69 research outputs found
Universal Hall Response in Synthetic Dimensions
We theoretically study the Hall effect on interacting -leg ladder systems,
comparing different measures and properties of the zero temperature Hall
response in the limit of weak magnetic fields. Focusing on symmetric
interacting bosons and fermions, as relevant for e.g. typical synthetic
dimensional quantum gas experiments, we identify an extensive regime in which
the Hall imbalance is universal and corresponds to a classical
Hall resistivity for a large class of quantum phases. Away
from this high symmetry point we observe interaction driven phenomena such as
sign reversal and divergence of the Hall response.Comment: 13 pages, 9 figure
Admittance of the SU(2) and SU(4) Anderson quantum RC circuits
We study the Anderson model as a description of the quantum RC circuit for
spin-1/2 electrons and a single level connected to a single lead. Our analysis
relies on the Fermi liquid nature of the ground state which fixes the form of
the low energy effective model. The constants of this effective model are
extracted from a numerical solution of the Bethe ansatz equations for the
Anderson model. They allow us to compute the charge relaxation resistance Rq in
different parameter regimes. In the Kondo region, the peak in Rq as a function
of the magnetic field is recovered and proven to be in quantitative agreement
with previous numerical renormalization group results. In the
valence-fluctuation region, the peak in Rq is shown to persist, with a maximum
value of h/2e^2, and an analytical expression is obtained using perturbation
theory. We extend our analysis to the SU(4) Anderson model where we also derive
the existence of a giant peak in the charge relaxation resistance.Comment: 13 pages, 11 figure
Controlled parity switch of persistent currents in quantum ladders
We investigate the behavior of persistent currents for a fixed number of
noninteracting fermions in a periodic quantum ladder threaded by Aharonov-Bohm
and transverse magnetic fluxes and . We show that the coupling
between ladder legs provides a way to effectively change the ground-state
fermion-number parity, by varying . Specifically, we demonstrate that
varying by (one flux quantum) leads to an apparent fermion-number
parity switch. We find that persistent currents exhibit a robust
periodicity as a function of , despite the fact that leads to modifications of order of the energy spectrum, where
is the number of sites in each ladder leg. We show that these parity-switch and
periodicity effects are robust with respect to temperature and disorder,
and outline potential physical realizations using cold atomic gases and, for
bosonic analogs of the effects, photonic lattices.Comment: 5 pages, 4 figures + Supplemental Materia
Regularization of the tunneling Hamiltonian and consistency between free and bosonized fermions
Tunneling between a point contact and a one-dimensional wire is usually
described with the help of a tunneling Hamiltonian that contains a δ function
in position space. Whereas the leading-order contribution to the tunneling
current is independent of the way this δ function is regularized, higher-order
corrections with respect to the tunneling amplitude are known to depend on the
regularization. Instead of regularizing the δ function in the tunneling
Hamiltonian, one may also obtain a finite tunneling current by invoking the
ultraviolet cutoffs in a field-theoretic description of the electrons in the
one-dimensional conductor, a procedure that is often used in the literature.
For the latter case, we show that standard ultraviolet cutoffs lead to
different results for the tunneling current in fermionic and bosonized
formulations of the theory, when going beyond leading order in the tunneling
amplitude. We show how to recover the standard fermionic result using the
formalism of functional bosonization and revisit the tunneling current to
leading order in the interacting case
The Kondo Temperature of SU(4) Symmetric Quantum Dots
A path integral approach is used to derive a closed analytical expression for
the Kondo temperature of the SU(4) symmetrical Anderson model. In contrast to
the SU(2) case, the prefactor of the Kondo temperature is found to display a
peculiar orbital energy (gate voltage) dependence, reflecting the presence of
various SU(4) mixed valence fixed points. Our analytical expressions are tested
against and confirmed by numerical renormalization group computations.Comment: 4 pages, 5 figures and Suppl. Materia
Drude weight fluctuations in many-body localized systems
We numerically investigate the distribution of Drude weights of many-body
states in disordered one-dimensional interacting electron systems across the
transition to a many-body localized phase. Drude weights are proportional to
the spectral curvatures induced by magnetic fluxes in mesoscopic rings. They
offer a method to relate the transition to the many-body localized phase to
transport properties. In the delocalized regime, we find that the Drude weight
distribution at a fixed disorder configuration agrees well with the
random-matrix-theory prediction , although
the distribution width strongly fluctuates between disorder
realizations. A crossover is observed towards a distribution with different
large- asymptotics deep in the many-body localized phase, which however
differs from the commonly expected Cauchy distribution. We show that the
average distribution width , rescaled by ,
being the average level spacing in the middle of the spectrum and
the systems size, is an efficient probe of the many-body localization
transition, as it increases/vanishes exponentially in the delocalized/localized
phase.Comment: 5 pages, 3 figures + 1 page Supplemental Material, 2 figure
Giant Charge Relaxation Resistance in the Anderson Model
We investigate the dynamical charge response of the Anderson model viewed as
a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a
generalized Korringa-Shiba formula is derived at zero temperature, and the
charge relaxation resistance is expressed solely in terms of static
susceptibilities which are accessible by Bethe ansatz. We identify a giant
charge relaxation resistance at intermediate magnetic fields related to the
destruction of the Kondo singlet. The scaling properties of this peak are
computed analytically in the Kondo regime. We also show that the resistance
peak fades away at the particle-hole symmetric point.Comment: 4 pages, 1 figur
Ballistic-to-diffusive transition in spin chains with broken integrability
We study the ballistic-to-diffusive transition induced by the weak breaking
of integrability in a boundary-driven XXZ spin-chain. Studying the evolution of
the spin current density as a function of the system size ,
we show that, accounting for boundary effects, the transition has a non-trivial
universal behavior close to the XX limit. It is controlled by the scattering
length , where is the strength of the integrability
breaking term. In the XXZ model, the interplay of interactions controls the
emergence of a transient "quasi-ballistic" regime at length scales much shorter
than . This parametrically large regime is characterized by a strong
renormalization of the current which forbids a universal scaling, unlike the XX
model. Our results are based on Matrix Product Operator numerical simulations
and agree with perturbative analytical calculations.Comment: 13 pages, 9 figure
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