arXiv subjects

Zlatko Papić

Publications and source records attributed to Zlatko Papić.

80 records · Page 5Linked to original sources

arXiv2017

Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders

Quantum spin liquids (QSLs) are long-range entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Here, we show, using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG) studies of concrete $SU(2)$ invariant spin models on honeycomb, triangular and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple-$Q$ spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Such ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. Our work provides a distinct unifying perspective on the emergence of CSLs, and suggests that materials with magnetic skyrmion crystal order might provide a good starting point to search for CSLs.

cond-mat.str-el↗

arXiv2017

Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect

We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems which are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that generalized pseudopotentials quantify the anisotropic contribution to the effective interaction potential, which can be particularly large in models of fractional Chern insulators.

cond-mat.str-el↗

arXiv2016

Geometric construction of Quantum Hall clustering Hamiltonians

Many fractional quantum Hall wave functions are known to be unique and highest-density zero modes of certain "pseudopotential" Hamiltonians. Examples include the Read-Rezayi series (in particular, the Laughlin, Moore-Read and Read-Rezayi Z_3 states), and more exotic non-unitary (Haldane-Rezayi, Gaffnian states) or irrational states (Haffnian state). While a systematic method to construct such Hamiltonians is available for the infinite plane or sphere geometry, its generalization to manifolds such as the cylinder or torus, where relative angular momentum is not an exact quantum number, has remained an open problem. Here we develop a geometric approach for constructing pseudopotential Hamiltonians in a universal manner that naturally applies to all geometries. Our method generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, valley) degrees of freedom. We demonstrate the utility of the approach through several examples, including certain non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and verify the method by numerically computing their entanglement properties.

cond-mat.str-el↗

arXiv2016

Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus

The $ν=12/5$ fractional quantum Hall plateau observed in $\mathrm{GaAs}$ semiconductor wells is a suspect in the search for non-Abelian Fibonacci anyons. Using the infinite density matrix renormalization group, we find clear evidence that fillings $ν= 12/5$ and $ν=13/5$ are in the $k = 3$ Read-Rezayi phase in the absence of particle-hole symmetry-breaking effects. The lowest energy charged excitation is identified as a non-Abelian Fibonacci anyon, distinguished from its Abelian counterpart by its local quadrupole moment. However, several experiments at $ν= 13/5$ observe a re-entrant integer quantum Hall effect, implying particle-hole symmetry is broken. We rule out spin polarization as the origin of the asymmetry. Further, we point out extremely close energetic competition between the Read-Rezayi phase and a re-entrant integer quantum Hall phase. This competition suggests that even small particle-hole symmetry-breaking perturbations can explain the experimentally observed asymmetry between $ν= 12/5$ and $13/5$. We find that at $ν=12/5$ Landau level mixing favors the Read-Rezayi phase over the re-entrant phase.

cond-mat.str-el↗

arXiv2016

Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid

Motivated by cold atom experiments on Chern insulators, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin-$1/2$ fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid (CSL) with gapped semion excitations. We formulate and study the Chern-Simons-Higgs field theory of the exotic CSL-to-tetrahedral spin crystallization transition.

cond-mat.str-el↗

arXiv2015

Competing Abelian and non-Abelian topological orders in $ν= 1/3+1/3$ quantum Hall bilayers

Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two sub-bands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling $ν= 1/3 + 1/3$. We first consider the Coulomb interaction at bilayer separation $d$, bilayer tunneling energy $Δ_\textrm{SAS}$, and individual layer width $w$, where we find a phase diagram which includes three competing Abelian phases: a bilayer-Laughlin phase (two nearly decoupled $ν= 1/3$ layers); a bilayer-spin singlet phase; and a bilayer-symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases have also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that $ν= 1/3 + 1/3$ systems merit further experimental study.

cond-mat.str-el↗

arXiv2014

Tunable Fractional Quantum Hall Phases in Bilayer Graphene

Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field electron interactions can cause spontaneous symmetry breaking within the spin and valley degrees of freedom, resulting in quantum Hall states (QHS) with complex order. Here we report fractional quantum Hall states (FQHS) in bilayer graphene which show phase transitions that can be tuned by a transverse electric field. This result provides a model platform to study the role of symmetry breaking in emergent states with distinct topological order.

cond-mat.mes-hall↗

arXiv2013

Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group

We determine the size of the elementary quasihole in $ν=1/3$ and $ν=7/3$ quantum Hall states via exact-diagonalization and density-matrix renormalization group calculations on the sphere and cylinder, using a variety of short- and long-range pinning potentials. The size of the quasihole at filling factor $ν=1/3$ is estimated to be $\approx 4\ell_B$, and that of $ν=7/3$ is $\approx 7\ell_B$, where $\ell_B$ is the magnetic length. In contrast, the size of the Laughlin quasihole, expected to capture the basic physics in these two states, is around $\approx 2.5\ell_B$. Our work supports the earlier findings that the quasihole in the first excited Landau level is significantly larger than in the lowest Landau level.

cond-mat.str-el↗