Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
arXiv:2410.22586 · doi:10.1103/mns1-l19c
Abstract
Understanding the physics of the integrable spin-1/2 XXZ chain has witnessed substantial progress, due to the development and application of sophisticated analytical and numerical techniques. In particular, infinite-temperature magnetization transport has turned out to range from ballistic, over superdiffusive, to diffusive behavior in different parameter regimes of the anisotropy. Since integrability is rather the exception than the rule, a crucial question is the change of transport under integrability-breaking perturbations. This question includes the stability of superdiffusion at the isotropic point and the change of diffusion constants in the easy-axis regime. In our work, we study this change of diffusion constants by a variety of methods and cover both, linear response theory in the closed system and the Lindblad equation in the open system, where we throughout focus on periodic boundary conditions. In the closed system, we compare results from the recursion method to calculations for finite systems and find evidence for a continuous change of diffusion constants over the full range of perturbation strengths. In the open system weakly coupled to baths, we find diffusion constants in quantitative agreement with the ones in the closed system in a range of nonweak perturbations, but disagreement in the limit of weak perturbations. Using a simple model in this limit, we point out the possibility of a diverging diffusion constant in such an open system.
12 pages, 12 figures
References in corpus (53)
- Many-Body Physics with Ultracold Gases
- Nonequilibrium dynamics of closed interacting quantum systems
- Efficient classical simulation of slightly entangled quantum computations
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Many-body localization, thermalization, and entanglement
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Efficient simulation of one-dimensional quantum many-body systems
- Quantum many-body systems out of equilibrium
- Transport and conservation laws
- Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
- Finite-temperature transport in one-dimensional quantum lattice models
- A Universal Operator Growth Hypothesis
- Spin transport in a one-dimensional anisotropic Heisenberg model
- Quasilocal charges in integrable lattice systems
- Families of quasi-local conservation laws and quantum spin transport
- Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
- Matrix product simulations of non-equilibrium steady states of quantum spin chains
- Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
- Diffusion in generalized hydrodynamics and quasiparticle scattering
- Super-diffusion in one-dimensional quantum lattice models
- Eigenstate thermalization within isolated spin-chain systems
- Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
- Transport in Almost Integrable Models: Perturbed Heisenberg Chains
- Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
- Stability of superdiffusion in nearly integrable spin chains
- Spin transport in the XXZ chain at finite temperature and momentum
- Transport in open spin chains: A Monte Carlo wave-function approach
- Spin conductivity in almost integrable spin chains
- Anomalous scaling of conductivity in integrable fermion systems
- High-temperature coherent transport in the XXZ chain in the presence of an impurity
- Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
- Weak integrability breaking: chaos with integrability signature in coherent diffusion
- Random State Technology
- Scaling of diffusion constants in the spin-1/2 XX ladder
- Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability
- Selected applications of typicality to real-time dynamics of quantum many-body systems
- Density dynamics from current auto-correlations at finite time- and length-scales
- Coexistence of Anomalous and Normal Diffusion in Integrable Mott Insulators
- Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
- Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
- Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
- Equivalence of transport coefficients in bath-induced and dynamical scenarios
- Diffusion constants from the recursion method
- Superdiffusion from nonabelian symmetries in nearly integrable systems
- Quantum Hydrodynamics in Spin Chains with Phase Space Methods
- Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
- Less is more: more scattering leading to less resistance
- Spin diffusion in perturbed isotropic Heisenberg spin chain
- From dissipationless to normal diffusion in easy-axis Heisenberg spin chain
- Parametrically long lifetime of superdiffusion in non-integrable spin chains
- Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions
- Real-time broadening of bath-induced density profiles from closed-system correlation functions
- Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions