176 research outputs found
Sine-square deformation of free fermion systems in one and higher dimensions
We study free fermion systems with the sine-square deformation (SSD), in
which the energy scale of local Hamiltonians is modified according to the
scaling function f(x)=sin^2[\pi(x-1/2)/L], where x is the position of the local
Hamiltonian and L is the length of the system in the x direction. It has been
revealed that when applied to one-dimensional critical systems the SSD realizes
the translationally-invariant ground state which is the same as that of the
uniform periodic system. In this paper, we propose a simple theory to explain
how the SSD maintains the translational invariance in the ground-state wave
function. In particular, for a certain one-dimensional system with SSD, it is
shown that the ground state is exactly identical with the Fermi sea of the
uniform periodic chain. We also apply the SSD to two-dimensional systems and
show that the SSD is able to suppress the boundary modulations from the open
edges extremely well, demonstrating that the SSD works in any dimensions and in
any directions.Comment: 9 pages, 6 figures. v2: accepted versio
Levitation and percolation in quantum Hall systems with correlated disorder
We investigate the integer quantum Hall system in a two dimensional lattice
model with spatially correlated disorder by using the efficient method to
calculate the Chern number proposed by Fukui \textit{et al}. Distribution of
charge density indicates that the extended states at the center of each Landau
band have percolating current paths, which are topologically equivalent to the
edge states that exist in a system with boundaries. As increasing the strength
of disorder, floating feature is observed in an averaged Hall conductance as a
function of filling factor. Its relation to the observed experiments is also
discussed
U(1) symmetry breaking in one-dimensional Mott insulator studied by the Density Matrix Renormalization Group method
A new type of external fields violating the particle number preservation is
studied in one-dimensional strongly correlated systems by the Density Matrix
Renormalization Group method. Due to the U(1) symmetry breaking, the ground
state has fluctuation of the total particle number, which implies injection of
electrons and holes from out of the chain. This charge fluctuation can be
relevant even at half-filling because the particle-hole symmetry is preserved
with the finite effective field. In addition, we discuss a quantum phase
transition obtained by considering the symmetry-breaking fields as a mean field
of interchain-hopping.Comment: 7 pages, 4 figure
Topological quantum phase transition in the BEC-BCS crossover phenomena
A crossover between the Bose Einstein condensation (BEC) and BCS
superconducting state is described topologically in the chiral symmetric
fermion system with attractive interaction. Using a local Z_2 Berry phase, we
found a quantum phase transition between the BEC and BCS phases without
accompanying the bulk gap closing.Comment: 4 pages, 5 figure
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