Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.Comment: 22 pages; 8 figure

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Transmission phase lapses in quantum dots: the role of dot-lead coupling asymmetry

Lapses of transmission phase in transport through quantum dots are ubiquitous already in the absence of interaction, in which case their precise location is determined by the signs and magnitudes of the tunnelling matrix elements. However, actual measurements for a quantum dot embedded in an Aharonov-Bohm interferometer show systematic sequences of phase lapses separated by Coulomb peaks -- an issue that attracted much attention and generated controversy. Using a two-level quantum dot as an example we show that this phenomenon can be accounted for by the combined effect of asymmetric dot-lead couplings (left lead/right lead asymmetry as well as different level broadening for different levels) and interaction-induced "population switching" of the levels, rendering this behaviour generic. We construct and analyse a mean field scheme for an interacting quantum dot, and investigate the properties of the mean field solution, paying special attention to the character of its dependence (continuous vs. discontinuous) on the chemical potential or gate voltage.Comment: 34 LaTeX pages in IOP format, 9 figures; misprints correcte

Hanbury-Brown and Twiss interference of anyons

We present a study of an Hanbury Brown and Twiss (HBT) interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate HBT cross-correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmuta- tion from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought as intermediate between bosons and fermions.Comment: Refs adde

Metric characterization of cluster dynamics on the Sierpinski gasket

We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring on cellular automata defined on an arbitrary structure. As a prototype for such systems we focus on the Ising model on a finite Sierpsinski Gasket, which is known to possess a complex thermodynamic behavior. Our algorithm requires the projection of evolving configurations into an appropriate partition space, where an information-based metrics (Rohlin distance) can be naturally defined and worked out in order to detect the changing and the stable components of clusters. The analysis highlights the existence of different temperature regimes according to the size and the rate of change of clusters. Such regimes are, in turn, related to the correlation length and the emerging "critical" fluctuations, in agreement with previous thermodynamic analysis, hence providing a non-trivial geometric description of the peculiar critical-like behavior exhibited by the system. Moreover, at high temperatures, we highlight the existence of different time scales controlling the evolution towards chaos.Comment: 20 pages, 8 figure

Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result

We give a rigorous proof of the existence of spontaneous magnetization at finite temperature for the Ising spin model defined on the Sierpinski carpet fractal. The theorem is inspired by the classical Peierls argument for the two dimensional lattice. Therefore, this exact result proves the existence of spontaneous magnetization for the Ising model in low dimensional structures, i.e. structures with dimension smaller than 2.Comment: 14 pages, 8 figure

What is the Thouless Energy for Ballistic Systems?

The Thouless energy, \Ec characterizes numerous quantities associated with sensitivity to boundary conditions in diffusive mesoscopic conductors. What happens to these quantities if the disorder strength is decreased and a transition to the ballistic regime takes place? In the present analysis we refute the intuitively plausible assumption that \Ec loses its meaning as an inverse diffusion time through the system at hand, and generally disorder independent scales take over. Instead we find that a variety of (thermodynamic) observables are still characterized by the Thouless energy.Comment: 4 pages REVTEX, uuencoded file. To appear in Physical Review Letter

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.Comment: 12 pages, 9 figure

Evolution of many-body systems under ancilla quantum measurements

Measurement-induced phase transitions are the subject of intense current research, both from an experimental and a theoretical perspective. We explore the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom (implemented using two additional sites), on which projective measurements are performed. We analyze the effect of repeated (``stroboscopic'') measurements on the dynamical correlations of interacting hard-core bosons in a one-dimensional chain. An important distinctive ingredient of the protocol is the fact that the detector ancillas are not re-initialized after each measurement step. The detector thus maintains memory of the accumulated influence by the measured correlated system. Initially, we consider a model in which the ancilla is coupled to a single lattice site. This setup allows obtaining information about the system through Rabi oscillations in the ancillary degrees of freedom, modulated by the ancilla-system interaction. The statistics of quantum trajectories exhibits a ``quantum-Zeno-valve effect'' that occurs when the measurement becomes strong, with sharp branching between low and high entanglement. We proceed by extending numerical simulations to the case of two ancillas and, then, to measurements on all sites. With this realistic measurement apparatus, we find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models. The dynamics features a broad distribution of the entanglement entropy.Comment: 23 pages, 17 figure

Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

We propose a method, based on matrix product states, for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by resolving time-dependent density correlations in the monitored system, we find important differences between different regions at the phase boundary. In particular, we observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.Comment: 13 pages, 11 figures, plus an appendix (13 pp., 1 figure). Comments welcom