arXiv subjects

Ronny Thomale

Publications and source records attributed to Ronny Thomale.

At least 217 records · Page 12Linked to original sources

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↗

arXiv2015

Triangular Spin-Orbit-Coupled Lattice with Strong Coulomb Correlations: Sn Atoms on a SiC(0001) Substrate

Two-dimensional (2D) atom lattices provide model setups for Coulomb correlations inducing competing ground states, partly with topological character. Hexagonal SiC(0001) is an intriguing wide-gap substrate, spectroscopically separated from the overlayer and hence reduced screening. We report the first study of an artificial high-Z atom lattice on SiC(0001) by Sn adatoms, based on combined experimental realization and theoretical modeling. Density-functional theory of our $\sqrt{3}$-structure model closely reproduces the scanning tunneling microscopy. Instead of metallic behavior, photoemission data show a deeply gapped state (~2 eV gap). Based on our calculations including dynamic mean-field theory, we argue that this reflects a pronounced Mott insulating scenario. We also find indications that the system is susceptible to antiferromagnetic superstructures. Such spin-orbit-coupled correlated heavy atom lattices on SiC(0001) thus form a novel testbed for peculiar quantum states of matter, with potential bearing for spin liquids and topological Mott insulators.

cond-mat.str-el↗

arXiv2014

Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions

We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both partitions, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling reveals that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in [Thomale et al., Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may in fact support the numerical study of physical transitions in the momentum space density matrix renormalization group.

cond-mat.str-el↗