Theory of the spin bath

Abstract

The quantum dynamics of mesoscopic or macroscopic systems is always complicated by their coupling to many "environmental" modes.At low T these environmental effects are dominated by localised modes, such as nuclear and paramagnetic spins, and defects (which also dominate the entropy and specific heat). This environment, at low energies, maps onto a "spin bath" model. This contrasts with "oscillator bath" models (originated by Feynman and Vernon) which describe {\it delocalised} environmental modes such as electrons, phonons, photons, magnons, etc. One cannot in general map a spin bath to an oscillator bath (or vice-versa); they constitute distinct "universality classes" of quantum environment. We show how the mapping to spin bath models is made, and then discuss several examples in detail, including moving particles, magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic spin environments. We show how to average over spin bath modes, using an operator instanton technique, to find the system dynamics, and give analytic results for the correlation functions, under various conditions. We then describe the application of this theory to magnetic and superconducting systems.Particular attention is given to recent work on tunneling magnetic macromolecules, where the role of the nuclear spin bath in controlling the tunneling is very clear; we also discuss other magnetic systems in the quantum regime, and the influence of nuclear and paramagnetic spins on flux dynamics in SQUIDs.

Invited article for Rep. Prog. Phys. to appear in April, 2000 (41 pages, latex, 13 figures. This is a strongly revised and extended version of previous preprint cond-mat/9511011)

References in corpus (14)

• Coherent control of macroscopic quantum states in a single-Cooper-pair box
• Josephson-Junction Qubits with Controlled Couplings
• Quiet SDS Josephson Junctions for Quantum Computing
• Observation of the distribution of molecular spin states by resonant quantum tunneling of the magnetization
• Interaction effects and phase relaxation in disordered systems
• Nuclear spin driven resonant tunnelling of magnetisation in Mn12 acetate
• Dephasing in Metals by Two-Level Systems in the 2-Channel-Kondo Regime
• Low-Temperature Dephasing in Disordered Conductors: the Effect of ``1/f'' Fluctuations
• Quantum Coherence in Fe8 Molecular Nanomagnets
• Phase Relaxation of Electrons in Disordered Conductors
• Persistent Current in Normal Metals
• Interaction and Quantum Decoherence
• Comment on "Quantum Decoherence in Disordered Mesoscopic Systems"
• Evidence for growth of collective excitations in glasses at low temperatures

Cited by in corpus (292)

• Will spin-relaxation times in molecular magnets permit quantum information processing?
• Fault-Tolerant Quantum Dynamical Decoupling
• Quantum Decoherence
• Prospects for Spin-Based Quantum Computing
• Magnetothermal properties of molecule-based materials
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Magnetic qubits as hardware for quantum computers
• Spin-Based Quantum Computers made by Chemistry: Hows and Whys
• Universal decoherence due to gravitational time dilation
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Information Loss
• Rare-earth solid-state qubits
• Decoherence in Crystals of Quantum Molecular Magnets
• Quantum many-body theory of qubit decoherence in a finite-size spin bath
• Decoherence induced by interacting quantum spin baths
• Direct Observation of Quantum Coherence in Single-Molecule Magnets
• An Introduction to Spontaneous Symmetry Breaking
• Quantum control and entanglement in a chemical compass
• Nuclear spin driven quantum relaxation in LiY_0.998Ho_0.002F_4
• Numerical Renormalization Group for Quantum Impurities in a Bosonic Bath
• Absence of many-body mobility edges
• Restoring Coherence Lost to a Slow Interacting Mesoscopic Bath
• Quantum thermodynamic cooling cycle
• Quantum systems under frequency modulation
• Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths
• Dynamics in many-body localized quantum systems without disorder
• Dissipative Landau-Zener transitions of a qubit: bath-specific and universal behavior
• Quantum Phase Transition of a Magnet in a Spin Bath
• Three addressable spin qubits in a molecular single-ion magnet
• Open quantum system dynamics and the mean force Gibbs state
• Decoherence from ensembles of two-level fluctuators
• Quantum algorithm for simulating the dynamics of an open quantum system
• Local observation of antibunching in a trapped Fermi gas
• Analog control of open quantum systems under arbitrary decoherence
• Quantum many-body theory of qubit decoherence in a finite-size spin bath. II. Ensemble dynamics
• Pair-wise decoherence in coupled spin qubit networks
• Numerical modeling of the central spin problem using the spin coherent states P-representation
• Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment
• Staying positive: going beyond Lindblad with perturbative master equations
• Combined encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing
• Control of electron spin decoherence caused by electron-nuclear spin dynamics in a quantum dot
• Single Electron Spin Decoherence by Nuclear Spin Bath: Linked Cluster Expansion Approach
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate
• Decoherence of a single-ion qubit immersed in a spin-polarized atomic bath
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
• Quantum speed limits for leakage and decoherence
• Dynamic entanglement in oscillating molecules and potential biological implications
• Adiabatic Landau-Zener-Stückelberg transition with or without dissipation in low spin molecular system V15
• Hyperfine interaction induced decoherence of electron spins in quantum dots
• Quantum Coherence between High Spin Superposition States of Single Molecule Magnet Ni${}_4$
• Effect of local Coulomb interactions on the electronic structure and exchange interactions in Mn12 magnetic molecules
• Spin decoherence of magnetic atoms on surfaces
• Non-Markovian dynamics of a qubit coupled to an Ising spin bath
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. II. Beyond Linear Response of Spin Baths
• Exact quantum jump approach to open systems in Bosonic and spin baths
• Parity Effects in Spin Decoherence
• Entanglement Sharing and Decoherence in the Spin-Bath
• Role of Nuclear Quadrupole Coupling on Decoherence and Relaxation of Central Spins in Quantum Dots
• Universal Scaling of Hyperfine-Induced Electron Spin Echo Decay
• Long-time electron spin storage via dynamical suppression of hyperfine-induced decoherence in a quantum dot
• Sensitivity of quantum information to environment perturbations measured with a non-local out-of-time-order correlation function
• Decoherence by a chaotic many-spin bath
• Quantum Otto engine with a spin $1/2$ coupled to an arbitrary spin
• Energy transport in the Anderson insulator
• Reduced density matrix for nonequilibrium steady states: A modified Redfield solution approach
• Magnetic long-range order induced by quantum relaxation in single-molecule magnets
• Coherent laser control of the current through molecular junctions
• Dynamics and decoherence in the central spin model using exact methods
• Collectively enhanced thermalization via multiqubit collisions
• Geometric Phase of a qubit interacting with a squeezed-thermal bath
• Uncovering many-body correlations in nanoscale nuclear spin baths by central spin decoherence
• Dynamical control of electron spin coherence in a quantum dot
• The low-$T$ phase diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Hyperfine interaction dominated dynamics of nuclear spins in self-assembled quantum dots
• The quantum dynamics of atomic magnets, co-tunneling and dipolar-biased tunneling
• Coherence Window in the dynamics of Quantum Nanomagnets
• Hierarchical equations for open system dynamics in fermionic and bosonic environments
• Spectral diffusion and scaling of many-body delocalization transitions
• Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems
• Algorithmic simulation of far-from-equilibrium dynamics using quantum computer
• Quantum Walks, Quantum Gates and Quantum Computers
• Multiphoton coherent manipulation in large-spin qubits
• Heat flux operator, current conservation and the formal Fourier's law
• Dissipative quantum dynamics with the Surrogate Hamiltonian approach. A comparison between spin and harmonic baths
• Suppression of decoherence via strong intra-environmental coupling
• Spin-wave contributions to current-induced domain wall dynamics
• Decoherence without Dissipation
• Quantum simulations and experiments on Rabi oscillations of spin qubits: intrinsic {\sl vs} extrinsic damping
• Teleportation in the presence of common bath decoherence at the transmitting station
• Engineering random spin models with atoms in a high-finesse cavity
• Environmental Decoherence versus Intrinsic Decoherence
• Spin-lattice relaxation of magnetic centers in molecular crystals at low temperature
• Decoherence induced by a chaotic environment: A quantum walker with a complex coin
• Time evolution and decoherence of a spin-1/2 particle coupled to a spin bath in thermal equilibrium
• Dynamical decoupling sequences for multi-qubit dephasing suppression and long-time quantum memory
• Bang-Bang control of a qubit coupled to a quantum critical spin bath
• Mechanisms of Decoherence at Low Temperatures
• Master equation approach to line shape in dissipative systems
• Quantum correlations at infinite temperature: the dynamical Nagaoka effect
• Magnetization Process of Single Molecule Magnets at Low Temperatures
• Dynamics and thermodynamics of a central spin immersed in a spin bath
• Quantum Rydberg Central Spin Model
• Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields
• Large Random Arrowhead Matrices: Multifractality, Semi-Localization, and Protected Transport in Disordered Quantum Spins Coupled to a Cavity
• Decoherence by a spin thermal bath: Role of the spin-spin interactions and initial state of the bath
• Decoherence by engineered quantum baths
• Decoherence and Quantum Walks: anomalous diffusion and ballistic tails
• From Zeno to anti-Zeno: decoherence-control dependence on the quantum statistics of the bath
• Decoherence by a spin thermal bath: Role of the spin-spin interactions
• Initial Decoherence of Open Quantum Systems
• Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths
• Phase-locking between different partial-waves in atom-ion spin-exchange collisions
• Decoherence-assisted transport in quantum networks
• Effect of random interactions in spin baths on decoherence
• Quantum Walk in Degenerate Spin Environments
• The non-Markovian quantum behavior of open systems: An exact Monte Carlo method employing stochastic product states
• Relaxation of Shallow Donor Electron Spin due to Interaction with Nuclear Spin Bath
• Rabi oscillations of solitons in spin-chains: a new route to quantum computation and communication
• Coherent propagation of quasiparticles in topological spin liquids at finite temperature
• Non-ideality of quantum operations with the electron spin of a 31P donor in a Si crystal due to interaction with a nuclear spin system
• Phonon-mediated decoherence in triple quantum dot interferometers
• Rabi oscillations, decoherence, and disentanglement in a qubit-spin-bath system: exact dynamics
• 'Hole-digging' in ensembles of tunneling Molecular Magnets
• Long-lived memory for electronic spin in a quantum dot: Numerical analysis
• Decoherence in a N-qubit solid-state quantum computer
• Comparison among Various Expressions of Complex Admittance for Quantum System in Contact with Heat Reservoir
• Non-Markoffian effects of a simple nonlinear bath
• Broken Time Translation Symmetry as a model for Quantum State Reduction
• Influence of an external magnetic field on the decoherence of a central spin coupled to an antiferromagnetic environment
• Parametric representation of open quantum systems and crossover from quantum to classical environment
• Giant isotope effect in the incoherent tunneling specific heat of the molecular nanomagnet Fe8
• Dynamics of two qubits in a spin-bath of Quantum anisotropic Heisenberg XY coupling type
• A Landau-Zener Lindblad equation and work extraction from coherences
• Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems
• Qubit decoherence by low-frequency noise
• A Nanoscale Experiment Measuring Gravity's Role in Breaking the Unitarity of Quantum Dynamics
• Strong Coupling between Whispering Gallery Modes and Chromium Ions in Ruby
• Phonon-mediated spin-flipping mechanism in the spin ices Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$
• Evolution of a quantum spin system to its ground state: Role of entanglement and interaction symmetry
• Detecting initial system-environment correlations: Performance of various distance measures for quantum states
• Using thermal boundary conditions to engineer the quantum state of a bulk magnet
• Short-Time Decoherence and Deviation from Pure Quantum States
• Controlling decoherence speed limit of a single impurity atom in a Bose-Einstein-condensate reservoir
• Spin Bath Decoherence of Quantum Entanglement
• Decoherence of coupled electron spins via nuclear spin dynamics in quantum dots
• Two-level system in spin baths: Non-adiabatic dynamics and heat transport
• Effect of system level structure and spectral distribution of the environment on the decoherence rate
• Dynamics and thermalization of the nuclear spin bath in the single-molecule magnet Mn12-ac: test for the theory of spin tunneling
• Open quantum systems coupled to finite baths: A hierarchy of master equations
• Dispersive readout of molecular spin qudits
• Percolation transition and dissipation in quantum Ising magnets
• Giant enhancement of quantum decoherence by frustrated environments
• Spin gases as microscopic models for non-Markovian decoherence
• Faraday rotation echo spectroscopy and detection of quantum fluctuations
• Crossovers in spin-boson and central spin models
• Combined Error Correction Techniques for Quantum Computing Architectures
• A Luttinger Liquid Coupled to a Quantum Spin Bath: Flow Equation Approach to the Kondo Necklace Model
• Decoherence of a single spin coupled to an interacting spin bath
• Self-gravitating Interferometry and Intrinsic Decoherence
• Decoherence in quantum walks and quantum computers
• Optical conductivity of charge carriers interacting with a two-level systems reservoir
• An Anisotropic Landau-Lifschitz-Gilbert model of dissipation in qubits
• Quantum sensing and control of spin state dynamics in the radical pair mechanism
• Controllable dynamics of two separate qubits in Bell states
• Correlated errors can lead to better performance of quantum codes
• What are the interactions in quantum glasses?
• Direct Observation of Collective Electronuclear Modes About a Quantum Critical Point
• Polynomial scheme for time evolution of open and closed quantum systems
• Quantum correlations and speed limit of central spin system
• High-fidelity quantum memory utilizing inhomogeneous nuclear polarization in a quantum dot
• Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment
• Controlled dynamics of qubits in the presence of decoherence
• Cluster-correlation expansion for studying decoherence of clock transitions in spin baths
• Strong coupling non-Markovian quantum thermodynamics of a finite-bath system
• Tunneling and inversion symmetry in single-molecule magnets: the case of the Mn12 wheel molecule
• Discrimination of thermal baths by single qubit probes
• Controlled doping of a bosonic quantum gas with single neutral atoms
• The characteristic functions of quantum heat with baths at different temperatures
• Initial correlation in a system of a spin coupled to a spin bath through an intermediate spin
• Arbitrary spin in a spin bath: Exact dynamics and approximation techniques
• Dynamics of a two-level system under the simultaneous influence of a spin bath and a boson bath
• Quasi-Hamiltonian Method for Computation of Decoherence Rates
• Exactly solvable model for the dynamics of two spin-1/2 particles embedded in separate spin star environments
• Destruction of the Kondo effect by a local measurement
• Quantum Projection in an Ising Spin Liquid
• Qubit Entanglement Dephasing Dynamics Driven by a Bath of Spins
• Efficient variational approach to dynamics of a spatially extended bosonic Kondo model
• Does temperature favor quantum coherence of a dissipative two-level system?
• Universal quantum uncertainty relations between non-ergodicity and loss of information
• Quantum homogenization in non-Markovian collisional model
• Electron induced nanoscale nuclear spin relaxation probed by hyperpolarization injection
• How systems of single-molecule magnets magnetize at low temperatures
• Quantum Decoherence with Holography
• Relaxation dynamics in double-spin systems
• Dephasing dynamics of an impurity coupled to an anharmonic environment
• Dynamics of a quantum system interacting with white non-Gaussian baths: Poisson noise master equation
• Exact dynamics of the homogeneous two-qubit $XXZ$ central spin model with the spin bath prepared in superpositions of symmetric Dicke states
• The role of chaos in quantum communication through a dynamical dephasing channel
• Decoherence and relaxation of qubits coupled to low- and medium-frequency Ohmic baths directly and via a harmonic oscillator
• Quantum frustration of dissipation by a spin bath
• Fluctuation corrections on thermodynamic functions: Finite size effect
• How to cross an energy barrier at zero Kelvin without tunneling effect
• Quantum and classical contributions to entropy production in fermionic and bosonic Gaussian systems
• Enhancement of nuclear spin coherence times by driving dynamic nuclear polarization at defect centers in solids
• Relating Heat and Entanglement in Strong Coupling Thermodynamics
• Decoherence and relaxation of a qubit coupled to an Ohmic bath directly and via an intermediate harmonic oscillator
• Error channels in quantum nondemolition measurements on spin systems
• Emergence of highly coherent quantum subsystems of a noisy and dense spin system
• Qubit-environment entanglement outside of pure decoherence: hyperfine interaction
• Functional integral treatment of some quantum nondemolition systems
• Non-classical measurement statistics induced by a coherent spin environment
• Suppression of Quantum Phase Interference in Molecular Magnets Fe₈ with Dipolar-Dipolar Interaction
• Decoherence of a singlet-triplet superposition state under dipolar interactions of an uncorrelated environment
• Physics at the FQMT'04 conference
• Quantum Dynamics in Classical Spin Baths
• Solomon equations for qubit and two-level systems: Insights into non-Poissonian quantum jumps
• Computer Simulation of Quantum Dynamics in a Classical Spin Environment
• Decoherence of intermolecular entanglement in exchange-coupled nanomagnets
• The importance of level statistics for the decoherence of a central spin due to a spin environment
• Flight of a heavy particle nonlinearly coupled to a quantum bath
• Finite-temperature decoherence of spin states in a $\text{{}{\text{Cu}}_3\text{}}$ single molecular magnet
• Negativity of quantumness and non-Markovianity in a qubit coupled to a thermal Ising spin bath system
• Analytical model of non-Markovian decoherence in donor-based charge quantum bits
• Dynamical Quantum Phase Transitions in presence of a spin bath
• Classical Simulation of Arbitrary Quantum Noise
• Energy transfer dynamics and thermalization of two oscillators interacting via chaos
• Temperature crossover of decoherence rates in chaotic and regular bath dynamics
• Propagators in the Correlated Worldline Theory of Quantum Gravity
• Low temperature breakdown of coherent tunneling in amorphous solids induced by the nuclear quadrupole interaction
• Quantum pathology of static internal imperfections in flawed quantum computers
• Noise-tolerant quantum speedups in quantum annealing without fine tuning
• Pure Phase Decoherence in a Ring Geometry
• Long-time memory effects in a localizable central spin problem
• Antiferromagnetic order without recourse to staggered fields
• Partitioned Density Matrices and Entanglement Correlators
• Transition rates for a S \ge 1 model coupled to a phonon bath
• Quantum bath statistics tagging
• Collapse and revival structure of information backflow for a central spin coupled to a finite spin bath
• Effects of nuclear spins on the coherent evolution of a phase qubit
• A Gallery of Soft Modes: Theory and Experiment at a Ferromagnetic Quantum Phase Transition
• Suppression of decoherence by bath ordering
• Decoherence of many-body systems due to many-body interactions
• Easy-axis ferromagnetic chain on a metallic surface
• Spin bath dynamics and dynamical Renormalization Group
• Density of states and quantum phase transition in the thermodynamic limit of the Mermin central-spin model
• A Quantum Model for Entropic Springs
• Multiparty Spohn's theorem for a combination of local Markovian and non-Markovian quantum dynamics
• Hyperfine interactions in open-shell planar $s{p}^2$-carbon nanostructures
• Transient effects in quantum refrigerators with finite environments
• Studies of decoherence in strongly anisotropic spin triangles with toroidal or general non-collinear easy axes
• Symmetry-protected Bose-Einstein condensation of interacting hardcore Bosons
• Survival Probability of a Doorway State in regular and chaotic environments
• Effects of a nonlinear bath at low temperatures
• Dynamical multipartite entanglement in a generalized Tavis-Cummings model with XY spin interaction
• Effective quantum dynamics induced by a driven two-level-system bath
• Non-equilibrium properties of the S=1/2 Heisenberg model in a time-dependent magnetic field
• Suppressing backscattering of helical edge modes with a spin bath
• Investigation of thermalization in giant-spin models by different Lindblad schemes
• Hierarchy of correlations for the Ising model in the Majorana representation
• Aspects of the decoherence in high spin environments: Breakdown of the mean-field approximation
• Probing magneto-elastic phenomena through an effective spin-bath coupling model
• Dissipative evolution of a two-level system through a geometry-based classical mapping
• Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation
• Using a biased qubit to probe complex systems
• Effect of a magnetic field on molecule-solvent angular momentum transfer
• Dissipative quantum disordered models
• Dissipation and resonance frequency shift of a resonator magnetically coupled to a semiclassical spin
• Spin Bath Decoherence Mediated by Phonons
• Open quantum-classical systems: A hybrid MASH master equation
• Quantum system dynamics with a weakly nonlinear Josephson junction bath
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Fast partial decoherence of a superconducting flux qubit in a spin bath
• Towards Understanding Prolate 4$f$ Monomers: Numerical Predictions and Experimental Validation of Electronic Properties and Slow Relaxation in a Muffin-shaped Er${}^{\mathrm{III}}$ Complex
• Phonon-induced entanglement dynamics of two donor-based charge quantum bits
• On the role of the measurement apparatus in quantum measurements
• Observation of zero-point quantum fluctuations of a single-molecule magnet through the relaxation of its nuclear spin bath
• Hybrid quantum systems of ions and atoms
• Inducing nontrivial qubit coherence through a controlled dispersive environment
• Decoherence of a quantum memory coupled to a collective spin bath
• The initial system-bath state via the maximum-entropy principle
• Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems
• Dissipation in Lagrangian formalism
• Finite-Bath Open Quantum Systems: Exact Dynamics
• On the merit of a Central Limit Theorem-based approximation in statistical physics
• Berry phase with environment: classical versus quantum
• Collective Quantum Batteries and Charger-Battery Setup in Open Quantum Systems: Impact of Inter-Qubit Interactions, Dissipation, and Quantum Criticality
• Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results
• Quantum nanomagnets and nuclear spins: an overview
• Decohering histories and open quantum systems
• Charge carrier relaxation dynamics in the one-dimensional Kondo lattice model
• Oscillator bath simulation of the spin bath