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arXiv:1611.05713 · Annalen der Physik

Localization lifetime of a many‐body system with periodic constructed disorder

Michael Schecter, Michael Zalmanovich Shapiro, M. I. Dykman

Published Mar 27, 2017• 2 citations
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Abstract

We show that, in a many‐body system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such time‐domain formulation is complementary to the formulation of the many‐body localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a one‐dimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations. image

DOI
10.1002/andp.201600366

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We show that, in a many‐body system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such time‐domain formulation is complementary to the formulation of the many‐body localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a one‐dimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations. image
We demonstrate the onset of strong localization in a one dimensional fermion system, where all particles are almost completely confined to their sites. The on‐site localization is obtained by constructing a bounded one‐parameter sequence of site energies that eliminates resonant hopping between both nearest and remote sites. In an infinite system the time during which all many‐particle states remain on‐site localized scales as a high power of the ratio of the bandwidth of site energies to the hopping integral. The results apply to a system of perpetually coupled qubits and demonstrate that such system can be used for quantum computing.
We demonstrate that, in a many-particle system, particles can be strongly confined to their sites. The localization is obtained by constructing a sequence of on-site energies that efficiently suppresses resonant hopping. The time during which a many-particle state remains strongly localized in an infinite chain can exceed the reciprocal hopping frequency by $\agt 10^6$ already for a narrow energy bandwidth. The results show viability of quantum computers with time-independent qubit coupling.
We demonstrate the onset of strong on-site localization in a many-particle system, with effective localization length smaller than the intersite distance. The localization is obtained by constructing a bounded one-parameter sequence of on-site energies that eliminates resonant hopping between both nearest and remote sites. This sequence leads to quasiexponential decay of the single-particle transition amplitude. It also leads to on-site localization of stationary many-particle states in a finite-length chain. For an infinite many-particle system, we study the time during which all states remain on-site localized. We show that, for any number of particles, this time scales as a high power of the ratio of the bandwidth of on-site energies to the hopping integral. The proposed energy sequence is robust with respect to small errors. The formulation applies to fermions as well as perpetually coupled qubits. The results show viability of quantum computing with time-independent qubit coupling.
Many-particle confinement (localization) is studied for a 1D system of spinless fermions with nearest-neighbor hopping and interaction, or equivalently, for an anisotropic Heisenberg spin-1/2 chain. This system is frequently used to model quantum computers with perpetually coupled qubits. We construct a bounded sequence of site energies that leads to strong single-particle confinement of all states on individual sites. We show that this sequence also leads to a confinement of all many-particle states in an infinite system for a time that scales as a high power of the reciprocal hopping integral. The confinement is achieved for strong interaction between the particles while keeping the overall bandwidth of site energies comparatively small. The results show viability of quantum computing with time-independent qubit coupling.
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/{R}^{\ensuremath{\alpha}}$ is investigated combining analytical theory considering resonant interactions and a finite-size scaling of exact numerical solutions with number of spins NNN. The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for a ddd-dimensional system including the absence of localization in the infinite system at $\ensuremath{\alpha}<2d$ and a universal scaling of a critical energy disordering ${W}_{c}\ensuremath{\propto}{N}^{\frac{2d\ensuremath{-}\ensuremath{\alpha}}{d}}$.
We demonstrate that, in a quantum computer with perpetually coupled qubits, all excitations can be confined to their sites (qubits) even without refocusing. The on-site localization is obtained by constructing a sequence of qubit energies that efficiently suppresses resonant hopping. The time during which a many-excitation state remains strongly localized in an infinite chain can exceed the reciprocal hopping frequency by $\agt 10^5$ already for a moderate bandwidth of qubit energies. The proposed energy sequence is also convenient for performing quantum operations on the qubits.