arXiv subjects

Alexander G. Abanov

Publications and source records attributed to Alexander G. Abanov.

58 records · Page 4Linked to original sources

arXiv2004

Double Occupancy Errors in Quantum Computing Operations: Corrections to Adiabaticity

We study the corrections to adiabatic dynamics of two coupled quantum dot spin-qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling causes double occupancy at the conclusion of an operation and constitutes a processing error. We model the gate operation with an effective two-level system, where non-adiabatic transitions correspond to double occupancy. The model is integrable and possesses three independent parameters. We confirm the accuracy of Dykhne's formula, a nonperturbative estimate of transitions, and discuss physically intuitive conditions for its validity. Our semiclassical results are in excellent agreement with numerical simulations of the exact time evolution. A similar approach applies to two-level systems in different contexts.

cond-mat.mes-hall↗

arXiv2003

Emptiness Formation Probability for the Anisotropic XY Spin Chain in a Magnetic Field

We study an asymptotic behavior of the probability of formation of a ferromagnetic string (referred to as EFP) of length "n" in a ground state of the one-dimensional anisotropic XY model in a transversal magnetic field as n goes to infinity. We find that it is exponential everywhere in the phase diagram of the XY model except at the critical lines where the spectrum is gapless. One of those lines corresponds to the isotropic XY model where EFP decays in a Gaussian way, as was shown in cond-mat/0106062. The other line is at the critical value of the magnetic field. There, we show that EFP is still exponential but acquires a non-trivial power-law prefactor with a universal exponent.

cond-mat.str-el↗

arXiv2002

On the probability of ferromagnetic strings in antiferromagnetic spin chains

We study the probability of formation of ferromagnetic string in the antiferromagnetic spin-1/2 XXZ chain. We show that in the limit of long strings with weak magnetization per site the bosonization technique can be used to address the problem. At zero temperature the obtained probability is Gaussian as a function of the length of the string. At finite but low temperature there is a crossover from the Gaussian behavior at intermediate lengths of strings to the exponential decay for very long strings. Although the weak magnetization per site is a necessary small parameter justifying our results, the extrapolation of obtained results to the case of maximally ferromagnetic strings is in qualitative agreement with known numerics and exact results. The effect of an external magnetic field on the probability of formation of ferromagnetic strings is also studied.

cond-mat.str-el↗

arXiv2000

Hopf term induced by fermions

We derive an effective action for Dirac fermions coupled to O(3) non-linear sigma-model (NLSM) through the Yukawa-type interaction. The nonperturbative (global) quantum anomaly of this model results in a Hopf term for the effective NLSM. We obtain this term using the ``embedding'' of the CP$^1$ model into the CP$^M$ generalization of the model which makes the quantum anomaly perturbative. This perturbative anomaly is calculated by means of a gradient expansion of a fermionic determinant and is given by the Chern-Simons term for an auxiliary gauge field.

hep-th↗