Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport

Abstract

Symmetries are important for understanding equilibrium as well as nonequilibrium properties like transport. In translationally invariant extended systems one might expect symmetry generators to also be homogeneous. Studying qubit circuits with nearest-neighbor U(1) gates we show that this needs not be the case. We find new inhomogeneous screw SU(2) and ${\mathrm{U}}_q({\mathrm{sl}}_2)$ symmetries whose generators exhibit a spatial quasi-momentum modulation. They can be viewed as a parameter-dependent generalization of the standard rotational symmetry of the Heisenberg model and can be identified by the Ruelle-Pollicott spectrum of a momentum-resolved propagator. Rich integrability structure is reflected also in transport: picking an arbitrary U(1) gate and varying the gate duration one will transition through different phases, including fractal ballistic transport, Kardar-Parisi-Zhang superdiffusion at the critical manifold that also contains helix states, diffusion, and localization. To correctly explain transport the non-local SU(2) symmetries do not matter, while the inhomogeneous local ones that almost commute with the propagator do.

9 pages

References in corpus (25)

• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Exact scaling functions for one-dimensional stationary KPZ growth
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Ballistic spin transport in a periodically driven integrable quantum system
• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Kardar-Parisi-Zhang universality from soft gauge modes
• Catching Bethe phantoms and quantum many-body scars: Long-lived spin-helix states in Heisenberg magnets
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
• Conserved charges in the quantum simulation of integrable spin chains
• Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
• Uncovering Local Integrability in Quantum Many-Body Dynamics
• Strong zero modes in integrable quantum circuits
• Global Quenches after Localised Perturbations
• The Floquet Baxterisation
• Emergence of steady quantum transport in a superconducting processor
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Superdiffusive magnetization transport in the XX spin chain with non-local dephasing
• Universality in relaxation of spin helices under the $XXZ$- spin chain dynamics
• Superdiffusive transport on lattices with nodal impurities
• Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions

Cited by in corpus (5)

• Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit
• Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
• $su(2)$ symmetry of XX spin chains