We perform the standard spin-wave analysis of triangluar Heisenberg quantum antiferromagnet. Contrary to variational calculation Anderson, we diagonalize exactly quadratic part Hamiltonian and obtain results in a 1/S expansion. compute ground-state staggered magnetization per spin energy. For (1/2, agreement with values Huse Elser suggests that trangular lattice has long-range magnetic order.

We study the quantum Hall phases that appear in dilute limit of rotating Bose-Einstein condensates. By exact diagonalization a spherical geometry we obtain ground state and low-lying excited states small number bosons as function filling fraction nu, ratio to vortices. show occurrence Jain principal sequence incompressible liquids for nu=2/3,3/4,4/3,5/4 addition Laughlin nu=1/2 well Pfaffian nu=1. give gap estimates by finite-size scaling both charged neutral excitations.

Vector-spin models with competing interactions have in general nontrivial ground states which completely break rotational invariance. We study the prototypical stacked triangular Heisenberg antiferromagnet by means of a O(3)\ifmmode\times\else\texttimes\fi{}O(2)/O(2) nonlinear \ensuremath{\sigma} model 2+\ensuremath{\epsilon} expansion. find dynamically generated O(4) symmetry. propose that such systems three dimensions first-order transition or second-order one either N=4 tricritical...

Quantum simulation can provide insight into physical systems that are too complex for traditional computing techniques. A new proposal describes how a quantum simulator could be realized using laser-trapped circular Rydberg atoms, whose long lifetimes and stability beneficial simulations lasting up to seconds.

Most of the present understanding S=1 quantum spin chains displaying Haldane gap is coming from so-called valence-bond-solid (VBS) Hamiltonian which has an exactly known ground state. We show that this point characterized by onset short-range incommensurate correlations in one-parameter family Hamiltonians ${\mathit{H}}_{\mathrm{\ensuremath{\theta}}}$=...

We present results of exact diagonalizations the isotropic antiferromagnetic S=1 Heisenberg chain by Lanczos method, for finite rings up to N=22 sites. The Haldane gap G(N) and ground state energy per site e(N) converge, with increasing N, faster than a power law. By VBS Shanks transformations, extrapolated values are G=0.41049(2) e=-1.401485(2). spin-spin correlation function is well fit exp(-r/xi)/sqrt(r) xi=6.2.

We find the finite width, i.e., layer thickness, of experimental quasi-two-dimensional systems produces a physical environment sufficient to stabilize Moore-Read Pfaffian state thought describe fractional quantum Hall effect at filling factor nu=5/2. This conclusion is based on exact calculations performed in spherical and torus geometries, studying wave function overlap ground degeneracy.

We analyze the possible existence of incommensurate correlations in t-J model as a function doping and ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$-${\mathit{J}}_{3}$ spin-1/2 Heisenberg frustration using exact diagonalization techniques on small lattices. For we found that when holes are introduced spin structure factor S(q) shifts position its maximum away from (\ensuremath{\pi},\ensuremath{\pi}). However, do not observe indications long-range order. The frustrated is analyzed spin-wave...

We study the S=1/2 Heisenberg antiferromagnet on a triangular lattice with both nearest-neighbor (${\mathit{J}}_{1}$) and next-to-nearest-neighbor (${\mathit{J}}_{2}$) couplings. have performed spin-wave analysis around classical ground state. At large (${\mathit{J}}_{2}$/${\mathit{J}}_{1}$) N\'eel state is destabilized system exhibits ``order from disorder'' phenomenon threefold-degenerate that spontaneously breaks rotational invariance. These results are in agreement Lanczos of 12-site...

Quantized resistance---the fractional quantum Hall effect---was used to uncover the mysterious so-called 5/2 state. Theoretical modeling suggests that spin-polarized electrons in GaAs semiconductors defining this state host a fundamentally new type of particle.

We have investigated Haldane's conjecture for the S = 2 antiferromagnetic quantum spin chain with nearest-neighbour exchange J. Using a density matrix renormalization group algorithm chains up to L 350 spins, we show that ground state has hidden topological order: physics of can be captured by valence bond solid description. also observe effective free spin-1 states at ends an open chain. find in thermodynamic limit gap Δ 0.085(5) J and correlation length ξ 49(1) lattice spacings isotropic...

We study a Heisenberg antiferromagnetic chain of spin S=1 with nearest-neighbor exchange interaction J and easy-plane single-ion anisotropy D. follow the splitting Haldane gap into two components as function anisotropy. Chains length up to 16 sites are studied by Lancz\"os method longer chains 32 have been investigated quantum Monte Carlo simulation for D/J=0.10, 0.15, 0.20, 0.25. A careful finite-size scaling treatment our data leads values that directly relevant interpretation experiments...

The fractional quantum Hall effect (FQHE) in the second orbital Landau level at even-denominator filling factor of 5/2 remains enigmatic and motivates our work. We theoretically consider quasi-two-dimensional (2D) nature experimental system on a number FQH states (filling factors: 1/3, 1/5, 1/2) lowest, second, third levels (LLL, SLL, TLL, respectively) by calculating wave-function overlap, as function quasi-2D layer thickness, between exact ground state model Hamiltonian consensus...

Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect is dominated by long-range Coulomb interactions which are invariant under rotations spin-valley space. This SU(4) symmetry spontaneously broken at most filling factors, also weakly atomic scale valley-dependent valley-exchange coupling constants $g_{z}$ $g_{\perp}$. In this paper we demonstrate that when $g_{z}=-g_{\perp}$ an exact SO(5) survives unifies...

The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems is explained by the emergent composite fermions (CF) out of ordinary electrons. It possible to write down explicit wavefunctions explaining many if not all FQHE states. In bilayer there a regime at integer filling lowest Landau level that displays spontaneous breakdown U(1) relative phase between two layers. This can be seen as interlayer coherence (ILC) terms Recent experiments double layer samples...

We discuss the magnetic ground state and properties of a frustrated two-dimensional classical Heisenberg model interacting hexagonal clusters spins. The energy states is found exactly for arbitrary values ${J}_{1}$ (intracluster couplings) ${J}_{2}$ (intercluster couplings). Our main results concern region phase diagram, where we show that set has degeneracy larger than due to global rotation symmetry. Furthermore, manifold does not have fixed total magnetization: there range allowed values....

We study the Heisenberg antiferromagnet on a triangular lattice with nearest- (J) and next-nearest- (\ensuremath{\alpha}J) neighbor exchange interactions. For \ensuremath{\alpha}>1/8, this system is known to have an accidental degeneracy at classical level, which lifted by quantum fluctuations (``order from disorder'' phenomena). use large-S perturbation theory confirm previous spin-wave numerical observations that always select planar arrangement: There thus no chiral symmetry breaking....

We have studied magnetic excitations in the dimerized spin-Peierls phase of CuGeO3, by high resolution inelastic neutron scattering. measured well-defined spin triplet dispersive mode which is gapped throughout whole Brillouin zone. also observed that this separated an unexpected second gap order 2 meV from a continuum extending to higher energy. The first (or 'triplet gap') and its associated due breaking singlet dimer into delocalized triplet. propose 'solitonic correspond dissociation two...

The nonperturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. system neutral in a rapidly rotating atomic trap is equivalent to charged coupled magnetic field, which has opened up the possibility fractional quantum Hall for with short-range interaction. Motivated by composite fermion theory electrons, we test idea that map onto noninteracting spinless fermions carrying one vortex each, comparing wave functions incorporating this...

We give a physical description in terms of percolation theory the phase transition that occurs when disorder increases random antiferromagnetic spin-1 chain between gapless with hidden topological order and singlet phase. study statistical properties clusters by numerical simulations, we compute exact exponents characterizing real-space renormalization group calculation.

We study the quantum Hall phases that appear in fast-rotation limit for Bose-Einstein condensates of spinless bosonic atoms. use exact diagonalization a spherical geometry to obtain low-lying states small number bosons as function angular momentum. This allows us understand or guess physics at given filling fraction $\ensuremath{\nu}$, ratio vortices. is also factor lowest Landau level. In addition well-known Bose-Laughlin state $\ensuremath{\nu}=1∕2$, we give evidence Jain principal...

We have investigated Haldane's conjecture for the S=2 antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm chains up to L=350 spins, we find in thermodynamic limit finite gap of \ensuremath{\Delta}=0.085(5)J and spin-spin correlation length \ensuremath{\xi}=49(1) lattice spacings. confirmed value by zero-temperature Monte Carlo study. show that ground state has hidden topological order is revealed nonlocal string...