18 research outputs found
Numerical studies of ground state fidelity of the Bose-Hubbard model
We compute ground state fidelity of the one-dimensional Bose-Hubbard model at
unit filling factor. To this aim, we apply the DMRG algorithm to systems with
open and periodic boundary conditions. We find that fidelity differs
significantly in the two cases and study its scaling properties in the quantum
critical regime.Comment: 8 pages, 13 figure
Tunneling-Induced Restoration of the Degeneracy and the Time-Reversal Symmetry Breaking in Optical Lattices
We study the ground-state properties of bosons loaded into the -band of a
one dimensional optical lattice. We show that the phase diagram of the system
is substantially affected by the anharmonicity of the lattice potential. In
particular, for a certain range of tunneling strength, the full many-body
ground state of the system becomes degenerate. In this region, an additional
symmetry of the system, namely the parity of the occupation number of the
chosen orbital, is spontaneously broken. The state with nonvanishing staggered
angular momentum, which breaks the time-reversal symmetry, becomes the true
ground state of the system.Comment: 5 pages, 2 figure
Contracting a planar graph efficiently
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in O(1) time. Moreover, it can report all the arising self-loops and parallel edges.
By applying the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar graph problems, including decremental 2-vertex and 3-edge connectivity, and we show that using our data structure in a black-box manner, one obtains conceptually simple optimal algorithms for computing MST and 5-coloring in planar graphs