arXiv subjects

Lukas Janssen

Publications and source records attributed to Lukas Janssen.

At least 55 records · Page 3Linked to original sources

arXiv2020

Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion

The exact solution of Kitaev's spin-$1/2$ honeycomb spin-liquid model has sparked an intense search for Mott insulators hosting bond-dependent Kitaev interactions, of which $\mathrm{Na}_{2}\mathrm{IrO}_{3}$ and $α-\mathrm{RuCl}_{3}$ are prime examples. Subsequently, it has been proposed that also spin-$1$ and spin-$3/2$ analogs of Kitaev interactions may occur in materials with strong spin-orbit coupling. As a minimal model to describe these Kitaev materials, we study the Heisenberg-Kitaev Hamiltonian in a consistent $1/S$ expansion, with $S$ being the spin size. We present a comprehensive study of this model in the presence of an external magnetic field applied along two different directions, [001] and [111], for which an intricate classical phase diagram has been reported. In both settings, we employ spin-wave theory in a number of ordered phases to compute phase boundaries at the next-to-leading order in $1/S$ and show that quantum corrections substantially modify the classical phase diagram. More broadly, our work presents a consistent route to investigate the leading quantum corrections in spin models that break spin-rotational symmetry.

cond-mat.str-el↗

arXiv2020

High-field thermal transport properties of the Kitaev quantum magnet alpha-RuCl3: evidence for low-energy excitations beyond the critical field

We investigate the phononic in-plane longitudinal low-temperature thermal conductivity kappa_ab of the Kitaev quantum magnet alpha-RuCl3 for large in-plane magnetic fields up to 33 T. Our data reveal for fields larger than the critical field Bc ~ 8 T, at which the magnetic order is suppressed, a dramatic increase of kappa_ab at all temperatures investigated. The analysis of our data shows that the phonons are not only strongly scattered by a magnetic mode at relatively large energy which scales roughly linearly with the magnetic field, but also by a small-energy mode which emerges near Bc with a square-root-like field dependence. While the former is in striking agreement with recent spin wave theory (SWT) results of the magnetic excitation spectrum at the Gamma point, the energy of the latter is too small to be compatible with the SWT-expected magnon gap at the M point, despite the matching field dependence. Therefore, an alternative scenario based on phonon scattering off the thermal excitation of random-singlet states is proposed.

cond-mat.str-el↗

arXiv2020

Susceptibility anisotropy and its disorder evolution in models for Kitaev materials

Mott insulators with strong spin-orbit coupling display a strongly anisotropic response to applied magnetic fields. This applies in particular to Kitaev materials, with $α$-RuCl$_3$ and Na$_2$IrO$_3$ representing two important examples. Both show a magnetically ordered zigzag state at low temperatures, and considerable effort has been devoted to properly modeling these systems in order to identify routes towards realizing a quantum spin liquid. Here, we investigate the relevant Heisenberg-Kitaev-$Γ$ model primarily at elevated temperatures, focusing on the characteristic anisotropy between the in-plane and out-of-plane uniform susceptibility. For $α$-RuCl$_3$, we find that the experimentally observed anisotropy, including its temperature dependence, can be reproduced by combining a large off-diagonal $Γ_1$ coupling with a moderate $g$-factor anisotropy. Moreover, we study in detail the effect of magnetic dilution and provide predictions for the doping evolution of the temperature-dependent susceptibilities.

cond-mat.str-el↗

arXiv2020

Observation of a random singlet state in a diluted Kitaev honeycomb material

We report a $^{35}$Cl nuclear magnetic resonance (NMR) study of the diluted Kitaev material $α$-Ru$_{1-x}$Ir$_x$Cl$_3$ ($x=0.1$ and $0.2$) where non-magnetic Ir$^{3+}$ dopants substitute Ru$^{3+}$ ions. Upon dilution, the $^{35}$Cl spectra exhibit unusual large magnetic inhomogeneity, which sets in at temperatures below the Kitaev exchange energy scale. At the same time, the $^{35}$Cl spin-lattice relaxation rate $T_1^{-1}$ as a function of dilution and magnetic field unravels a critical doping of $x_c\approx 0.22$, towards which both the field-induced spin gap and the zero-field magnetic ordering are simultaneously suppressed, while novel gapless low-energy spin excitations dominate the relaxation process. These NMR findings point to the stabilization of a random singlet phase in $α$-Ru$_{1-x}$Ir$_x$Cl$_3$, arising from the interplay of dilution and exchange frustration in the quantum limit.

cond-mat.str-el↗

arXiv2020

Soluble Fermionic Quantum Critical Point in Two Dimensions

We study a model for a quantum critical point in two spatial dimensions between a semimetallic phase, characterized by a stable quadratic Fermi node, and an ordered phase, in which the spectrum develops a band gap. The quantum critical behavior can be computed exactly, and we explicitly derive the scaling laws of various observables. While the order-parameter correlation function at criticality satisfies the usual power law with anomalous exponent $η_ϕ= 2$, the correlation length and the expectation value of the order parameter exhibit essential singularities upon approaching the quantum critical point from the insulating side, akin to the Berezinskii-Kosterlitz-Thouless transition. The susceptibility, on the other hand, has a power-law divergence with non-mean-field exponent $γ= 2$. On the semimetallic side, the correlation length remains infinite, leading to an emergent scale invariance throughout this phase.

cond-mat.str-el↗

arXiv2020

Magnon dispersion and dynamic spin response in three-dimensional spin models for $α$-RuCl$_3$

In the search for experimental realizations of bond-anisotropic Kitaev interactions and resulting spin-liquid phases, the layered magnet $α$-RuCl$_3$ is a prime candidate. Its modelling typically involves Heisenberg, Kitaev, and symmetric off-diagonal $Γ$ interactions on the two-dimensional honeycomb lattice. However, recent neutron-scattering experiments point towards a sizeable magnetic interlayer coupling. Here we study three-dimensional exchange models for $α$-RuCl$_3$, for both possible $R\bar{3}$ and $C2/m$ crystal structures. We discuss the symmetry constraints on the interlayer couplings, construct minimal models, and use them to compute the magnetic mode dispersion and the dynamical spin structure factor, in both the zero-field zigzag phase and the paramagnetic high-field phase. Our predictions for the interlayer mode dispersion shall guide future experiments; they also call for a reevaluation of the quantitative model parameters relevant for $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2020

Confinement transition in the QED$_3$-Gross-Neveu-XY universality class

The coupling between fermionic matter and gauge fields plays a fundamental role in our understanding of nature, while at the same time posing a challenging problem for theoretical modeling. In this situation, controlled information can be gained by combining different complementary approaches. Here, we study a confinement transition in a system of $N_f$ flavors of interacting Dirac fermions charged under a U(1) gauge field in 2+1 dimensions. Using Quantum Monte Carlo simulations, we investigate a lattice model that exhibits a continuous transition at zero temperature between a gapless deconfined phase, described by three-dimensional quantum electrodynamics, and a gapped confined phase, in which the system develops valence-bond-solid order. We argue that the quantum critical point is in the universality class of the QED$_3$-Gross-Neveu-XY model. We study this field theory within a $1/N_f$ expansion in fixed dimension as well as a renormalization group analysis in $4-ε$ space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.

cond-mat.str-el↗

arXiv2019

Emergent symmetries and coexisting orders in Dirac fermion systems

The quantum phase diagram and critical behavior of two-dimensional Dirac fermions coupled to two compatible order-parameter fields with $O(N_1)\oplus O(N_2)$ symmetry is investigated. Recent numerical studies of such systems have reported evidence for non-Landau-Ginzburg-Wilson transitions and emergent $O(N_1+N_2)$ symmetry between the two ordered states, which has been interpreted within a scenario of deconfined quantum criticality in (2+1)-dimensional Dirac materials. Here, we provide two theoretical approaches to refine the phase diagrams of such systems. In the immediate vicinity of the multicritical point between the ordered phases and the semimetallic phase, we employ a non-perturbative field-theoretical analysis based on the functional renormalization group. For the particular case of $N_1=3$, $N_2=1$, we perform a large-scale quantum Monte Carlo analysis of the strong-coupling region, where both orders meet. Our findings support the robust emergence of enhanced symmetry at the multicritical point and suggest the transition between the two ordered phases to take place via a sequence of continuous transitions. In particular, we find that intermediate regimes of coexistence are present in the phase diagram for all values of $N_1$ and $N_2$.

cond-mat.str-el↗

arXiv2019

Heisenberg-Kitaev Models on Hyperhoneycomb and Stripyhoneycomb Lattices: 3D-2D Equivalence of Ordered States and Phase Diagrams

We discuss magnetically ordered states, arising in Heisenberg-Kitaev and related spin models, on three-dimensional (3D) harmonic honeycomb lattices. For large classes of ordered states, we show that they can be mapped onto two-dimensional (2D) counterparts on the honeycomb lattice, with the classical energetics being identical in the 2D and 3D cases. As an example, we determine the phase diagram of the classical nearest-neighbor Heisenberg-Kitaev model on the hyperhoneycomb lattice in a magnetic field: This displays rich and complex behavior akin to its 2D counterpart, with most phases and phase boundaries coinciding exactly. To make contact with the physics of the hyperhoneycomb iridate $β$-Li$_2$IrO$_3$, we also include a symmetric off-diagonal $Γ$ interaction, discuss its 3D-2D mapping, and determine the relevant phase diagrams. In particular, we demonstrate explicitly the adiabatic equivalence of the spiral magnetic orders in $α$- and $β$-Li$_2$IrO$_3$. Our results pave the way to a systematic common understanding of 2D and 3D Kitaev materials.

cond-mat.str-el↗

arXiv2019

Heisenberg-Kitaev physics in magnetic fields

Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions. We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators $α$-RuCl$_3$ and Na$_2$IrO$_3$, which are believed to realize this fascinating physics.

cond-mat.str-el↗

arXiv2018

Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching

We consider two-dimensional Fermi systems with quadratic band touching and $C_3$ symmetry, as realizable in Bernal-stacked honeycomb bilayers. Within a renormalization-group analysis, we demonstrate the existence of a quantum critical point at a finite value of the density-density interactions, separating a semimetallic disordered phase at weak coupling from a gapped ordered phase at strong coupling. The latter may be characterized by, for instance, antiferromagnetic, quantum anomalous Hall, or charge density wave order. In the semimetallic phase, each point of quadratic band touching splits into four Dirac cones as a consequence of the nontrivial interaction-induced self-energy correction, which we compute to the two-loop order. We show that the quantum critical point is in the $(2+1)$-dimensional Gross-Neveu universality class characterized by emergent Lorentz invariance and a dynamic critical exponent $z=1$. At finite temperatures, $T > 0$, we hence conjecture a crossover between $z=2$ at intermediate $T$ and $z=1$ at low $T$, and we construct the resulting nontrivial phase diagram as function of coupling strength and temperature.

cond-mat.str-el↗

arXiv2018

Deconfined criticality from the QED$_3$-Gross-Neveu model at three loops

The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade approximants of their series expansion in epsilon. We find that these estimates, within the spread of the Pade approximants, satisfy a nontrivial scaling relation which follows from the emergent SO(5) symmetry implied by the duality conjecture. We also construct explicit evidence for the equivalence between the QED$_3$-Gross-Neveu model and a corresponding critical four-fermion gauge theory that was previously studied within the 1/N expansion in space-time dimensions 2<D<4.

cond-mat.str-el↗

arXiv2018

Compatible orders and fermion-induced emergent symmetry in Dirac systems

We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with $O(N_1)$ and $O(N_2)$ symmetry, respectively. Using $ε$ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent $O(N_1+N_2)$ symmetry for arbitrary values of $N_1$ and $N_2$ and fermion flavor numbers $N_f$, as long as the corresponding representation of the Clifford algebra exists. Small $O(N)$-breaking perturbations near the chiral $O(N)$ fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic $O(N)$ fixed point, which is stable only when $N < 3$. As a by-product, we obtain predictions for the critical behavior of the chiral $O(N)$ universality classes for arbitrary $N$ and fermion flavor number $N_f$. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.

cond-mat.str-el↗

arXiv2017

Critical behavior of the QED$_3$-Gross-Neveu model: Duality and deconfined criticality

We study the critical properties of the QED$_3$-Gross-Neveu model with $2N$ flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For $N=1$, this theory has recently been suggested to be dual to the SU(2) noncompact CP$^1$ model that describes the deconfined phase transition between the Neel antiferromagnet and the valence bond solid on the square lattice. For $N=2$, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-$1/2$ systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED$_3$-Gross-Neveu model for all values of $N$. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED$_3$ (without scalar-field coupling) unstable at low values of $N$. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter $ε= 4-D$. We compute the scalar-field anomalous dimension $η_ϕ$, the correlation-length exponent $ν$, as well as the scaling dimension of the flavor-symmetry-breaking bilinear $\barψσ^zψ$ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.

cond-mat.str-el↗

arXiv2017

Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $α$-RuCl$_3$ and Na$_2$IrO$_3$

We study the field-induced magnetization processes of extended Heisenberg-Kitaev models on the honeycomb lattice, taking into account off-diagonal and longer-range exchange interactions, using a combination of Monte-Carlo simulations, classical energy minimization, and spin-wave theory. We consider a number of different parameter sets, previously proposed to describe the magnetic behavior of $α$-RuCl$_3$ and Na$_2$IrO$_3$ with their antiferromagnetic zigzag ground states. By classifying these parameter sets, we reveal the existence of three distinct mechanisms to stabilize zigzag states, which differ in the sign of the nearest-neighbor Kitaev interaction, the role of longer-range interactions, and the magnitude of the off-diagonal $Γ_1$ interaction. While experimentally hardly distinguishable at zero field, we find that the three different scenarios lead to significantly different magnetization processes in applied magnetic fields. In particular, we show that a sizable off-diagonal interaction $Γ_1 > 0$ naturally explains the strongly anisotropic field responses observed in $α$-RuCl$_3$ without the need for a strong anisotropy in the effective $g$ tensor. Moreover, for a generic field direction, it leads to a high-field state with a finite transversal magnetization, which should be observable in $α$-RuCl$_3$.

cond-mat.str-el↗

arXiv2017

Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+ε$ expansion, $4-ε$ expansion, and functional renormalization group

Several materials in the regime of strong spin-orbit interaction such as HgTe, the pyrochlore iridate Pr$_2$Ir$_2$O$_7$, and the half-Heusler compound LaPtBi, as well as various systems related to these three prototype materials, are believed to host a quadratic band touching point at the Fermi level. Recently, it has been proposed that such a three-dimensional gapless state is unstable to a Mott-insulating ground state at low temperatures when the number of band touching points $N$ at the Fermi level is smaller than a certain critical number $N_c$. We further substantiate and quantify this scenario by various approaches. Using $ε$ expansion near two spatial dimensions, we show that $N_c = 64/(25 ε^2) + O(1/ε)$ and demonstrate that the instability for $N < N_c$ is towards a nematic ground state that can be understood as if the system were under (dynamically generated) uniaxial strain. We also propose a truncation of the functional renormalization group equations in the dynamical bosonization scheme which we show to agree to one-loop order with the results from $ε$ expansion both near two as well as near four dimensions, and which smoothly interpolates between these two perturbatively accessible limits for general $2<d<4$. Directly in $d=3$ we therewith find $N_c = 1.86$, and thus again above the physical $N=1$. All these results are consistent with the prediction that the interacting ground state of pure, unstrained HgTe, and possibly also Pr$_2$Ir$_2$O$_7$, is a strong topological insulator with a dynamically-generated gap -- a topological Mott insulator.

cond-mat.str-el↗

arXiv2016

Spontaneous breaking of Lorentz symmetry in $(2+ε)$-dimensional QED

The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N > N_c^{conf}$ the system is in a conformal gapless state, while for small $N < N_c^{χSB}$ the fermions are expected to develop a dynamical mass due to spontaneous chiral symmetry breaking. Using $ε$ expansion near the lower critical dimension of 2, as well as the recent results on the generalization of the $F$ theorem to continuous dimension, we show that $N_c^{conf} > N_c^{χSB}$. There is therefore an intermediate range of values of $N$ at which a third phase is stabilized. We demonstrate that this phase is characterized by spontaneous breaking of Lorentz symmetry, in which a composite vector boson field acquires a vacuum expectation value with the fermions and the photon remaining massless.

hep-th↗

arXiv2016

Honeycomb-lattice Heisenberg-Kitaev model in a magnetic field: Spin canting, metamagnetism, and vortex crystals

The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A$_2$IrO$_3$ (A = Na, Li) and $α$-RuCl$_3$. Here we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte-Carlo simulations and spin-wave theory we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction. We also discuss quantum corrections in the high-field phase.

cond-mat.str-el↗