arXiv subjects

Ronny Thomale

Publications and source records attributed to Ronny Thomale.

At least 217 records · Page 12Linked to original sources

arXiv2016

Evolution of superconducting gap anisotropy in hole-doped 122 iron pnictides

Motivated by recent experimental findings, we investigate the evolution of the superconducting gap anisotropy in 122 iron pnictides as a function of hole doping. Employing both a functional and a weak coupling renormalization group approach (FRG and WRG), we analyse the Fermi surface instabilities of an effective 122 model band structure at different hole dopings x, and derive the gap anisotropy from the leading superconducting instability. In the transition regime from collinear magnetism to s_{\pm}-wave, where strong correlations are present, we employ FRG to identify a non- monotonous change of the gap anisotropy in qualitative agreement with new experimental findings. From the WRG, which is asymptotically exact in the weak coupling limit, we find an s_{\pm}-wave to d-wave transition as a function of hole doping, complementing previous findings from FRG [Thomale et al., Phys. Rev. Lett. 107, 117001 (2011)]. The gap anisotropy of the s_{\pm}-wave monotonously increases towards the transition to d-wave as a function of x.

cond-mat.supr-con↗

arXiv2016

Band flatness optimization through complex analysis

Narrow band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects. Examples include magnetic materials, heavy fermion systems, and topological phases such as fractional quantum Hall states and their lattice-based cousins, the fractional Chern insulators (FCIs). Here we discuss the problem of designing models with optimal band flatness, subject to constraints on the range of electron hopping. In particular, we show how the imaginary gap, which serves as a proxy for band flatness, can be optimized by appealing to Rouche's theorem, a familiar result from complex analysis. This leads to an explicit construction which we illustrate through its application to two-band FCI models with nontrivial topology (i.e. nonzero Chern numbers). We show how the imaginary gap perspective leads to an elegant geometric picture of how topological properties can obstruct band flatness in systems with finite ranged hopping.

cond-mat.str-el↗

arXiv2016

Spin liquid nature in the Heisenberg $J_{1}$-$J_{2}$ triangular antiferromagnet

We investigate the spin-$\frac{1}{2}$ Heisenberg model on the triangular lattice in the presence of nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic couplings. Motivated by recent findings from density-matrix renormalization group (DMRG) claiming the existence of a gapped spin liquid with signatures of spontaneously broken lattice point group symmetry [Zhu and White, Phys. Rev. B 92, 041105 (2015); Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403 (2015)], we employ the variational Monte Carlo (VMC) approach to analyze the model from an alternative perspective that considers both magnetically ordered and paramagnetic trial states. We find a quantum paramagnet in the regime $0.08\lesssim J_2/J_1\lesssim 0.16$, framed by $120^{\circ}$ coplanar (stripe collinear) antiferromagnetic order for smaller (larger) $J_2/J_1$. By considering the optimization of spin-liquid wave functions of a different gauge group and lattice point group content as derived from Abrikosov mean-field theory, we obtain the gapless $U(1)$ Dirac spin liquid as the energetically most preferable state in comparison to all symmetric or nematic gapped $\mathbb{Z}_{2}$ spin liquids so far advocated by DMRG. Moreover, by the application of few Lanczos iterations, we find the energy to be the same as the DMRG result within error-bars. To further resolve the intriguing disagreement between VMC and DMRG, we complement our methodological approach by the pseudofermion functional renormalization group (PFFRG) to compare the spin structure factors for the paramagnetic regime calculated by VMC, DMRG, and PFFRG. This model promises to be an ideal test-bed for future numerical refinements in tracking the long-range correlations in frustrated magnets.

cond-mat.str-el↗

arXiv2016

Laughlin states and their quasi-particle excitations on the torus

We provide a full derivation of Laughlin's Jastrow-type wave functions for quantized Hall states subject to periodic boundary conditions using an operator formalism. The construction includes the quasi-hole and the technically more challenging quasi-electron excitation, which was left as an open problem in the classic paper by Haldane and Rezayi [Phys. Rev. B 31, 2529 (1985)].

cond-mat.str-el↗

arXiv2016

Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model

In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength $U$ and various antiferromagnetic insulators at large $U$, we find an intermediate-$U$ antiferromagnetic metal. Most interestingly, we also identify a non-magnetic insulating region, extending from intermediate to strong $U$. Using VCA results in the large-$U$ limit, we establish the phase diagram of the corresponding $J_1$-$J_2$-$J_3$ Heisenberg model. This is qualitatively confirmed - including the non-magnetic region - using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the $J_1$-$J_2$ square-lattice Heisenberg model, suggesting that the non-magnetic region hosts a 3D spin-liquid phase.

cond-mat.str-el↗

arXiv2016

Spin-orbit coupling and odd-parity superconductivity in the quasi-one-dimensional compound Li$_{0.9}$Mo$_6$O$_{17}$

Previous theoretical studies [W. Cho, C. Platt, R. H. McKenzie, and S. Raghu, Phys. Rev. B 92, 134514 (2015); N. Lera and J. V. Alvarez, Phys. Rev. B 92, 174523 (2015)] have suggested that Li$_{0.9}$Mo$_6$O$_{17}$, a quasi-one dimensional "purple bronze" compound, exhibits spin-triplet superconductivity and that the gap function changes sign across the two nearly degenerate Fermi surface sheets. We investigate the role of spin-orbit coupling (SOC) in determining the symmetry and orientation of the $d$-vector associated with the superconducting order parameter. We propose that the lack of local inversion symmetry within the four-atom unit cell leads to a staggered spin-orbit coupling analogous to that proposed for graphene, MoS$_2$, or SrPtAs. In addition, from a weak-coupling renormalization group treatment of an effective model Hamiltonian, we find that SOC favors the odd parity $A_{1u}$ state with $S_z = \pm 1$ over the $B$ states with $S_z=0$, where $z$ denotes the least-conducting direction. We discuss possible definitive experimental signatures of this superconducting state.

cond-mat.supr-con↗

arXiv2016

Wire deconstructionism of two-dimensional topological phases

A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions. We devise models for such states by coupling wires of non-chiral Luttinger liquids of electrons, that are arranged in a periodic array. Which inter-wire couplings are allowed is dictated by symmetry and the compatibility criterion that they can simultaneously acquire a finite expectation value, opening a spectral gap between the ground state(s) and all excited states in the bulk. First, with these criteria at hand, we reproduce the tenfold classification table of integer topological insulators, where their stability against interactions becomes immediately transparent in the Luttinger liquid description. Second, we construct an example of a strongly interacting fermionic topological phase of matter with short-range entanglement that lies outside of the tenfold classification. Third, we expand the table to long-range entangled topological phases with intrinsic topological order and fractional excitations.

cond-mat.str-el↗

arXiv2015

Universal entanglement spectra in critical spin chains

We advocate that in critical spin chains, and possibly in a larger class of 1D critical models, a gap in the momentum-space entanglement spectrum separates the universal part of the spectrum, which is determined by the associated conformal field theory, from the non-universal part, which is specific to the model. To this end, we provide affirmative evidence from multicritical spin chains with low energy sectors described by the SU(2)$_2$ or the SU(3)$_1$ Wess-Zumino-Witten model.

cond-mat.str-el↗

arXiv2015

Paramagnetism in the kagome compounds (Zn,Mg,Cd)Cu$_{3}$(OH)$_{6}$Cl$_{2}$

Frustrated magnetism on the kagome lattice has been a fertile ground for rich and fascinating physics, ranging from experimental evidence of a spin liquid to theoretical predictions of exotic superconductivity. Among experimentally realized spin-$\frac{1}{2}$ kagome magnets, herbertsmithite, kapellasite, and haydeeite [(Zn,Mg)Cu$_{3}$(OH)$_{6}$Cl$_{2}$] are all well described by a three-parameter Heisenberg model, but they exhibit distinctly different physics. We address the problem using a pseudofermion functional renormalization-group approach and analyze the low-energy physics in the experimentally accessible parameter range. Our analysis places kapellasite and haydeeite near the boundaries between magnetically ordered and disordered phases, implying that slight modifications could dramatically affect their magnetic properties. Inspired by this, we perform \textit{ab initio} density functional theory calculations of (Zn,Mg,Cd)Cu$_{3}$ (OH)$_{6}$Cl$_{2}$ at various pressures. Our results suggest that by varying pressure and composition one can traverse a paramagnetic regime between different magnetically ordered phases.

cond-mat.str-el↗

arXiv2015

Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet

We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na$_2$IrO$_3$, and may also play a role in $α$-RuCl$_3$ and Li$_2$IrO$_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na$_2$IrO$_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.

cond-mat.str-el↗

arXiv2015

Band-structure effects on superconductivity in Hubbard models

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find: 1) As a function of increasing nematicity, starting from the square lattice (zero nematicity) limit where nodal d-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a p-wave- and a d-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces---a situation which may be relevant to the Bechgaard salts. 2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a d-wave to an $s_{\pm}$-wave state reminiscent of the iron-based superconductors. 3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from $d_{x^2-y^2} to $d_{xy}$; in the context of the cuprates, this suggests that were the pseudo-gap entirely due to a competing order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment).

cond-mat.supr-con↗

arXiv2015

Phase diagram of the Hubbard model on the anisotropic triangular lattice

We investigate the Hubbard model on the anisotropic triangular lattice as a suggested effective description of the Mott phase in various triangular organic compounds. Employing the variational cluster approximation and the ladder dual-fermion approach as complementary methods to adequately treat the zero-temperature and the finite-temperature domains, we obtain a consistent picture of the phase diagram as a function of anisotropy and interaction strength. The metal-insulator transition substantially depends on the anisotropy, and so does the nature of magnetism and the emergence of a nonmagnetic insulating phase. We further find that geometric anisotropy significantly influences the thermodynamics of the system. For increased frustration induced by anisotropy, the entropy of the system increases with interaction strength, opening the possibility of adiabatically cooling a frustrated system by an enhancement of electronic correlations.

cond-mat.str-el↗

arXiv2015

Coupled wire construction of chiral spin liquids

We develop a coupled wire construction of chiral spin liquids. The starting point are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit coupling. Suitable spin-flip couplings between the wires yield an Abelian chiral spin liquid state which supports spinon excitations above a bulk gap, and chiral edge states. The approach generalizes to non-Abelian chiral spin liquids at level k with parafermionic edge states.

cond-mat.mes-hall↗

arXiv2015

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.

cond-mat.str-el↗

arXiv2015

Topological nature and the multiple Dirac cones hidden in Bismuth high-Tc superconductors

Recent theoretical studies employing density-functional theory have predicted BaBiO$_{3}$ (when doped with electrons) and YBiO$_{3}$ to become a topological insulator (TI) with a large topological gap (~ 0.7 eV). This, together with the natural stability against surface oxidation, makes the Bismuth-Oxide family of special interest for possible applications in quantum information and spintronics. The central question, we study here, is whether the hole-doped Bismuth Oxides, i.e. Ba$_{1-x}$K$_{x}$BiO$_{3}$ and BaPb$_{1-x}$Bi$_{x}$O$_{3}$, which are "high-Tc" bulk superconducting near 30 K, additionally display in the further vicinity of their Fermi energy $E_{F}$ a topological gap with a Dirac-type of topological surface state. Our electronic structure calculations predict the K-doped family to emerge as a TI, with a topological gap above $E_{F}$. Thus, these compounds can become superconductors with hole-doping and potential TIs with additional electron doping. Furthermore, we predict the Bismuth-Oxide family to contain an additional Dirac cone below $E_{F}$ for further hole doping, which manifests these systems to be candidates for both electron- and hole-doped topological insulators.

cond-mat.mtrl-sci↗

arXiv2015

Quantum paramagnet in a $π$ flux triangular lattice Hubbard model

We propose the $π$ flux triangular lattice Hubbard model ($π$-THM) as a prototypical setup to stabilize magnetically disordered quantum states of matter in the presence of charge fluctuations. The quantum paramagnetic domain of the $π$-THM which we identify for intermediate Hubbard U is framed by a Dirac semi-metal for weak coupling and by 120${}^{\circ}$ Néel order for strong coupling. Generalizing the Klein duality from spin Hamiltonians to tight-binding models, the $π$-THM maps to a Hubbard model which corresponds to the $(J_H, J_K)=(-1,2)$ Heisenberg-Kitaev model in its strong coupling limit. The $π$-THM provides a promising microscopic testing ground for exotic finite-U spin liquid ground states amenable to numerical investigation.

cond-mat.str-el↗

arXiv2015

Accessing topological superconductivity via a combined STM and renormalization group analysis

The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and fault-tolerant quantum computing. We propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunneling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor state. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.

cond-mat.supr-con↗

arXiv2015

Entanglement analysis of isotropic spin-1 chains

We investigate entanglement spectra of the SO(3) bilinear-biquadratic spin-1 chain, a model with phases exhibiting spontaneous symmetry breaking (both translation and spin rotation), points of enlarged symmetry, and a symmetry-protected topological phase (the Haldane phase). Our analysis reveals how these hallmark features are manifested in the entanglement spectra, and highlights the versatility of entanglement spectra as a tool to study one-dimensional quantum systems via small finite size realisations.

cond-mat.str-el↗