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arXiv:2401.04809 · Physical Review Letters

Robust Spectral π Pairing in the Random-Field Floquet Quantum Ising Model

Harald Schmid, Alexander-Georg Penner, Kang Yang, L. I. Glazman, Felix von Oppen

Published May 20, 2024• 11 citations
arXivHTMLPDF

Abstract

Motivated by an experiment on a superconducting quantum processor [X. Mi et al., Science 378, 785 (2022).SCIEAS0036-807510.1126/science.abq5769], we study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The pairings derive from Majorana zero and π modes when writing the spin model in Jordan-Wigner fermions. Both splittings have log-normal distributions with random transverse fields. In contrast, random longitudinal fields affect the zero and π splittings in drastically different ways. While zero pairings are rapidly lifted, the π pairings are remarkably robust, or even strengthened, up to vastly larger disorder strengths. We explain our results within a self-consistent Floquet perturbation theory and study implications for boundary spin correlations. The robustness of π pairings against longitudinal disorder may be useful for quantum information processing.

DOI
10.1103/physrevlett.132.210401

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Motivated by an experiment on a superconducting quantum processor [X. Mi et al., Science 378, 785 (2022).SCIEAS0036-807510.1126/science.abq5769], we study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The pairings derive from Majorana zero and π modes when writing the spin model in Jordan-Wigner fermions. Both splittings have log-normal distributions with random transverse fields. In contrast, random longitudinal fields affect the zero and π splittings in drastically different ways. While zero pairings are rapidly lifted, the π pairings are remarkably robust, or even strengthened, up to vastly larger disorder strengths. We explain our results within a self-consistent Floquet perturbation theory and study implications for boundary spin correlations. The robustness of π pairings against longitudinal disorder may be useful for quantum information processing.
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Floquet time crystals are characterized by the subharmonic behavior of temporal correlation functions. Studying the paradigmatic time crystal based on the disordered Floquet quantum Ising model, we show that its temporal spin correlations are directly related to spectral characteristics and that this relation provides analytical expressions for the correlation function of finite chains, which compare favorably with numerical simulations. Specifically, we show that the disorder-averaged temporal spin correlations are proportional to the Fourier transform of the splitting distribution of the pairs of eigenvalues of the Floquet operator, which differ by π to exponential accuracy in the chain length. We find that the splittings are well described by a log-normal distribution, implying that the temporal spin correlations are characterized by two parameters. We discuss possible implications for the phase diagram of Floquet time crystals.
In one-dimensional topological superconductors driven periodically with the frequency omega, two types of topological edge modes may appear, the well-known Majorana zero mode and a Floquet Majorana mode located at the quasienergy PLANCK CONSTANT OVER TWO PI omega/2. We investigate two Josephson-coupled topological quantum wires in the presence of Coulomb interactions, forming a so-called Majorana box qubit. An oscillating gate voltage can induce Floquet Majorana modes in both wires. This allows for the encoding of three qubits in a sector with fixed electron parity. If such a system is prepared by increasing the amplitude of oscillations adiabatically, it is inherently unstable as interactions resonantly create quasiparticles. This can be avoided by using instead a protocol where the oscillation frequency is increased slowly. In this case, one can find a parameter regime where the system remains stable.