Importance of level statistics in the decoherence of a central spin due to a spin environment

Brox, Håkon; Bergli, Joakim; Galperin, Y. M.

doi:10.1103/physreva.85.052117

Cited by 9 publications

(16 citation statements)

References 30 publications

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“…This integrability is encoded in (quasi-) local integrals of motion (LIOM's), also referred to as l-bits (for localized) 14,[40][41][42][43][44] . We will see in the remainder of this Letter that the combination of the aforementioned phenomena, i.e., violation of ETH, the change in level statistics, and the emergent integrability will largely influence the decoherence properties of the attached probe spin 26,34 .…”

Section: Modelmentioning

confidence: 97%

“…In particular, the roles of soft modes close to second order phase transition 27,33 , or the presence of a non-vanishing order-parameter in the bath have been studied in depth. Moreover, the relation of the level statistics of the bath to the decoherence properties of the single spin is well established 34 . Here, we want to capitalize on these insights in order to use the decoherence of a single spin as a probe for a many-body localized system.…”

Section: Introductionmentioning

confidence: 99%

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Single spin probe of many-body localization

2016

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We use an external spin as a dynamical probe of many body localization. The probe spin is coupled to an interacting and disordered environment described by a Heisenberg spin chain in a random field. The spin-chain environment can be tuned between a thermalizing delocalized phase and non-thermalizing localized phase, both in its ground-and high-energy states. We study the decoherence of the probe spin when it couples to the environment prepared in three states: the groundstate, the infinite temperature state and a high energy Néel state. In the non-thermalizing many body localized regime, the coherence shows scaling behaviour in the disorder strength. The long-time dynamics of the probe spin shows a logarithmic dephasing in analogy with the logarithmic growth of entanglement entropy for a bi-partition of a many-body localized system. In summary, we show that decoherence of the probe spin provides clear signatures of many-body localization.

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Section: Modelmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Single spin probe of many-body localization

2016

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“…1). Past simulations have shown that a high connectivity spin-glass type of environment is extremely efficient to decohere a system [16,[28][29][30], so we may expect that the one-dimensional ring is one of the most difficult geometries to obtain decoherence in short times.…”

Section: E Model and Methodsmentioning

confidence: 99%

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

et al. 2013

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We consider the decoherence of a quantum system S coupled to a quantum environment E. For states chosen uniformly at random from the unit hypersphere in the Hilbert space of the closed system S + E we derive a scaling relationship for the sum of the off-diagonal elements of the reduced density matrix of S as a function of the size D E of the Hilbert space of E. This sum decreases as 1/ √ D E as long as D E 1. We test this scaling prediction by performing large-scale simulations which solve the time-dependent Schrödinger equation for a ring of spin-1/2 particles, four of them belonging to S and the others to E, and for this ring with small world bonds added in E and/or between S and E. The spin-1/2 particles experience nearest-neighbor interactions that are identical for the interactions within S and random for the interactions within E and between S and E, or that are all identical. Provided that the time evolution drives the whole system from the initial state toward a scaling state, a state which has similar properties as states belonging to the class of quantum states for which we derived the scaling relationship, the scaling prediction holds. We examine various interaction parameters and initial states for our model system to find whether or not the time evolution reaches the class of states that have the scaling property. For the homogeneous ring we find that the evolution for select initial states does not reach these scaling states. This conclusion is not modified if we add some homogeneous random connections. For a ring we find that some randomness in the interaction parameters is required so that most initial configurations are driven toward the scaling state. Furthermore, if the amount of randomness is small the time required to reach the scaling states may be very large. For the case of all random interactions in E the ring is driven toward the scaling state. Adding small world bonds between S and E with random interaction strengths may decrease the time required to reach the scaling state or may prevent the scaling state from being reached. For the latter case we show that increasing the complexity of the environment by adding extra connections within the environment suffices to observe the predicted scaling behavior.

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“…These processes have a consequence on each component of the system, and could induce decoherence and relaxation. ( [1,2,3,4,5,6,7,8,9]). In order to explore this problem we consider the interesting example of a multipartite quantum system represented by a spin chain, i.e.…”

Section: Introductionmentioning

confidence: 99%

Analyses of the transmission of the disorder from a disturbed environment to a spin chain

Aubourg

Viennot

2014

Quantum Inf Process

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We study spin chains submitted to disturbed kick trains described by classical dynamical processes. The spin chains are described by Heisenberg and Ising models. We consider decoherence, entanglement and relaxation processes induced by the kick irregularity in the multipartite system (the spin chain). We show that the different couplings transmit the disorder along the chain differently and also to each spin density matrix with different efficiencies. In order to analyze and to interpret the observed effects we use a semi-classical analysis across the Husimi distribution. It consists to consider the classical spin orientation movements. A possibility of conserving the order into the spin chain is finally analyzed.

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Importance of level statistics in the decoherence of a central spin due to a spin environment

Cited by 9 publications

References 30 publications

Single spin probe of many-body localization

Single spin probe of many-body localization

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

Analyses of the transmission of the disorder from a disturbed environment to a spin chain

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