
Quantum Ice Water ice comprises a looselypacked lattice of water molecules, held together by hydrogen bonds. This structure hides a puzzle — chemical bonding alone does not select a unique orientation of the water molecules. As a result each water molecule has a finite ground state entropy s_{0} ≈ k_{B} log(3/2), in violation of the third law of thermodynamics. The same degeneracy, and the same contradiction, arises in problems of frustrated charge order on the pyrochlore lattice, and in the family of rareearth 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 different ice states. Here we show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilising a unique "quantum ice" ground state. This quantum ice has excitations described by the Maxwell action of 3+1 – dimensional quantum electrodynamics. We further show how such a quantum ice state might be distinguished in neutron scattering experiments on a spin ice material.
Nic Shannon, Olga Sikora, Frank Pollmann, Karlo Penc, Peter Fulde, Phys. Rev. Lett. 108, 067204/15 (2012)


Exact ground states with deconfined gapless excitations for the 3 leg spin1/2 tube We consider a 3leg spin1/2 ladder with periodic boundary conditions (a spin tube) with a Hamiltonian given by two projection operators, one on the triangles, and the other on the square plaquettes on the side of the tube, that can be written in terms of Heisenberg and four spin ring exchange interactions. Depending on the relative strength of these two operators, we identify 3 phases: (i) for strongly antiferromagnetic exchange on the triangles, an exact dimerized ground state wave function with a gapped spectrum can be given as an alternation of spin and chirality valence bonds between nearest triangles; (ii) for ferromagnetic exchanges on the triangle we recover the phase of the spin3/2 Heisenberg chain; (iii) between these two phases a gapless incommensurate phase exists. Furthermore, we explicitly construct an exact ground state wave function with two deconfined domain walls and gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phase.
Miklós Lajkó, Philippe Sindzingre, Karlo Penc, arXiv:1107.5501


Simultaneous dimerization and SU(4) symmetry breaking of 4color fermions on the square lattice Using infinite project entangled pair states (iPEPS), exact diagonalization, and flavorwave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast to its SU(2) and SU(3) counterparts, which develop Neel and threesublattice stripelike longrange order. Since the ground state of a dimer is not a singlet for SU(4) but a 6dimensional irrep, this leaves the door open for further symmetry breaking. We provide evidence that, unlike in SU(4) ladders, where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is additionally broken, leading to a gapless spectrum in spite of the broken translational symmetry.
Philippe Corboz, Andreas M. Läuchli, Karlo Penc, Matthias Troyer, Frédéric Mila, arXiv:1108.2857


Effect of DzyaloshinskiiMoriya interactions on the phase diagram and magnetic excitations of SrCu_{2}(BO_{3})_{2} The orthogonal dimer structure of the SrCu_{2}(BO_{3})_{2} spin1/2 magnet provides a realization of the ShastrySutherland model. Using a dimerproduct variational wave function, we map out the phase diagram of the ShastrySutherland model including anisotropies. Based on the variational solution, we construct a bondwave approach to obtain the excitation spectra as a function of the magnetic field. The characteristic features of the experimentally measured neutron and ESR spectra are reproduced, like the anisotropyinduced zerofield splittings and the persistent gap at higher fields.
Judit Romhányi, Keisuke Totsuka, Karlo Penc, Phys. Rev. B 83, 024413 (2011).


ThreeSublattice Ordering of the SU(3) Heisenberg Model of ThreeFlavor Fermions on the Square and Cubic Lattices Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops threesublattice longrange order. This surprising pattern for a bipartite lattice with only nearestneighbor interactions is shown to be the consequence of a subtle quantum orderbydisorder mechanism. By contrast, thermal fluctuations favor twosublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mottinsulating states of threeflavor fermionic atoms in optical lattices are discussed.
Tamás A. Tóth, Andreas M. Läuchli, Frédéric Mila, Karlo Penc, Phys. Rev. Lett 105, 265301 (2010).


A quantum liquid with deconfined fractional excitations in three dimensions Excitations which carry ``fractional" quantum numbers are known to exist in one dimension in polyacetylene, and in two dimensions, in the fractional quantum Hall effect. Fractional excitations have also been invoked to explain the breakdown of the conventional theory of metals in a wide range of threedimensional materials. However the existence of fractional excitations in three dimensions remains highly controversial. In this Letter we report direct numerical evidence for the existence of a quantum liquid phase supporting fractional excitations in a concrete, threedimensional microscopic model  the quantum dimer model on a diamond lattice. We demonstrate explicitly that the energy cost of separating fractional monomer excitations vanishes in this liquid phase, and that its energy spectrum matches that of the Coulomb phase in (3+1) dimensional quantum electrodynamics.
Olga Sikora, Frank Pollman, Nic Shannon, Karlo Penc, Peter Fulde, Phys. Rev. Lett. 103, 247001 (2009)
