Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems

Abstract

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental observations have demonstrated that spin transport in this paradigmatic model falls into the Kardar-Parisi-Zhang (KPZ) universality class. This has inspired the significantly stronger conjecture that KPZ dynamics, in fact, occur in all integrable spin chains with non-Abelian symmetry. Here, we provide extensive numerical evidence affirming this conjecture. Moreover, we observe that KPZ transport is even more generic, arising in both supersymmetric and periodically-driven models. Motivated by recent advances in the realization of SU(N)-symmetric spin models in alkaline-earth-based optical lattice experiments, we propose and analyze a protocol to directly investigate the KPZ scaling function in such systems.

arXiv comment7+13 pages, 3+13 figures

References in corpus (62)

• The density-matrix renormalization group in the age of matrix product states
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Single-Spin Addressing in an Atomic Mott Insulator
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Resolving the gravitational redshift within a millimeter atomic sample
• Single-atom imaging of fermions in a quantum-gas microscope
• A Quantum Gas Microscope for Fermionic Atoms
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory
• Site-resolved Imaging of Fermionic Lithium-6 in an Optical Lattice
• Free-energy distribution of the directed polymer at high temperature
• Spin diffusion from an inhomogeneous quench in an integrable system
• Exact scaling functions for one-dimensional stationary KPZ growth
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• New Exactly Solvable Model of Strongly Correlated Electrons Motivated by High T_c Superconductivity
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Microscopic Observation of Pauli Blocking in Degenerate Fermionic Lattice Gases
• Exact height distributions for the KPZ equation with narrow wedge initial condition
• Super-diffusion in one-dimensional quantum lattice models
• A quantum hydrodynamical description for scrambling and many-body chaos
• Direct observation of coherent inter-orbital spin-exchange dynamics
• The KPZ fixed point
• Direct probing of the Mott crossover in the SU($N$) Fermi-Hubbard model
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• An ytterbium quantum gas microscope with narrow-line laser cooling
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Fibonacci family of dynamical universality classes
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Quantum dynamics of thermalizing systems
• Observing emergent hydrodynamics in a long-range quantum magnet
• Ballistic spin transport in a periodically driven integrable quantum system
• Diffusive hydrodynamics from integrability breaking
• The algebraic Bethe ansatz for rational braid-monoid lattice models
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Antiferromagnetic spin correlation of SU($\mathcal{N}$) Fermi gas in an optical super-lattice
• Superuniversality of superdiffusion
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Many-body delocalization in the presence of a quantum bath
• Site-resolved imaging of ytterbium atoms in a two-dimensional optical lattice
• Superdiffusion from emergent classical solitons in quantum spin chains
• Tropical Combinatorics and Whittaker functions
• Kardar-Parisi-Zhang universality from soft gauge modes
• Stability of superdiffusion in nearly integrable spin chains
• Thermodynamics of a deeply degenerate SU($N$)-symmetric Fermi gas
• Absence of Normal Fluctuations in an Integrable Magnet
• The exact solution and the finite size behaviour of the $Osp(1|2)$ invariant spin chain
• Emergent hydrodynamics in non-equilibrium quantum systems
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Integrable Matrix Models in Discrete Space-Time
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• Diffusion and superdiffusion from hydrodynamic projections
• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
• Site-resolved imaging of a bosonic Mott insulator using ytterbium atoms
• Exact solution of the simplest super-orthosymplectic invariant magnet
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• $OSp(n|2m)$ quantum chains with free boundaries

Cited by in corpus (29)

• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Generalized hydrodynamics: a perspective
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Anomalous transport from hot quasiparticles in interacting spin chains
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Dynamical criticality of magnetization transfer in integrable spin chains
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Exploiting disorder to probe spin and energy hydrodynamics
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Kardar-Parisi-Zhang scaling in the Hubbard model
• Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
• Parametrically long lifetime of superdiffusion in non-integrable spin chains
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• Quantum many-body spin ratchets
• Open-system spin transport and operator weight dissipation in spin chains
• Diffusive charge transport in the gapped 1D Hubbard model at all finite temperatures
• Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders
• Superdiffusive transport on lattices with nodal impurities
• Floquet Flux Attachment in Cold Atomic Systems
• Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions
• Finite-temperature transport in the gapped spin-1/2 XXZ chain and one-dimensional lattice spinless fermion model
• Diagnosing quantum transport from wave function snapshots
• Dynamic scaling and Family-Vicsek universality in $SU(N)$ quantum spin chains
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Emergent non-Hermitian conservation laws at exceptional points
• Family-Vicsek universality of the binary intrinsic dimension of nonequilibrium data
• Universal scaling of higher-order cumulants in quantum isotropic spin chains