Kwon Park

Ground States of Quantum Antiferromagnets in Two Dimensions

Abstract We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and Jalabert (1990, Mod. Phys. Lett. B4, 1043). The minimal model for square lattice antiferromagnets is a lattice discretization of the quantum nonlinear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with Neel order at weak coupling and a confining paramagnetic ground state with bond charge (e.g., spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry groups is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring noncollinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S=1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models.

Bond operator theory of doped antiferromagnets: from Mott insulators with bond-centered charge order, to superconductors with nodal fermions

The ground states and excitations of two-dimensional insulating and doped Mott insulators are described by a bond-operator formalism. While the method represents the degrees of freedom of an arbitrary antiferromagnet exactly, it is especially suited to systems in which there is a natural pairing of sites into bonds, as in states with spontaneous or explicit spin-Peierls order (or bond-centered charge order). In the undoped insulator, as discussed previously, we obtain both paramagnetic and magnetically ordered states. We describe the evolution of superconducting order in the ground state with increasing doping\char22{}at low doping, the superconductivity is weak, can coexist with magnetic order, and there are no gapless spin-1/2 fermionic excitations; at high doping, the magnetic order is absent and we obtain a BCS d-wave superconductor with gapless spin-1/2 nodal fermions. We present the critical theory describing the onset of these nodal fermionic excitations. We discuss the evolution of the spin spectrum and obtain regimes where a spin-1 exciton contributes a sharp resonance in the dynamic spin susceptibility. We also discuss the experimental consequences of low-energy, dynamically fluctuating spin-Peierls order in an isotropic

Correlation effects on 3D topological phases: from bulk to boundary.

{\mathrm{CuO}}_{2}

Competing crystal phases in the lowest Landau level.

plane\char22{}we compute consequences for the damping and dispersion of an optical phonon involving primarily the O ions and compare the results with recent neutron scattering measurements of phonon spectra.

Chirality in quantum computation with spin cluster qubits.

Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit a quantized electromagnetic response and/or protected surface states. We examine such phenomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators, with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean-field theory, a method that incorporates quantum many-body effects and allows us to evaluate the magnetoelectric topological response coefficient in correlated systems. This invariant is used to unravel the presence of an interacting axion insulator absent within a simple mean-field study. We corroborate our bulk results by studying the evolution of the topological boundary states in the presence of interactions. Consequences for experiments and for the search for correlated materials with symmetry-protected topological order are given.

Coherent tunneling in exciton condensates of bilayer quantum Hall systems

We show that the solid phase between the 1/5 and 2/9 fractional quantum Hall states arises from an extremely delicate interplay between type-1 and type-2 composite fermion crystals, clearly demonstrating its nontrivial, strongly correlated character. We also compute the phase diagram of various crystals occurring over a wide range of filling factors and demonstrate that the elastic constants exhibit nonmonotonic behavior as a function of the filling factor, possibly leading to distinctive experimental signatures that can help mark the phase boundaries separating different kinds of crystals.

Dielectric breakdown via emergent nonequilibrium steady states of the electric-field-driven Mott insulator

We study corrections to the Heisenberg interaction between several lateral, single-electron quantum dots. We show, using exact diagonalization, that three-body chiral terms couple triangular configurations to external sources of flux rather strongly. The chiral corrections impact single-qubit encodings utilizing loops of three or more Heisenberg coupled quantum dots.

Bond and Néel order and fractionalization in ground states of easy-plane antiferromagnets in two dimensions

Due to strong interlayer correlations, the bilayer quantum Hall system is a single coherent system as a whole rather than a weakly coupled set of two independent systems, which makes conventional tunneling theories inapplicable. In this paper, we develop a theory of interlayer tunneling in coherent exciton condensates of bilayer quantum Hall systems at total filling factor

Doped valence-bond solid and superconductivity on the Shastry-Sutherland lattice

{\ensuremath{\nu}}_{T}=1

Superconducting order parameter for the even-denominator fractional quantum Hall effect

. One of the most important consequences of our theory is that the zero-bias interlayer tunneling conductance peak is strongly enhanced, but fundamentally finite even at zero temperature. We explicitly compute the height of the conductance peak as a function of interlayer distance, which is compared with experiment. It is emphasized that the interlayer distance dependence of the conductance peak is one of the key properties distinguishing between the spontaneous coherence due to many-body effects of the Coulomb interaction and the induced coherence due to the single-particle tunneling gap. It is also emphasized that, though the strongly enhanced tunneling conductance originates from the interlayer phase coherence, it is not the usual Josephson effect. We propose an experimental setup for the true Josephson effect in counterflowing current measurements for a coupled set of two bilayer quantum Hall systems, which is a more precise analogy with the real Josephson effect in superconductivity.