arXiv subjects

K. Shtengel

Publications and source records attributed to K. Shtengel.

6 recordsLinked to original sources

arXiv2023

Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding

The quantum Hall states at filling factors $ν=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. The non-Abelian statistics of the latter has been predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of magnetic field in Fabry-Pérot interferometers using new high purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at $ν=7/2$. At both $ν=5/2$ and $7/2$ we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantly $π$ phase flips, consistent with either fermion parity change or change in the number of the enclosed $e/4$ quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.

cond-mat.mes-hall↗

arXiv2013

Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2

We show that the resistance of the v=5/2 quantum Hall state, confined to an interferometer, oscillates with magnetic field consistent with an Ising-type non-Abelian state. In three quantum Hall interferometers of different sizes, resistance oscillations at v=7/3 and integer filling factors have the magnetic field period expected if the number of quasiparticles contained within the interferometer changes so as to keep the area and the total charge within the interferometer constant. Under these conditions, an Abelian state such as the (3,3,1) state would show oscillations with the same period as at an integer quantum Hall state. However, in an Ising-type non-Abelian state there would be a rapid oscillation associated with the "even-odd effect" and a slower one associated with the accumulated Abelian phase due to both the Aharonov-Bohm effect and the Abelian part of the quasiparticle braiding statistics. Our measurements at v=5/2 are consistent with the latter.

cond-mat.mes-hall↗

arXiv2008

Kinetic ferromagnetism on a kagome lattice

We study strongly correlated electrons on a kagome lattice at 1/6 and 1/3 filling. They are described by an extended Hubbard Hamiltonian. We are concerned with the limit |t|<<V<<U with hopping amplitude t, nearest-neighbor repulsion V and on-site repulsion U. We derive an effective Hamiltonian and show, with the help of the Perron-Frobenius theorem, that the system is ferromagnetic at low temperatures. The robustness of ferromagnetism is discussed and extensions to other lattices are indicated.

cond-mat.str-el↗

arXiv2006

Correlated Fermions on a Checkerboard Lattice

A model of strongly correlated spinless fermions hopping on a checkerboard lattice is mapped onto a quantum fully-packed loop model. We identify a large number of fluctuationless states specific to the fermionic case. We also show that for a class of fluctuating states, the fermionic sign problem can be gauged away. This claim is supported by numerically evaluating the energies of the low-lying states. Furthermore, we analyze in detail the excitations at the Rokhsar-Kivelson point of this model thereby using the relation to the height model and the single-mode approximation.

cond-mat.str-el↗

arXiv1999

Lebowitz Inequalities for Ashkin-Teller Systems

We consider the Ashkin-Teller model with negative four-spin coupling but still in the region where the ground state is ferromagnetic. We establish the standard Lebowitz inequality as well as the extension that is necessary to prove a divergent susceptibility.

cond-mat.stat-mech↗

arXiv1998

The Mean Field Theory for Percolation Models of the Ising Type

The $q=2$ random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values as the critical point is approached from the high density side which vindicates the results of earlier studies. In particular, the exponent $\tilde γ^\prime$ which characterises the divergence of the average size of finite clusters is 1/2 and $\tildeν^\prime$, the exponent associated with the length scale of finite clusters is 1/4. The full collection of exponents indicates an upper critical dimension of 6. The standard mean field exponents of the Ising system are also present in this model ($ν^\prime = 1/2$, $γ^\prime = 1$) which implies, in particular, the presence of two diverging length scales. Furthermore, the finite cluster exponents are stable to the addition of disorder which, near the upper critical dimension, may have interesting implications concerning the generality of the disordered system/correlation length bounds.

cond-mat.stat-mech↗