Karlo Penc

Hungarian Academy of Sciences, Budapeŝto, Budapest, Hungary

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Publications (112)349.21 Total impact

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    ABSTRACT: Recent experiments on the spin ice Dy$_2$Ti$_2$O$_7$, suggest that the Pauling "ice entropy", characteristic of its Coulombic spin-liquid state, may be lost at low temperatures [D. Pomaranski et al., Nature Phys. 9, 353 (2013)]. However, despite nearly two decades of intensive study, the nature of the equilibrium ground state of spin-ice remains uncertain. Here we explore how long-range dipolar interactions $D$, short-range exchange interactions and quantum fluctuations combine to determine the ground state of dipolar spin ice. We find that ordered ground states are selected from a set of "chain states" in which dipolar interactions are exponentially screened. Using both quantum and classical Monte Carlo simulation, we establish phase diagrams as a function of quantum tunneling $g$, and temperature $T$, and find that only a very small $g_c \ll D$ is needed to stabilize a quantum spin-liquid ground state. We discuss the implications of these results for Dy$_2$Ti$_2$O$_7$, and for the "quantum spin ice" materials Yb$_2$Ti$_2$O$_7$, Tb$_2$Ti$_2$O$_7$ and Pr$_2$Zr$_2$O$_7$.
  • Judit Romhányi, Karlo Penc, R. Ganesh
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    ABSTRACT: The celebrated Shastry Sutherland model has a gapped dimer singlet ground state. The material SrCu$_2$(BO$_3$)$_2$ serves as a good realization of this model, upto small anisotropies arising from Dzyaloshinskii Moriya (DM) interactions. The DM interactions admix a triplet component into the singlet ground state and give rise to weakly dispersing triplon bands. We show that an applied magnetic field splits the triplon modes and opens band gaps. Surprisingly, we are left with topological bands with Chern numbers $\pm 2$. SrCu$_2$(BO$_3$)$_2$ thus supports topologically protected triplonic edge modes and is a magnetic analogue of the integer quantum Hall effect. At a critical value of the magnetic field set by the strength of DM interactions, the three triplon bands touch once again in a spin-1 generalization of a Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.
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    ABSTRACT: We study electrons hopping on a kagome lattice at third filling described by an extended Hubbard Hamiltonian with on-site and nearest-neighbour repulsions in the strongly correlated limit. As a consequence of the commensurate filling and the large interactions, each triangle has precisely two electrons in the effective low energy description, and these electrons form chains of different lengths. The effective Hamiltonian includes the ring exchange around the hexagons as well as the nearest- neighbor Heisenberg interaction. Using large scale exact diagonalization, we find that the effective model exhibits two different phases: If the charge fluctuations are small, the magnetic fluctuations confine the charges to short loops around hexagons, yielding a gapped charge ordered phase. When the charge fluctuations dominate, the system undergoes a quantum phase transition to a resonating plaquette phase with ordered spins and gapless spin excitations. We find that a peculiar conservation law is fulfilled: the electron in the chains can be divided into two sublattices, and this division is conserved by the ring exchange term.
    Physical Review B 02/2014; 90(3). · 3.66 Impact Factor
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    ABSTRACT: We investigate the effect of the Berry phase on quadrupoles that occur for example in the low-energy description of spin models. Specifically we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a non-dimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory, and then verify the predictions using large scale density-matrix renormalization group (DMRG) simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions.
    Physical review letters. 01/2014; 113(2).
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    ABSTRACT: We investigate the ground-state properties of the highly degenerate non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice with Monte Carlo simulations. For that purpose, we introduce an Ising pseudospin representation of the ground states, and we use a simple Metropolis algorithm with local updates, as well as a powerful cluster algorithm. At sizes that can be sampled with local updates, the presence of long-range order is surprisingly combined with an algebraic decay of correlations and the complete disordering of the chirality. It is only thanks to the investigation of unusually large systems (containing $\sim 10^8$ spins) with cluster updates that the true asymptotic regime can be reached and that the system can be proven to consist of equivalent (i.e., equally ordered) sublattices. These large-scale simulations also demonstrate that the scalar chirality exhibits long-range order at zero temperature, implying that the system has to undergo a finite-temperature phase transition. Finally, we show that the average distance in the order parameter space, which has the structure of an infinite Cayley tree, remains remarkably small between any pair of points, even in the limit when the real space distance between them tends to infinity.
    Physical review. B, Condensed matter 05/2013; 88(9). · 3.77 Impact Factor
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    Miklos Lajko, Karlo Penc
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    ABSTRACT: The SU(4) Heisenberg model can serve as a low energy model of the Mott insulating state in materials where the spins and orbitals are highly symmetric, or in systems of alkaline-earth atoms on optical lattice. Recently, it has been argued that on the honeycomb lattice the model exhibits a unique spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the algebraic spin-orbital liquid toward spontaneous formation of SU(4) singlet plaquettes (tetramerization). Using a variational Monte Carlo approach to evaluate the projected wave-function of fermions with $\pi$-flux state, we find that the algebraic liquid is robust, and that a finite value of the next nearest exchange is needed to induce tetramerization. We also studied the phase diagram of a model which interpolates between the nearest neighbor Heisenberg model and a Hamiltonian for which the singlet-plaquette product state is an exact ground state.
    Physical review. B, Condensed matter 03/2013; 87(22). · 3.77 Impact Factor
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    ABSTRACT: Ba2CoGe2O7 is a multiferroic material where spin waves exhibit giant directional dichroism and natural optical activity at THz frequencies due to the large ac magnetoelectric effect [S. Bordacs et al., Nature Physics 8, 734 (2012)]. We studied spin excitations in the magnetically ordered phase of the noncentrosymmetric Ba2CoGe2O7 in high magnetic fields up to 33 T [Penc et al., Phys. Rev. Lett. 108, 257203 (2012)]. In the ESR and THz absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. A multiboson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by an oscillating magnetic dipole and quadrupole moment. The lack of inversion symmetry allows each mode to become electric dipole active.
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    ABSTRACT: Dynamical properties of the lattice structure were studied by optical spectroscopy in ACr2O4 chromium spinel oxide magnetic semiconductors over a broad temperature region of T=10–335 K. The systematic change of the A-site ions (A= Mn, Fe, Co, Ni and Cu) showed that the occupancy of 3d orbitals on the A site has strong impact on the lattice dynamics. For compounds with orbital degeneracy (FeCr2O4, NiCr2O4, and CuCr2O4), clear splitting of infrared-active phonon modes and/or activation of silent vibrational modes have been observed upon the Jahn-Teller transition and at the onset of the subsequent long-range magnetic order. Although MnCr2O4 and CoCr2O4 show multiferroic and magnetoelectric character, no considerable magnetoelasticity was found in spinel compounds without orbital degeneracy as they closely preserve the high-temperature cubic spinel structure even in their magnetic ground state. Aside from lattice vibrations, intra-atomic 3d-3d transitions of the A2+ ions were also investigated to determine the crystal field and Racah parameters and the strength of the spin-orbit coupling.
    Physical review. B, Condensed matter 02/2013; 87(6). · 3.77 Impact Factor
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    ABSTRACT: Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension $D$. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small $D$ the dimer state has a lower variational energy than the plaquette state, however, for large $D$ it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are non-chiral flux states.
    Physical review. B, Condensed matter 02/2013; 87(19). · 3.77 Impact Factor
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    ABSTRACT: Faraday rotation and magneto-optical absorption spectral measurements were conducted on a spinel oxide, ZnCr2O4, a prototype of three-dimensional geometrically frustrated magnet. The measurements were carried out at temperatures down to 4.6 K under ultra-high magnetic fields of up to 600 T. The ultra-high magnetic fields were generated by the electro-magnetic flux compression method. We obtained a precise magnetization curve up to a fully polarized phase, where the phase transition takes place above 400 T. The experimental magnetization curves were compared with those obtained by Monte Carlo calculations with an effective spin model including spin--lattice coupling up to fully saturated magnetization. The absorption spectral peaks of the intra-d-band transitions in Cr3+ ions as well as the exciton--magnon--phonon transition were used for monitoring the crystal and magnetic structures subjected to a strong external magnetic field. A novel magnetic phase was found prior to the fully polarized phase, which was clarified by the change in magneto-absorption intensity around 350 T. An umbrella-like magnetic structure was proposed to be the most plausible candidate for the novel phase. A physical analogy between the magnetic structures of ZnCr2O4 and the quantum phases of 4He was discussed based on the similarity of symmetry breaking.
    Journal of the Physical Society of Japan 11/2012; 81(11):4701-. · 2.09 Impact Factor
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    ABSTRACT: In addition to low-energy spin fluctuations, which distinguish them from band insulators, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in most situations spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the SU(4) symmetric Kugel-Khomskii model on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breaking - lattice or SU(N) - is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave-function based on the \pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides a good starting point to understand the recently discovered spin-orbital liquid behavior of Ba_3CuSb_2O_9. The present results also suggest to choose optical lattices with honeycomb geometry in the search for quantum liquids in ultra-cold four-color fermionic atoms.
    Physical Review X 07/2012; 2(4). · 8.39 Impact Factor
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    Judit Romhányi, Karlo Penc
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    ABSTRACT: We consider the square-lattice antiferromagnetic Heisenberg Hamiltonian extended with a single-ion axial anisotropy term as a minimal model for the multiferroic Ba2CoGe2O7. Developing a multiboson spin-wave theory, we investigate the dispersion of the spin excitations in this spin-3/2 system. As a consequence of a strong single-ion anisotropy, a stretching (longitudinal) spin-mode appears in the spectrum. The inelastic neutron scattering spectra of Zheludev et al. [Phys. Rev. B 68, 024428 (2003)] are successfully reproduced by the low energy modes in the multiboson spin-wave theory, and we anticipate the appearance of the spin stretching modes at 4meV that can be identified using the calculated dynamical spin structure factors. We expect the appearance of spin stretching modes for any S>1/2 compound where the single-ion anisotropy is significant.
    Physical review. B, Condensed matter 05/2012; 86(17). · 3.77 Impact Factor
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    ABSTRACT: We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N=3) and the checkerboard lattice (for N=4), which are the line graphs of the honeycomb and square lattices and thus belong to the class of bisimplex lattices. Using infinite projected entangled-pair states (iPEPS) and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a two-fold ground state degeneracy, in which the N spins belonging to a simplex (i.e. a complete graph) form a singlet. Theses states can be seen as generalizations of valence bond solid states known to be stabilized in certain SU(2) spin models.
    Physical review. B, Condensed matter 04/2012; 86(4). · 3.77 Impact Factor
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    ABSTRACT: We studied spin excitations of the multiferroic Ba2CoGe2O7 in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multi-boson spin-wave theory can capture these unconventional modes, that include spin-stretching modes associated with an oscillating magnetic dipole (or only quadrupole) moment. The lack of the inversion symmetry allows these modes to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or non-centrosymmetric lattice structure.
    Physical Review Letters 02/2012; · 7.73 Impact Factor
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    ABSTRACT: We investigate the zero-temperature behavior of the classical Heisenberg model on the triangular lattice in which the competition between exchange interactions of different orders favors a relative angle between neighboring spins in the interval (0,2pi/3). In this situation, the ground states are noncoplanar and have an infinite discrete degeneracy. In the generic case, the set of the ground states is in one to one correspondence (up to a global rotation) with the non-crossing loop coverings of the three equivalent honeycomb sublattices into which the bonds of the triangular lattice can be partitioned. This allows one to identify the order parameter space as an infinite Cayley tree with coordination number 3. Building on the duality between a similar loop model and the ferromagnetic O(3) model on the honeycomb lattice, we argue that a typical ground state should have long-range order in terms of spin orientation. This conclusion is further supported by the comparison with the four-state antiferromagnetic Potts model [describing the case when the angle between neighboring spins is equal to arccos(-1/3)], which at zero temperature is critical and in terms of the solid-on-solid representation is located exactly at the point of roughening transition. At other values of the angle between neighboring spins an additional constraint appears, whose presence drives the system into an ordered phase (unless this angle is equal to pi/2, when another constraint is removed and the model becomes trivially exactly solvable).
    Physical review. B, Condensed matter 02/2012; 85(17). · 3.77 Impact Factor
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    ABSTRACT: Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as spin ice. Of particular interest at the moment are "quantum spin-ice" materials, where large quantum fluctuations may permit tunnelling between a macroscopic number of different classical ground states. Here we use zero-temperature quantum Monte Carlo simulations to show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilizing a unique "quantum-ice" ground state-a quantum liquid with excitations described by the Maxwell action of (3+1)-dimensional quantum electrodynamics. We further identify a competing ordered squiggle state, and show how both squiggle and quantum-ice states might be distinguished in neutron scattering experiments on a spin-ice material.
    Physical Review Letters 02/2012; 108(6):067204. · 7.73 Impact Factor
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    ABSTRACT: By applying external magnetic field the square-lattice antiferromagnet Ba2CoGe2O7 can be transformed to a chiral form, evidenced by large optical activity when the light is in resonance with spin excitations at sub-terahertz frequencies. We found that the magnetochiral effect, the absorption difference for the light beams propagating parallel and anti-parallel to the applied magnetic field, has an exceptionally large amplitude close to 100% and persists to fields up to 30,. All these features are ascribed to the magnetoelectric nature of spin excitations as they interact both with the electric and magnetic components of light. We observe a spin flop at 15,, that is consistent with our theoretical calculations.
  • 02/2012;
  • H.shiba, K.penc, F.mila
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    ABSTRACT: The strong coupling limit of one-dimensional correlated systems is nontrivial, but simple in some sense. Here we demonstrate it, discussing the wave functions for the 1D U→ +∞ Hubbard model, which are factorized as a direct product of the charge part and the spin part and determining the one-particle spectral functions explicitly.
    International Journal of Modern Physics B 01/2012; 13(05n06). · 0.46 Impact Factor
  • Physical Review Letters 01/2012; 108(2). · 7.73 Impact Factor

Publication Stats

1k Citations
349.21 Total Impact Points


  • 1994–2014
    • Hungarian Academy of Sciences
      • Institute for Solid State Physics and Optics
      Budapeŝto, Budapest, Hungary
  • 2012
    • University of Bristol
      Bristol, England, United Kingdom
  • 2011
    • ETH Zurich
      • Institute for Theoretical Physics
      Zürich, ZH, Switzerland
  • 2010
    • École Polytechnique Fédérale de Lausanne
      • Institut de théorie des phénomènes physiques
      Lausanne, VD, Switzerland
  • 2009
    • Max Planck Institute of Physics
      München, Bavaria, Germany
  • 2003–2005
    • University of Minho
      Bracara Augusta, Braga, Portugal
  • 2004
    • Instituto de Ciencia de Materiales de Madrid
      Madrid, Madrid, Spain
  • 2001
    • University of Lausanne
      • Institut de géophysique
      Lausanne, VD, Switzerland
  • 1995
    • Tokyo Institute of Technology
      • Department of Physics
      Tokyo, Tokyo-to, Japan
  • 1993–1994
    • Université de Neuchâtel
      • Institut de physique (IPH)
      Neuchâtel, NE, Switzerland