Scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points

Nag, Tanay; Divakaran, Uma; Dutta, Amit

doi:10.1103/physrevb.86.020401

Cited by 43 publications

(39 citation statements)

References 33 publications

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“…, there is a prominent Gaussian decay with time [16,17]. Using the dimensional analysis argument presented above, we immediately conclude thatα ) .…”

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confidence: 57%

Dynamics of decoherence: Universal scaling of the decoherence factor

2016

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We study the time dependence of the decoherence factor (DF) of a qubit globally coupled to an environmental spin system (ESS) which is driven across the quantum critical point (QCP) by varying a parameter of its Hamiltonian in time t as 1 − t/τ or −t/τ , to which the qubit is coupled starting at the time t → −∞; here, τ denotes the inverse quenching rate. In the limit of weak coupling, we analyze the time evolution of the DF in the vicinity of the QCP (chosen to be at t = 0) and define three quantities, namely, the generalized fidelity susceptibility χF (τ ) (defined right at the QCP), and the decay constants α1(τ ) and α2(τ ) which dictate the decay of the DF at a small but finite t(> 0). Using a dimensional analysis argument based on the Kibble-Zurek healing length, we show that χF (τ ) as well as α1(τ ) and α2(τ ) indeed satisfy universal power-law scaling relations with τ and the exponents are solely determined by the spatial dimensionality of the ESS and the exponents associated with its QCP. Remarkably, using the numerical t-DMRG method, these scaling relations are shown to be valid in both the situations when the ESS is integrable and non-integrable and also for both linear and non-linear variation of the parameter. Furthermore, when an integrable ESS is quenched far away from the QCP, there is a predominant Gaussian decay of the DF with a decay constant which also satisfies a universal scaling relation. PACS numbers:In the context of quantum computation and information [1, 2], one of the major issues is the study of decoherence [3, 4], namely, the loss of coherence in a quantum system due to its interaction with the environment. To investigate the environment induced decoherence of a qubit in the vicinity of a quantum critical point (QCP) [5, 6] of the environment, a paradigmatic model known as the central spin model (CSM) [7, 8] has been generalized to the context of a quantum phase transition [9].In the CSM a central spin (CS) or a qubit is globally coupled to an environmental quantum many body system, usually chosen to be a quantum spin system, referred to as the environmental spin system (ESS) in the subsequent discussions. The ESS is initially in its ground state while the CS is in a pure state; the global coupling between the qubit and the environment is so chosen that the subsequent time evolution of the initial ground state wave function of the ESS occurs along two channels dictated by two different Hamiltonians. Even though the qubit is initially in a pure state, it has been shown that it loses its purity (almost completely) [9] when the ESS is close to its quantum critical point (QCP). Question we address in this letter is as follows: what happens when the ESS is slowly driven across its QCP? Is there a universality associated with the dynamically generated decoherence quantified by the decoherence factor (DF) of the CS especially in a limit when the coupling between the CS and the spin chain is weak?Although we shall consider more generic nonintegrable models in this letter, let us first il...

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“…, there is a prominent Gaussian decay with time [16,17]. Using the dimensional analysis argument presented above, we immediately conclude thatα ) .…”

supporting

confidence: 57%

Dynamics of decoherence: Universal scaling of the decoherence factor

2016

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“…Subsequently, these studies have been generalized to twodimensional systems 13,14 and the role of topology 13 and the dynamical topological order parameter have been investigated 15 . We note in the passing that the rate function I(t) is related to the Loschmidt echo which has been studied in the context of decoherence [17][18][19][20][21][22][23][24][25][26] and the work-statistics 27,28 . The finite temperature counterpart of the Loschmidt echo 29 , namely the characteristic function has also been useful in studies of the entropy generation and emergent thermodynamics in quenched quantum systems 30,31 .…”

Section: Introductionmentioning

confidence: 99%

Tuning the presence of dynamical phase transitions in a generalizedXYspin chain

Divakaran¹,

Sharma²,

Dutta³

2016

Phys. Rev. E

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We study an integrable spin chain with three spin interactions and the staggered field (λ) while the latter is quenched either slowly (in a linear fashion in time (t) as t/τ where t goes from a large negative value to a large positive value and τ is the inverse rate of quenching) or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist non-analyticities (known as dynamical phase transitions (DPTs)) in the subsequent real time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when τ exceeds a critical value τ1), we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term (γ) and τ , thereby establishing the existence of boundaries in the (γ − τ ) plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value λi to a final value λ f , we show that the condition for the presence of DPTs is governed by relations involving λi, λ f and γ and the spin chain must be swept across λ = 0 for DPTs to occur.

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“…, is closely related to the Loschmidt echo which has been studied extensively close to a QCP both in equilibrium [65][66][67][68] and non-equilibrium situations [69][70][71][72] and shares a close connection with several other aspects of non-equilibrium dynamics of quenched closed quantum system [73][74][75][76][77]. Re[f (t)] can also be interpreted as the rate function of the return probability, so called because it can be connected to the singularities in the work distribution function corresponding to zero work following a double quenching process [32].…”

Section: Introductionmentioning

confidence: 99%

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

Bhattacharya

Dutta

2017

Phys. Rev. B

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We study the behavior of Fisher Zeros (FZs) and dynamical quantum phase transitions (DQPTs) for a linearly ramped Haldane model occurring in the subsequent temporal evolution of the same and probe the intimate connection with the equilibrium topology of the model. Here, we investigate the temporal evolution of the final state of the Haldane Hamiltonian (evolving with time-independent final Hamiltonian) reached following a linear ramping of the staggered (Semenoff) mass term from an initial to a final value, first selecting a specific protocol, so chosen that the system is ramped from one non-topological phase to the other through a topological phase. We establish the existence of three possible behaviour of areas of FZs corresponding to a given sector: (i) no-DQPT, (ii) one-DQPT (intermediate) and (iii)two-DQPTs (re-entrant), depending on the inverse quenching rate τ . Our study also reveals that the appearance of the areas of FZs is an artefact of the nonzero (quasi-momentum dependent) Haldane mass (MH ), whose absence leads to an emergent onedimensional behaviour indicated by the shrinking of the areas FZs to lines and the non-analyticity in the dynamical "free energy" itself. Moreover, the characteristic rates of crossover between the three behaviour of FZs are determined by the time-reversal invariant quasi-momentum points of the Brillouin zone where MH vanishes. Thus, we observe that through the presence or absence of MH , there exists an intimate relation to the topological properties of the equilibrium model even when the ramp drives the system far away from equilibrium.

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Scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points

Cited by 43 publications

References 33 publications

Dynamics of decoherence: Universal scaling of the decoherence factor

Dynamics of decoherence: Universal scaling of the decoherence factor

Tuning the presence of dynamical phase transitions in a generalizedXYspin chain

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

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