Real-time dynamics of a critical Resonating Valence Bond spin liquid

Abstract

Implementation of the hardcore-dimer Hilbert space in cold Rydberg-atom simulators opens a new route of investigating real-time dynamics of dimer liquids under Hamiltonian quench. Here, we consider an initial Resonating Valence Bond (RVB) state on the square lattice realizing a critical Coulomb phase with algebraic and dipolar correlations. Using its representation as a special point of a broad manifold of SU($2$)-symmetric, translationnally invariant, Projected Entangled Pair States (PEPS), we compute its non-equilibrium dynamics upon turning on inter-site Heisenberg interactions. We show that projecting the time-evolution onto the PEPS manifold remains accurate at small time scales. We also find that the state evolves within a PEPS sub-manifold characterized by a U($1$) gauge symmetry, suggesting that the Coulomb phase is stable under such unitary evolution.

18 pages, 21 figures. Update: The Appendix on the Variational Optimization scheme has been removed to be published in a separate article

References in corpus (6)

• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Resonating valence bond states in the PEPS formalism
• Dynamical preparation of quantum spin liquids in Rydberg atom arrays
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• On Ising and dimer models in two and three dimensions

Cited by in corpus (4)

• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States
• Dual-isometric Projected Entangled Pair States
• Tensor network variational optimizations for real-time dynamics: application to the time-evolution of spin liquids
• The ITransverse.jl library for transverse tensor network contractions