806 research outputs found
Aharonov-Bohm phase as quantum gate in two-electron charge qubits
We analyze the singlet-triplet splitting on a planar array of quantum dots
coupled capacitively to a set of external voltage gates. The system is modelled
using an extended Hubbard Hamiltonian keeping two excess electrons on the
array. The voltage dependence of the low-energy singlet and triplet states is
analyzed using the Feshbach formalism. The formation of a well decoupled
two-level system in the ground state is shown to rely on the fact of having two
particles in the system. Coherent operation of the array is studied with
respect to single quantum bit operations. One quantum gate is implemented via
voltage controls, while for the necessary second quantum gate, a uniform
external magnetic field is introduced. The Aharonov-Bohm phases on the closed
loop tunnel connections in the array are used to effectively suppress the
tunneling, despite a constant tunneling amplitude in the structure. This allows
one to completely stall the qubit in any arbitrary quantum superposition,
providing full control of this interesting quantum system.Comment: 6 pages, 5 figures (submitted to PRB
Potential landscapes and induced charges near metallic islands in three dimensions
We calculate electrostatic potential landscapes for an external probe charge
in the presence of a set of metallic islands. Our numerical calculation in
three dimensions (3D)uses an efficient grid relaxation technique. The
well-known relaxation algorithm for solving the Poisson equation in two
dimensions is generalized to 3D. In addition,all charges on the system, free as
well as induced charges,are determined accurately and self-consistently to
satisfy the desired boundary conditions. This allows the straightforward
calculation of the potential on the outer boundary using the free space
electrostatic Green's function,as well as the calculation of the entire
capacitance matrix of the system. Physically interesting examples of nanoscale
systems are presented and analyzed.Comment: 6 pages, 6 figures, submitted to PR
Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
We show how spectral functions for quantum impurity models can be calculated
very accurately using a complete set of ``discarded'' numerical renormalization
group eigenstates, recently introduced by Anders and Schiller. The only
approximation is to judiciously exploit energy scale separation. Our derivation
avoids both the overcounting ambiguities and the single-shell approximation for
the equilibrium density matrix prevalent in current methods, ensuring that
relevant sum rules hold rigorously and spectral features at energies below the
temperature can be described accurately.Comment: 4 pages + 1 page appendix, 2 figure
Matrix product state approach for a two-lead, multi-level Anderson impurity model
We exploit the common mathematical structure of the numerical renormalization
group and the density matrix renormalization group, namely, matrix product
states, to implement an efficient numerical treatment of a two-lead,
multi-level Anderson impurity model. By adopting a star-like geometry, where
each species (spin and lead) of conduction electrons is described by its own
Wilson chain, instead of using a single Wilson chain for all species together,
we achieve a very significant reduction in the numerical resources required to
obtain reliable results. We illustrate the power of this approach by
calculating ground state properties of a four-level quantum dot coupled to two
leads. The success of this proof-of-principle calculation suggests that the
star geometry constitutes a promising strategy for future calculations the
ground state properties of multi-band, multi-level quantum impurity models.
Moreover, we show that it is possible to find an "optimal" chain basis,
obtained via a unitary transformation (acting only on the index distinguishing
different Wilson chains), in which degrees of freedom on different Wilson
chains become effectively decoupled from each other further out on the Wilson
chains. This basis turns out to also diagonalize the model's chain-to-chain
scattering matrix. We demonstrate this for a spinless two-lead model,
presenting DMRG-results for the mutual information between two sites located
far apart on different Wilson chains, and NRG results with respect to the
scattering matrix.Comment: extended version, 11 pages, 12 figure
Charge qubits and limitations of electrostatic quantum gates
We investigate the characteristics of purely electrostatic interactions with
external gates in constructing full single qubit manipulations. The quantum bit
is naturally encoded in the spatial wave function of the electron system.
Single-electron{transistor arrays based on quantum dots or insulating
interfaces typically allow for electrostatic controls where the inter-island
tunneling is considered constant, e.g. determined by the thickness of an
insulating layer. A representative array of 3x3 quantum dots with two mobile
electrons is analyzed using a Hubbard Hamiltonian and a capacitance matrix
formalism. Our study shows that it is easy to realize the first quantum gate
for single qubit operations, but that a second quantum gate only comes at the
cost of compromising the low-energy two-level system needed to encode the
qubit. We use perturbative arguments and the Feshbach formalism to show that
the compromising of the two-level system is a rather general feature for
electrostatically interacting qubits and is not just related to the specific
details of the system chosen. We show further that full implementation requires
tunable tunneling or external magnetic fields.Comment: 7 pages, 5 figures, submitted to PR
Non-Fermi liquid behavior in transport through Co doped Au chains
We calculate the conductance as a function of temperature through Au
monoatomic chains containing one Co atom as a magnetic impurity, and connected
to two conducting leads with a 4-fold symmetry axis. Using the information
derived from {\it ab initio} calculations, we construct an effective model
\Heff that hybridizes a 3d quadruplet at the Co site with two 3d
triplets through the hopping of 5d and 5d electrons of Au. The
quadruplet is split by spin anisotropy due to spin-orbit coupling. Solving
\Heff with the numerical renormalization group (NRG) % Wb: reverted my own
change we find that at low temperatures and the ground
state impurity entropy is , a behavior similar to the two-channel
Kondo model. Stretching the chain leads to a non Kondo phase, with the physics
of the underscreened Kondo model at the quantum critical point.Comment: Accepted in Physical Review Letter
Variational matrix product state approach to quantum impurity models
We present a unified framework for renormalization group methods, including
Wilson's numerical renormalization group (NRG) and White's density-matrix
renormalization group (DMRG), within the language of matrix product states.
This allows improvements over Wilson's NRG for quantum impurity models, as we
illustrate for the one-channel Kondo model. Moreover, we use a variational
method for evaluating Green's functions. The proposed method is more flexible
in its description of spectral properties at finite frequencies, opening the
way to time-dependent, out-of-equilibrium impurity problems. It also
substantially improves computational efficiency for one-channel impurity
problems, suggesting potentially \emph{linear} scaling of complexity for
-channel problems.Comment: revised version with application to Kondo model at large magnetic
field (5 pages, 2 figures
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