Non-Abelian Braiding of Lattice Bosons

We report on a numerical experiment in which we use time-dependent potentials to braid non-abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where $\nu$, the ratio of particles to flux quanta, is near 1/2, 1 or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for $\nu$ near $1$ and $3/2$, with Berry matrices respectively consistent with Ising and Fibonacci anyons. Near $\nu=1/2$, the braids commute.Comment: 5 pages, 1 figur

S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case

A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S-matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c /T_F is approximately 0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3 approximately 1.3 where n is the density and lambda the thermal wavelength, which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure

Effect of Doublon-Holon Binding on Mott transition---Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models

To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length $\xi_{\rm dh}$ and the minimum D-D exclusion length $\xi_{\rm dd}$. Generally, a Mott transition occurs when $\xi_{\rm dh}$ becomes comparable to $\xi_{\rm dd}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other ($\xi_{\rm dh}>\xi_{\rm dd}$); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.Comment: 16 pages, 22 figures, submitted to J. Phys. Soc. Jp

Simulating the exchange of Majorana zero modes with a photonic system

The realization of Majorana zero modes is in the centre of intense theoretical and experimental investigations. Unfortunately, their exchange that can reveal their exotic statistics needs manipulations that are still beyond our experimental capabilities. Here we take an alternative approach. Through the Jordan-Wigner transformation, the Kitaev's chain supporting two Majorana zero modes is mapped to the spin-1/2 chain. We experimentally simulated the spin system and its evolution with a photonic quantum simulator. This allows us to probe the geometric phase, which corresponds to the exchange of two Majorana zero modes positioned at the ends of a three-site chain. Finally, we demonstrate the immunity of quantum information encoded in the Majorana zero modes against local errors through the simulator. Our photonic simulator opens the way for the efficient realization and manipulation of Majorana zero modes in complex architectures

Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wavefunctions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wavefunction is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.Comment: 4 pages, 3 figures. Published versio

Magnetic excitations of the classical spin liquid MgCr2O4

We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr2O4 in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in paramagnetic MgCr2O4 are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly-correlated paramagnetic background. Our results also suggest that MgCr2O4 is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, which has implications for the magneto-structural phase transition in MgCr2O4

Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices

In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice model, without the need of additional laser fields. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams. We finally suggest several experiments to observe the properties of the Dirac field in the setup