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Title: Long-time memory effects in a localizable central spin problem

Journal Article · · New Journal of Physics
ORCiD logo [1]; ORCiD logo [2]
  1. Univ. of California, Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Tel Aviv Univ., Tel Aviv (Israel). Sackler Center for Computational Molecular and Materials Science
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We study the properties of the Nakajima–Zwanzig memory kernel for a qubit immersed in a many-body localized (i.e. disordered and interacting) bath. We argue that the memory kernel decays as a power law in both the localized and ergodic regimes, and show how this can be leveraged to extract t → ∞ populations for the qubit from finite time (Jt ≤ 102) data in the thermalizing phase. This allows us to quantify how the long-time values of the populations approach the expected thermalized state as the bath approaches the thermodynamic limit. This approach should provide a good complement to state-of-the-art numerical methods, for which the long-time dynamics with large baths are impossible to simulate in this phase. Additionally, our numerics on finite baths reveal the possibility for unbounded exponential growth in the memory kernel, a phenomenon rooted in the appearance of exceptional points in the projected Liouvillian governing the reduced dynamics. In small systems amenable to exact numerics, we find that these pathologies may have some correlation with delocalization.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1856783
Journal Information:
New Journal of Physics, Journal Name: New Journal of Physics Journal Issue: 1 Vol. 24; ISSN 1367-2630
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English

References (71)

Local integrals of motion in many-body localized systems: Local integrals of motion in many-body localized systems journal May 2017
Analysis Technique for Exceptional Points in Open Quantum Systems and QPT Analogy for the Appearance of Irreversibility journal July 2012
Algorithmic simulation of far-from-equilibrium dynamics using quantum computer journal July 2018
The density-matrix renormalization group in the age of matrix product states journal January 2011
Many-body localization: An introduction and selected topics journal September 2018
Dynamics and transport at the threshold of many-body localization journal May 2020
The non-Markovian stochastic Schrödinger equation for open systems journal November 1997
Nuclear spin effects in semiconductor quantum dots journal May 2013
Decoherence and control of a qubit in spin baths: an exact master equation study journal January 2018
Controlling the quantum dynamics of a mesoscopic spin bath in diamond journal April 2012
Dissipation in media with memory: A master equation in the statistical resonance approximation journal May 2001
Spectral density, memory function, and mean relaxation time for resonant subsystem-reservoir interactions journal January 2001
Ensemble Method in the Theory of Irreversibility journal November 1960
Dynamics of a two-level system coupled to a bath of spins journal December 2012
On the memory kernel and the reduced system propagator journal September 2018
Nonuniqueness of generalized quantum master equations for a single observable journal October 2021
Theory of the spin bath journal March 2000
Avoided level crossing and exceptional points journal April 1990
Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei journal December 2003
Perturbation theory in the complex plane: exceptional points and where to find them journal June 2021
The spin- s homogeneous central spin model: exact spectrum and dynamics journal October 2018
The physics of exceptional points journal October 2012
Thermal inclusions: how one spin can destroy a many-body localized phase
  • Ponte, Pedro; Laumann, C. R.; Huse, David A.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 375, Issue 2108 https://doi.org/10.1098/rsta.2016.0428
journal October 2017
Correlated projection operator approach to non-Markovian dynamics in spin baths journal November 2007
Dynamical typicality of embedded quantum systems journal July 2017
Decoherence of ensembles of nitrogen-vacancy centers in diamond journal October 2020
Electron spin evolution induced by interaction with nuclei in a quantum dot journal May 2003
Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics journal November 2004
Exact dynamics in the inhomogeneous central-spin model journal July 2007
Semiclassical dynamics and long-time asymptotics of the central-spin problem in a quantum dot journal July 2007
Many-body localization in the Heisenberg X X Z magnet in a random field journal February 2008
Spectral functions in one-dimensional quantum systems at finite temperature using the density matrix renormalization group journal June 2009
Free-induction decay and envelope modulations in a narrowed nuclear spin bath journal April 2010
Dynamics and decoherence in the central spin model using exact methods journal October 2010
Memory effects in nonequilibrium quantum impurity models journal August 2011
Master equation approach to the central spin decoherence problem: Uniform coupling model and role of projection operators journal October 2011
Perturbative regimes in central spin models journal June 2012
Nonperturbative stochastic method for driven spin-boson model journal January 2013
Numerically exact long-time magnetization dynamics at the nonequilibrium Kondo crossover of the Anderson impurity model journal May 2013
Bistability in a nonequilibrium quantum system with electron-phonon interactions journal July 2013
Spin decoherence due to a randomly fluctuating spin bath journal August 2013
Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state journal May 2014
Analytic solutions to the central-spin problem for nitrogen-vacancy centers in diamond journal August 2014
Phenomenology of fully many-body-localized systems journal November 2014
Solving nonequilibrium dynamical mean-field theory using matrix product states journal December 2014
Low-frequency conductivity in many-body localized systems journal September 2015
Detection and characterization of many-body localization in central spin models journal October 2018
Efficiently solving the dynamics of many-body localized systems at strong disorder journal June 2019
Phase transitions in open quantum systems journal July 1999
Exceptional points near first- and second-order quantum phase transitions journal January 2018
Electron Spin Decoherence in Isotope-Enriched Silicon journal October 2010
Unbounded Growth of Entanglement in Models of Many-Body Localization journal July 2012
Nonperturbative Master Equation Solution of Central Spin Dephasing Dynamics journal October 2012
Absence of Diffusion in an Interacting System of Spinless Fermions on a One-Dimensional Disordered Lattice journal March 2015
10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit journal November 2017
Simple and Accurate Method for Central Spin Problems journal June 2018
Coulomb Analogy for Non-Hermitian Degeneracies near Quantum Phase Transitions journal September 2007
Sensitivity of quantum information to environment perturbations measured with a nonlocal out-of-time-order correlation function journal February 2020
Many-body localization transition in large quantum spin chains: The mobility edge journal August 2020
Integrability and dark states in an anisotropic central spin model journal August 2020
Depolarization of Electronic Spin Qubits Confined in Semiconductor Quantum Dots journal December 2018
Dynamics of the dissipative two-state system journal January 1987
Colloquium : Exactly solvable Richardson-Gaudin models for many-body quantum systems journal August 2004
The kernel polynomial method journal March 2006
Colloquium : Many-body localization, thermalization, and entanglement journal May 2019
Coherent Dynamics of a Single Spin Interacting with an Adjustable Spin Bath journal April 2008
On Quantum Theory of Transport Phenomena: Steady Diffusion journal December 1958
Transport, Collective Motion, and Brownian Motion journal March 1965
Many-Body Localization and Thermalization in Quantum Statistical Mechanics journal March 2015
Propagation Methods for Quantum Molecular Dynamics journal October 1994
Information Entropy-Based Intention Prediction of Aerial Targets under Uncertain and Incomplete Information journal February 2020

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
central spin systems
generalized quantum master equations
many-body localization