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arXiv:2208.13505

Dephasing and Decorrelation of Spins in a Disordered Environment

Shreyas Raman, Subroto Mukerjee

Published Aug 29, 2022• 0 citations
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Abstract

Dephasing of spins is a major roadblock to scaling up the size of quantum computing systems. We explore the possibility of utilizing highly disordered environments which are in the Many-Body Localized phase to arrest this dephasing. We embedded 2 `special' spins in such a highly disordered environment of Heisenberg spins to act as the target qubits and use the long-time value of the spin-spin correlator $\langle \vecσ_i \cdot \vecσ_j\rangle$ as an order parameter to quantify the transition between the thermal and MBL phases of this system. It is seen that the dephasing between spins, as encoded in this correlator, is impeded in a disordered environment when the system is fully localized. The order parameter yields a critical exponent, to characterize the transition between the thermal and MBL phases, that appears to be robust to changes in microscopic parameters of the system or the choice of pair of spins.

DOI
10.48550/arxiv.2208.13505

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Dephasing of spins is a major roadblock to scaling up the size of quantum computing systems. We explore the possibility of utilizing highly disordered environments which are in the Many-Body Localized phase to arrest this dephasing. We embedded 2 `special' spins in such a highly disordered environment of Heisenberg spins to act as the target qubits and use the long-time value of the spin-spin correlator ⟨σ⃗i⋅σ⃗j⟩\langle \vecσ_i \cdot \vecσ_j\rangle⟨σi​⋅σj​⟩ as an order parameter to quantify the transition between the thermal and MBL phases of this system. It is seen that the dephasing between spins, as encoded in this correlator, is impeded in a disordered environment when the system is fully localized. The order parameter yields a critical exponent, to characterize the transition between the thermal and MBL phases, that appears to be robust to changes in microscopic parameters of the system or the choice of pair of spins.
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 nonthermalizing 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 ground state, the infinite temperature state, and a high-energy N\'eel state. In the nonthermalizing many-body localized regime, the coherence shows scaling behavior 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 bipartition of a many-body localized system. In summary, we show that decoherence of the probe spin provides clear signatures of many-body localization.
The failure of quantum thermalization due to Many-Body Localization (MBL) has evolved from a theoretical concept in spin chains to an experimental reality in synthetic quantum platforms, most notably superconducting circuits based on transmon qubits. Despite its significance, the MBL transition has been studied primarily under purely random disorder and local couplings, leaving more complex and realistic configurations largely unexplored. Here, we investigate the quantum dynamics of transmon networks subject to the unavoidable competing effects of correlated disorder and network-mediated non-local interactions. First, we show how to engineer the physical parameters of the quantum hardware to systematically control the correlated disorder patterns emerging in the system. Then, we demonstrate that the MBL phase transition is robust against such correlations, which is essential for tuning localization properties in realistic transmon devices. This robustness is established through the analysis of the block entanglement entropy variance across disorder realizations, which precisely locates the MBL critical point. Independently, we introduce a local memory parameter, whose dynamics at long evolution times reveals memory retention in the localized phase and yields a critical point consistent with the entropy analysis. These results provide a framework for understanding localization in complex quantum network topologies, with potential implications for multi-qubit processor design.
We present a theoretical and numerical study of the many-body localization (MBL) transition and entanglement dynamics in disordered spin-fermion chains with long-range interactions. Moving beyond standard single-particle pictures, we investigate the breakdown of ergodicity and thermalization by constructing an effective Hamiltonian via iterative Schrieffer-Wolff transformations and utilizing the local integrals of motion (l-bits) formalism. Our analysis examines entanglement entropy growth, level spacing statistics, and the transition from Wigner-Dyson to Poisson statistics. Furthermore, we derive analytical estimates for the dephasing rate scaling as a function of long-range potential parameters and validate the theoretical findings using exact diagonalization (ED) numerical protocols with finite-size scaling.
Considerable evidence supports the existence of many-body localization (MBL) phase transitions, although accurately determining the critical disorder intensity remains challenging due to significant instabilities in system size within the examined parameters. In this study, we employ the global quantum discord (GQD) to investigate MBL phase transitions and identify the critical points of the quantum Ising spin chain subjected to both disordered interacting and disordered external fields. Our analysis of GQD demonstrates its effectiveness in identifying the critical points between the thermal and the MBL phases. We further utilize the temporal evolution of GQD to comprehensively explore the characteristics of MBL phase transitions in the disordered quantum Ising spin chain. Our findings suggest that MBL phase transitions adhere to the same generality category based on the scaling analysis. Additionally, we investigate the effects of these examined parameters on the GQD and its dynamics and use them to estimate the critical points.
We investigate the mixed-state entanglement between two spins embedded in the XXZ Heisenberg chain under thermal equilibrium. By deriving an analytical expression for the entanglement of two-spin thermal states and extending this analysis to larger spin chains, we demonstrate that mixed-state entanglement is profoundly shaped by both disorder and temperature. Our results reveal a sharp distinction between many-body localized (MBL) and ergodic phases, with entanglement vanishing above different finite temperature thresholds. Furthermore, by analyzing non-adjacent spins, we uncover an approximate exponential decay of entanglement with separation. This work advances the understanding of the quantum-to-classical transition by linking the entanglement properties of small subsystems to the broader thermal environment, offering a explanation for the absence of entanglement in macroscopic systems. These findings provide critical insights into quantum many-body physics, bridging concepts from thermalization, localization, and quantum information theory.
It is known that strong disorder in closed quantum systems leads to many-body localization (MBL), and that this quantum phase can be destroyed by coupling to an infinitely large Markovian environment. However, the stability of the MBL phase is less clear when the system and environment are of finite and comparable size. Here, we study the stability and eventual localization properties of a disordered Heisenberg spin chain coupled to a finite environment, and extensively explore the effects of environment disorder, geometry, initial state and system-bath coupling strength. Our numerical results indicate that in most cases, the system retains its localization properties despite the coupling to the finite environment, albeit to a reduced extent. However, in cases where the system and environment is strongly coupled in the ladder configuration, the eventual localization properties are highly dependent on the initial state, and could lead to either thermalization or localization.