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

TL;DR

This paper investigates the real-time evolution of a critical Resonating Valence Bond spin liquid on a square lattice using PEPS representations, revealing stability within a U(1) gauge symmetry during Hamiltonian quenches.

Contribution

It introduces a PEPS-based approach to simulate non-equilibrium dynamics of RVB states, demonstrating phase stability and gauge symmetry preservation under unitary evolution.

Findings

PEPS accurately captures short-time dynamics of RVB states.

The Coulomb phase remains stable under Heisenberg interactions.

State evolution is confined within a U(1) gauge symmetric sub-manifold.

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.