Non-Markovian dynamcis of a central Ising spin model

We study the decoherence of a central spin- $1∕2$ induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferromagnetic and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising bath. We present analytic results for the Ising spin chain bath at arbitrary temperature for different distributions of the intrabath interaction strengths. We find clear evidence of non-Markovian behavior in the low temperature regime. We also consider baths described by Ising models on higher-dimensional lattices. We find that interactions lead to a significant reduction of the decoherence. An important feature of interacting spin baths is the saturation of the asymptotic Markovian decay rate at high temperatures, as opposed to the conventional Ohmic boson bath.We study the decoherence of a central spin-$1∕2$ induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferromagnetic and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising bath. We present analytic results for the Ising spin chain bath at arbitrary temperature for different distributions of the intrabath interaction strengths. We find clear evidence of non-Markovian behavior in the low temperature regime. We also consider baths described by Ising models on higher-dimensional lattices. We find that interactions lead to a significant reduction of the decoherence. An important feature of interacting spin baths is the saturation of the asymptotic Markovian decay rate at high temperatures, as opposed to the conventional Ohmic boson bath.

arXiv:cond-mat/0610874Physical Review BMar 29, 200730 citations

Non Markovian Effects and Evolution of Entropy in Spin Systems

J. Philippot, Daniel D. Walgraef

Jan 1, 19670 citations

Suppressing information storage in a structured thermal bath: Objectivity and non-Markovianity

Wilson S. Martins, Diogo O. Soares-Pinto

Quantum systems interacting with environments tend to have their information lost from transmission through the correlations generated with the degrees of freedom of the environment. For situations where we have non- Markovian environments, the information contained in the environment may return to the system and such effect can be captured by non-Markovian witnesses. In the present work, we use a central qubit coupled to a spin chain with Ising interactions subject to a magnetic field, i.e., a central spin model, and solve the exact dynamics of a system subject to dephasing dynamics via Kraus operators. For such we use two witnesses to analyze the presence of non-Markovianity: the BLP trace-based measure and the conditional past-future correlator (CPF). Furthermore, we see how such behavior suppresses the classic plateau in Partial Information Plot (PIP) from the paradigm of quantum Darwinism, as well as objective information from Spectrum Broadcast Structure (SBS). In addition to the system point of view, we show the impossibility of encoding accessible information for measurement in the environment for any model limit.Quantum systems interacting with environments tend to have their information lost from transmission through the correlations generated with the degrees of freedom of the environment. For situations where we have non- Markovian environments, the information contained in the environment may return to the system and such effect can be captured by non-Markovian witnesses. In the present work, we use a central qubit coupled to a spin chain with Ising interactions subject to a magnetic field, i.e., a central spin model, and solve the exact dynamics of a system subject to dephasing dynamics via Kraus operators. For such we use two witnesses to analyze the presence of non-Markovianity: the BLP trace-based measure and the conditional past-future correlator (CPF). Furthermore, we see how such behavior suppresses the classic plateau in Partial Information Plot (PIP) from the paradigm of quantum Darwinism, as well as objective information from Spectrum Broadcast Structure (SBS). In addition to the system point of view, we show the impossibility of encoding accessible information for measurement in the environment for any model limit.

arXiv:2110.03490Oct 7, 20212 citations

Exact solutions of non-Markovian dissipative Ising models

Mohammad Maghrebi

Applications of quantum devices and simulators require an accurate understanding of their dynamics as well as the effects of environmental noise. While some sources of noise can be modeled as Markovian dissipation, coupling to resonators or vibrational modes often produces non-Markovian dynamics as well, making it difficult to characterize the system, particularly for interacting many-body systems. Here, we identify a broad class of exactly solvable many-body quantum systems with both non-Markovian dynamics and Markovian dissipation. We consider a prototypical model of spins coupled to lossy bosonic modes that mediate Ising-type interactions. We exclude a transverse field but allow local spin dissipation that need not commute with the interactions, including dephasing, relaxation, pumping, and even processes that generate coherences. Using an exact stochastic representation, we decouple the many-body dynamics into the evolution of individual spins, yielding exact spin observables and correlations without adiabatically eliminating the bosons. In the Markovian limit, our solutions describe Ising models with correlated dephasing and nonreciprocal interactions. An example of spin squeezing shows that both the achievable squeezing and its optimal preparation time depend strongly on the interplay between non-Markovian dynamics and Markovian dissipation.Applications of quantum devices and simulators require an accurate understanding of their dynamics as well as the effects of environmental noise. While some sources of noise can be modeled as Markovian dissipation, coupling to resonators or vibrational modes often produces non-Markovian dynamics as well, making it difficult to characterize the system, particularly for interacting many-body systems. Here, we identify a broad class of exactly solvable many-body quantum systems with both non-Markovian dynamics and Markovian dissipation. We consider a prototypical model of spins coupled to lossy bosonic modes that mediate Ising-type interactions. We exclude a transverse field but allow local spin dissipation that need not commute with the interactions, including dephasing, relaxation, pumping, and even processes that generate coherences. Using an exact stochastic representation, we decouple the many-body dynamics into the evolution of individual spins, yielding exact spin observables and correlations without adiabatically eliminating the bosons. In the Markovian limit, our solutions describe Ising models with correlated dephasing and nonreciprocal interactions. An example of spin squeezing shows that both the achievable squeezing and its optimal preparation time depend strongly on the interplay between non-Markovian dynamics and Markovian dissipation.

quant-pharXiv:2610.12546Oct 12, 20260 citations

Critical dynamics of finite Ising model

Jean Christian Anglès d’Auriac, R. Maynard, R. Rammal

Journal of Statistical PhysicsJun 1, 198227 citations

We study the decoherence of a central spin-

1∕2

induced by a spin bath with intrabath interactions. Since we are interested in the cumulative effect of interaction and disorder, we study baths comprising Ising spins with random ferromagnetic and antiferromagnetic interactions between the spins. Using the resolvent operator method which goes beyond the standard Born-Markov master equation approach, we show that, in the weak coupling regime, the decoherence of the central spin at all times is entirely determined by the local-field distribution or equivalently, the dynamical structure factor of the Ising bath. We present analytic results for the Ising spin chain bath at arbitrary temperature for different distributions of the intrabath interaction strengths. We find clear evidence of non-Markovian behavior in the low temperature regime. We also consider baths described by Ising models on higher-dimensional lattices. We find that interactions lead to a significant reduction of the decoherence. An important feature of interacting spin baths is the saturation of the asymptotic Markovian decay rate at high temperatures, as opposed to the conventional Ohmic boson bath.