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arXiv:2305.06734 · Physical review. B./Physical review. B

Nonmonotonic buildup of spin-singlet correlations in a double quantum dot

Kacper Wrześniewski, Tomasz Ślusarski, Ireneusz Weymann

Published Oct 27, 2023• 4 citations
arXivHTMLPDF

Abstract

Dynamical buildup of spin-singlet correlations between the two quantum dots is investigated by means of the time-dependent numerical renormalization group method. By calculating the time evolution of the spin-spin expectation value upon a quench in the hopping between the quantum dots, we examine the timescales associated with the development of an entangled spin-singlet state in the system. Interestingly, we predict a nonmonotonic buildup of entanglement between the two dots. In particular, we find that in short timescales the effective exchange interaction between the quantum dots is of ferromagnetic type, favoring spin-triplet correlations, as opposed to the long-time limit, when strong antiferromagnetic correlations develop and eventually an entangled spin-singlet state is formed between the dots. We also numerically determine the relevant timescales and show that the physics is generally governed by the interplay between the Kondo correlations on each dot and exchange interaction between the spins of both quantum dots.

DOI
10.1103/physrevb.108.144307

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Dynamical buildup of spin-singlet correlations between the two quantum dots is investigated by means of the time-dependent numerical renormalization group method. By calculating the time evolution of the spin-spin expectation value upon a quench in the hopping between the quantum dots, we examine the timescales associated with the development of an entangled spin-singlet state in the system. Interestingly, we predict a nonmonotonic buildup of entanglement between the two dots. In particular, we find that in short timescales the effective exchange interaction between the quantum dots is of ferromagnetic type, favoring spin-triplet correlations, as opposed to the long-time limit, when strong antiferromagnetic correlations develop and eventually an entangled spin-singlet state is formed between the dots. We also numerically determine the relevant timescales and show that the physics is generally governed by the interplay between the Kondo correlations on each dot and exchange interaction between the spins of both quantum dots.
We investigate the quench dynamics of a quantum dot strongly coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework. We examine the system's response to a quench in the spin-dependent coupling strength to ferromagnetic leads as well as in the position of the dot's orbital level. The spin dynamics is analyzed by calculating the time-dependent expectation values of the quantum dot's magnetization and occupation. Based on these, we determine the time dependence of a ferromagnetic-contact-induced exchange field and predict its nonmonotonic buildup. In particular, two timescales are identified, describing the development of the exchange field and the dot's magnetization sign change. Finally, we study the effects of finite temperature on the dynamical behavior of the system.
We investigate the entanglement between the spins of two quantum dots that are not connected at once to the same system. Quantum entanglement between localized spins is an essential property for the development of quantum computing and quantum information. It is for this reason that generating and controlling an entangled state between quantum dots received great attention in the later years. In this work, we show that the information on the spin orientation of a quantum dot can be kept, using the Kondo entanglement, in a reservoir of electrons. Then, this information can be transmitted to another dot after the first dot has been uncoupled from the reservoirs. We use a double quantum dot system in a parallel geometry to construct the initial state, where each dot interacts with reservoirs of different symmetries. We chose a phase in the couplings to induce an antiferromagnetic spin correlation between the dots. The time evolution of the initial state has been analyzed using the time-dependent density matrix renormalization group method. We found that a partially entangled state between the dots can be obtained, even if they are not connected at the same time. This entangled state is formed just during the transient and is destroyed in the stationary state. The stability of the state found in the transient is shown. To understand the details of these phenomena, a canonical transformation of the real space is used.
We study the interplay between Kondo correlations and the singlet-triplet exchange splitting K between the two spins in a double quantum dot. We calculate the cotunneling current with elastic and inelastic contributions and its renormalization due to Kondo correlations, away and at the degeneracy point K = 0. We show that these Kondo correlations induce pronounced peaks in the conductance G as a function of magnetic field B , inter-dot coupling t H , and temperature. The long-range part of the Coulomb interaction becomes visible due to Kondo correlations resulting in an additional peak in G vs. t H with a strong B -field dependence. These conductance peaks thus provide direct experimental access to K , and thus to a crucial control parameter for spin-based qubits and entanglement.
By means of the numerical renormalization group method, I study the Kondo effect and quantum phase transitions in a double quantum dot system with on-site repulsion UUU, interdot repulsion V,V,V, and magnetic field BBB. At zero temperature and B=0B=0B=0, there is a local spin triplet-singlet transition of the Kosterlitz-Thouless type when VVV increases to a critical value ${V}_{c}\ensuremath{\approx}U$. With increasing BBB, a singlet-triplet transition of the second order occurs at a critical magnetic field ${B}_{c}\ensuremath{\approx}V\ensuremath{-}U$. The magnetic susceptibility and the first derivatives of the spin correlation and double occupation are expected to diverge at Bc{B}_{c}Bc​ and to have different critical exponents, which are universal for different parameters. An appropriate magnetic field can restore the Kondo effect.
Semiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.
Abstract. The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U ′, in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U ′/U. The spin-Kondo effect arising for U ′ = 0 (SU(2) × SU(2)) is found to persist robustly with increasing U ′/U, before a rapid but continuous crossover to (a) the SU(4) point U ′ = U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U ′ c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U, U ′)-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.