Johannes Reuther

Bio: Johannes Reuther is an academic researcher from Free University of Berlin. The author has contributed to research in topics: Quantum spin liquid & Heisenberg model. The author has an hindex of 26, co-authored 59 publications receiving 2052 citations. Previous affiliations of Johannes Reuther include California Institute of Technology & Helmholtz-Zentrum Berlin.

Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3.

Abstract: Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates ${A}_{2}{\mathrm{IrO}}_{3}$ ($A=\mathrm{Na}$, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital $S=1/2$ moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from $\ensuremath{\theta}\ensuremath{\approx}\ensuremath{-}125\text{ }\text{ }\mathrm{K}$ for ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ to $\ensuremath{\theta}\ensuremath{\approx}\ensuremath{-}33\text{ }\text{ }\mathrm{K}$ for ${\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$, while the ordering temperature remains roughly the same ${T}_{N}\ensuremath{\approx}15\text{ }\text{ }\mathrm{K}$. Using functional renormalization group calculations we show that this evolution of $\ensuremath{\theta}$ and ${T}_{N}$ as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ is deep in a magnetically ordered regime, while ${\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ appears to be close to a spin-liquid regime.

Finite-temperature phase diagram of the Heisenberg-Kitaev model

Abstract: We discuss the finite-temperature phase diagram of the Heisenberg-Kitaev model on the hexagonal lattice, which has been suggested to describe the spin-orbital exchange in the Mott-insulating iridate Na${}_{2}$IrO${}_{3}$. The model exhibits magnetically ordered ground states well beyond the isotropic Heisenberg limit as well as a gapless spin-liquid phase around the anisotropic Kitaev limit. Using a pseudofermion functional renormalization group (RG) approach we extract both the Curie-Weiss scale and the critical ordering scale from the RG flow of the magnetic susceptibility. The Curie-Weiss scale switches sign---indicating a transition of the dominant exchange from antiferromagnetic to ferromagnetic---deep in the magnetically ordered regime for which we find no significant frustration. We discuss our results in light of recent susceptibility measurements for Na${}_{2}$IrO${}_{3}$.

Physical realization of a quantum spin liquid based on a complex frustration mechanism

Abstract: A detailed and systematic study of Ca10Cr7O28 reveals all the hallmarks of spin-liquid behaviour, in spite of the compound’s unusually complex structure.

J 1 − J 2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group

Abstract: We study the ground-state properties of the two-dimensional spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on a square lattice, within diagrammatic approximations using an auxiliary-fermion formulation with exact projection. In a first approximation, we assume a phenomenological width of the pseudofermion spectral function to calculate the magnetization, susceptibilities, and the spin-correlation length within random-phase approximation, demonstrating the appearance of a paramagnetic phase between the N\'eel-ordered and Collinear-ordered phases, at sufficiently large pseudofermion damping. Second we use a functional renormalization-group formulation. We find that the conventional truncation scheme omitting three-particle and higher-order vertices is not sufficient. We therefore include self-energy renormalizations in the single-scale propagator as recently proposed by Katanin, to preserve Ward identities in a better way. We find N\'eel order at $g={J}_{2}/{J}_{1}\ensuremath{\lesssim}{g}_{\text{c}1}\ensuremath{\approx}0.4\dots{}0.45$ and Collinear order at $g\ensuremath{\gtrsim}{g}_{\text{c}2}\ensuremath{\approx}0.66\dots{}0.68$, which is in good agreement with results obtained by numerical studies. In the intervening quantum paramagnetic phase, we find enhanced columnar dimer and plaquette fluctuations of equal strength.

Functional renormalization group for the anisotropic triangular antiferromagnet

Abstract: We present a functional renormalization group scheme that allows us to calculate frustrated magnetic systems of arbitrary lattice geometry beyond $O(200)$ sites from first principles. We study the magnetic susceptibility of the antiferromagnetic (AFM) spin-$1/2$ Heisenberg model ground state on the spatially anisotropic triangular lattice, where ${J}^{\ensuremath{'}}$ denotes the coupling strength of the intrachain bonds along one lattice direction and $J$ the coupling strength of the interchain bonds. We identify three distinct phases of the Heisenberg model. Increasing $\ensuremath{\xi}={J}^{\ensuremath{'}}/J$ from the effective square lattice $\ensuremath{\xi}=0$, we find an AFM N\'eel order to spiral order transition at ${\ensuremath{\xi}}_{c1}~0.6--0.7$, with an indication that it is of second order. In addition, above the isotropic point at ${\ensuremath{\xi}}_{c2}~1.1$, we find a first-order transition to a magnetically disordered phase with collinear AFM stripe fluctuations.

Quantum Spin Liquids

Abstract: Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons that are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments to study quantum spin liquids, and to the diverse probes used therein.

Quantum spin liquids: a review.

Abstract: Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

Quantum spin liquid states

Abstract: This is an introductory review of the physics of quantum spin liquid states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semiclassical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semiclassical approaches fail once quantum mechanics become important and then describe the alternative approaches for addressing the problem. Mainly spin-1/2 systems are discussed, and most of the time is spent in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called SU(2), U(1), or Z2 spin liquid states. A review is given of the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin (S>1/2) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular-lattice systems [κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2], kagome-lattice system [ZnCu3(OH)6Cl2], and hyperkagome lattice system (Na4Ir3O8), is reviewed and compared against the corresponding theories.