J1-J2 model on the BCC lattice

We present the high-temperature expansion up to 11th order for the specific heat $C$ and the uniform susceptibility $χ_0$ and up to 9th order for the structure factor $S_{\bf Q}$ of the frustrated spin-half $J_1$-$J_2$ Heisenberg model on the BCC lattice. We consider ferromagnetic as well as antiferromagnetic nearest-neighbor exchange $J_1$ and frustrating antiferromagnetic next-nearest-neighbor exchange $J_2$. We discuss the influence of frustration on the temperature dependence of these quantities. Furthermore, we use the HTE series to determine the critical temperature $T_c$ as a function of the frustration parameter $J_2$.

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arXiv2016

The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half {\it XXZ} antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter $Δ$ in the range $-1 \leq Δ< \infty$ of interest, including both the easy-plane $(-1 < Δ< 1)$ and easy-axis $(Δ> 1)$ regimes, where $Δ\rightarrow \infty$ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point ($Δ= 1$), where the model undergoes a phase transition from a gapped state (for $Δ> 1$) to a gapless state (for $Δ\leq 1$), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at $Δ=1$ for the present model with spins of spin quantum number $s=\frac{1}{2}$ that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-$s$ counterpart.

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