arXiv subjects

Richard Berkovits

Publications and source records attributed to Richard Berkovits.

At least 37 records · Page 2Linked to original sources

arXiv2013

Enhanced compressibility due to repulsive interaction in the Harper model

We study the interplay between repulsive interaction and an almost staggered on-site potential in one-dimension. Specifically, we address the Harper model for spinless fermions with nearest-neighbor repulsion, close to half-filling. Using density matrix renormalization group (DMRG), we find that, in contrast to standard behavior, the system becomes more compressible as the repulsive interaction is increased. By generating a low-energy effective model, we unveil the effect of interactions using mean-field analysis: the density of a narrow band around half-filling is anti-correlated with the on-site potential, whereas the density of lower occupied bands follows the potential and strengthens it. As a result, the states around half-filling are squeezed by the background density, their band becomes flatter, and the compressibility increases.

cond-mat.mes-hall↗

arXiv2013

Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization

The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitation shows a crossover from metallic behavior at short sample sizes to localized at longer length. The dependence of the crossover as function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many particle critical energy in the vicinity of the Fermi energy. Implications of these results to experiments are discussed.

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arXiv2013

Two particle excited states entanglement entropy in a one-dimensional ring

The properties of the entanglement entropy (EE) of two particle excited states in a one-dimensional ring are studied. For a clean system we show analytically that as long as the momenta of the two particles are not close, the EE is twice the value of the EE of any single particle state. For almost identical momenta the EE is lower than this value. The introduction of disorder is numerically shown to lead to a decrease in the median EE of a two particle excited state, while interactions (which have no effect for the clean case) mitigate the decrease. For a ring which is of the same size as the localization length, interaction increase the EE of a typical two particle excited state above the clean system EE value.

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arXiv2012

Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires

We study a quantum phase transition which occurs in a system composed of two impurities (or quantum dots) each coupled to a different interacting (Luttinger-liquid) lead. While the impurities are coupled electrostatically, there is no tunneling between them. Using a mapping of this system onto a Kondo model, we show analytically that the system undergoes a Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the Luttinger liquid parameter in the leads and the dot-lead interaction. The phase with low values of the Luttinger-liquid parameter is characterized by an abrupt switch of the population between the impurities as function of a common applied gate voltage. However, this behavior is hard to verify numerically since one would have to study extremely long systems. Interestingly though, at the transition the entanglement entropy drops from a finite value of $\ln(2)$ to zero. The drop becomes sharp for infinite systems. One can employ finite size scaling to extrapolate the transition point and the behavior in its vicinity from the behavior of the entanglement entropy in moderate size samples. We employ the density matrix renormalization group numerical procedure to calculate the entanglement entropy of systems with lead lengths of up to 480 sites. Using finite size scaling we extract the transition value and show it to be in good agreement with the analytical prediction.

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arXiv2012

Entanglement entropy in one-dimensional disordered interacting system: The role of localization

The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on length scale exceeding the localization length. This is verified by numerically calculating the EE for an ensemble of disordered realizations using density matrix renormalization group (DMRG). A heuristic expression describing the dependence of the EE on the localization length, which takes into account finite size effects, is proposed. This is used to extract the localization length as function of the interaction strength. The localization length dependence on the interaction fits nicely with the expectations.

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arXiv2011

A dynamical phase transition in ferromagnetic granular materials

We study, using simulations the dynamical properties of complex ferromagnetic granular materials. The system of grains is modeled by a disordered two-dimensional lattice in which the grains are embedded, while the magnitude and direction of the easy axis are random. Using the monte-carlo method we track the dynamics of the magnetic moments of the grains. We observe a transition of the system from a macroscopic blocked (ferromagnetic) phase at low temperature in which the grain's magnetic moment do not flip to the other direction to an unblocked (superparamagnetic) phase at high temperature in which the magnetic moment is free to rotate. Our results suggest that this transition exhibits the characteristics of a second order phase transition such as the appearance of a giant cluster of unblocked grains which is fractal at the critical temperature, a peak in the size of the second largest cluster at the same temperature and a power law distribution of cluster sizes near the criticality.

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arXiv2011

Interacting resonant level coupled to a Luttinger liquid: Population vs. density of states

We consider the problem of a single level quantum dot coupled to the edge of a one-dimensional Luttinger liquid wire by both a hopping term and electron-electron interactions. Using bosonization and Coulomb gas mapping of the Anderson-Yuval type we show that thermodynamic properties of the level, in particular, its occupation, depend on the various interactions in the system only through a single quantity --- the corresponding Fermi edge singularity exponent. However, dynamical properties, such as the level density of states, depend in a different way on each type of interaction. Hence, we can construct different models, with and without interactions in the wire, with equal Fermi edge singularity exponents, which have identical population curves, although they originate from very different level densities of states. The latter may either be regular or show a power-law suppression or enhancement at the Fermi energy. These predictions are verified to a high degree of accuracy using the density matrix renormalization group algorithm to calculate the dot occupation, and classical Monte Carlo simulations on the corresponding Coulomb gas model to extract the level density of states.

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arXiv2011

Capacitance of a resonant level coupled to Luttinger liquids

In this paper we study the differential capacitance of a single-level quantum dot attached to quantum wires in the Luttinger liquid phase, or to fractional quantum Hall edges, by both tunneling and interactions. We show that logarithmic or even power-law divergence of the capacitance at low temperatures may result in a substantial region of the parameter space (including the $ν=1/3$ filling). This behavior is a manifestation of generalized two channel Kondo physics, and can be used to extract Luttinger liquid parameters from thermodynamic measurements.

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arXiv2011

Density of states of a dissipative quantum dot coupled to a quantum wire

We examine the local density of states of an impurity level or a quantum dot coupled to a fractional quantum Hall edge, or to the end of a single one-dimensional Luttinger-liquid lead. Effects of an Ohmic dissipative bath are also taken into account. Using both analytical and numerical techniques we show that, in general, the density of states exhibits power-law frequency dependence near the Fermi energy. In a substantial region of the parameter space it simply reflects the behavior of the tunneling density of states at the end of a Luttinger-liquid, and is insensitive either to the value of the dot-lead interaction or to the strength of dissipation; otherwise it depends on these couplings too. This behavior should be contrasted with the thermodynamic properties of the level, in particular, its occupancy, which were previously shown to depend on the various interactions in the system only through the corresponding Fermi edge singularity exponent, and thus cannot display any Luttinger-liquid specific power-law. Hence, we can construct different models, some with and some without interactions in the wire (but with equal Fermi edge singularity exponents), which would have very different level densities of states, although they all result in the same level population vs. energy curves.

cond-mat.mes-hall↗

arXiv2011

Duality between different geometries of a resonant level in a Luttinger liquid

We prove an exact duality between the side-coupled and embedded geometries of a single level quantum dot attached to a quantum wire in a Luttinger liquid phase by a tunneling term and interactions. This is valid even in the presence of a finite bias voltage. Under this relation the Luttinger liquid parameter g goes into its inverse, and transmittance maps onto reflectance. We then demonstrate how this duality is revealed by the transport properties of the side-coupled case. Conductance is found to exhibit an antiresonance as a function of the level energy, whose width vanishes (enhancing transport) as a power law for low temperature and bias voltage whenever g>1, and diverges (suppressing transport) for g<1. On resonance transmission is always destroyed, unless g is large enough.

cond-mat.mes-hall↗

arXiv2011

Population switching and charge sensing in quantum dots: A case for a quantum phase transition

A broad and a narrow level of a quantum dot connected to two external leads may swap their respective occupancies as a function of an external gate voltage. By mapping this problem onto a multi-flavored Coulomb-gas we show that such population switching is not abrupt. However, trying to measure it by adding a third electrostatically coupled lead may render this switching an abrupt first order quantum phase transition. This is related to the interplay of the Mahan mechanism versus the Anderson orthogonality catastrophe, in similitude to the Fermi edge singularity. A concrete setup for experimental observation of this effect is also suggested.

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arXiv2011

Interacting resonant level coupled to a Luttinger liquid: Universality of thermodynamic properties

We investigate a model of a single resonant level coupled to the edge of a quantum wire in the Luttinger liquid phase or to the middle of a chiral Luttinger liquid via both tunneling and a contact interaction. Utilizing the Yuval-Anderson approach, we map this model onto a classical 1D Coulomb gas in which all the details of both the interactions in the lead and the level-lead interaction enter only through the corresponding Fermi-edge singularity exponent, which we explicitly evaluate using the Bethe ansatz solution for a particular model of the lead. Thus the population, dynamical capacitance and level entropy are universal in the sense of being equal for models with interactions differing in magnitude and even in sign. We demonstrate this to hold quantitatively using density matrix renormalization group calculations. Since the Coulomb gas description is of the single channel Kondo type, we infer that the universality we found implies that Luttinger liquid physics has no qualitative effect on these properties, in contrast with perturbative results.

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arXiv2010

Coexistence of Coulomb blockade and zero bias anomaly in a strongly coupled quantum dot

The current-voltage characteristics through a metallic quantum dot which is well coupled to a metallic lead are measured. It is shown that the I-V curves are composed of two contributions. One is a suppression of the tunneling conductivity at the Fermi level and the second is an oscillating feature which shifts with gate voltage. The results indicate that Zero-Bias-Anomaly and Coulomb Blockade phenomena coexist in an asymmetric strongly coupled quantum dot.

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arXiv2009

The effect of a small magnetic flux on the metal-insulator transition

We numerically show that very small magnetic flux can significantly shift the metal-insulator transition point in a disordered electronic system. The shift we observe for the 3d Anderson model obeys a power law as predicted by Larkin and Khmel'nitskii (1981). We compute the exponent and find good agreement with the prediction. However, the power law holds only for much smaller magnetic fields than has been previously assumed, and is accompanied by a large prefactor, leading to a surprising strong dependence of the transition point on the applied magnetic field. Furthermore, we show that the critical level-spacing distribution is identical in the presence and absence of a magnetic field if hard-wall boundary conditions are applied. This result is surprising since both cases belong to different universality classes and different distributions have been reported for periodic boundary conditions.

cond-mat.dis-nn↗

arXiv2008

Transmission phase of a quantum dot: Testing the role of population switching

We propose a controlled experiment to clarify the physical mechanism causing phase lapses of the amplitude for electron transmission through nanoscale devices. Such lapses are generically observed in valleys between adjacent Coulomb--blockade peaks. The experiment involves two quantum dots embedded in the same arm of an Aharonov--Bohm interferometer. It offers a decisive test of "population switching", one of the leading contenders for an explanation of the phenomenon.

cond-mat.mes-hall↗

arXiv2008

Significant g-factor values of a two-electron ground state in quantum dots with spin-orbit coupling

The magnetization of semiconductor quantum dots in the presence of spin-orbit coupling and interactions is investigated numerically. When the dot is occupied by two electrons we find that a level crossing between the two lowest many-body eigenstates may occur as a function of the spin-orbit coupling strength. This level crossing is accompanied by a non-vanishing magnetization of the ground-state. Using first order perturbation theory as well as exact numerical diagonalization of small clusters we show that the tendency of interactions to cause Stoner-like instability is enhanced by the SO coupling. The resulting g-factor can have a significant value, and thus may influence g-factor measurements. Finally we propose an experimental method by which the predicted phenomenon can be observed.

cond-mat.str-el↗

arXiv2008

Finite doping of a one-dimensional charge density wave: solitons vs. Luttinger liquid charge density

The effects of doping on a one-dimensional wire in a charge density wave state are studied using the density-matrix renormalization group method. We show that for a finite number of extra electrons the ground state becomes conducting but the particle density along the wire corresponds to a charge density wave with an incommensurate wave number determined by the filling. We find that the absence of the translational invariance can be discerned even in the thermodynamic limit, as long as the number of doping electrons is finite. Luttinger liquid behavior is reached only for a finite change in the electron filling factor, which for an infinite wire corresponds to the addition of an infinite number of electrons. In addition to the half filled insulating Mott state and the conducting states, we find evidence for subgap states at fillings different from half filling by a single electron or hole. Finally, we show that by coupling our system to a quantum dot, one can have a discontinuous dependence of its population on the applied gate voltage in the thermodynamic limit, similarly to the one predicted for a Luttinger liquid without umklapp processes.

cond-mat.str-el↗

arXiv2007

A generation-based particle-hole density-matrix renormalization group study of interacting quantum dots

The particle-hole version of the density-matrix renormalization-group method (PH-DMRG) is utilized to calculate the ground-state energy of an interacting two-dimensional quantum dot. We show that a modification of the method, termed generation-based PH-DMRG, leads to significant improvement of the results, and discuss its feasibility for the treatment of large systems. As another application we calculate the addition spectrum.

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