Diffusive-to-ballistic crossover of symmetry violation in open many-body systems

Abstract

Conservation laws in a quantum many-body system play a direct role in its dynamic behavior. Understanding the effect of weakly breaking a conservation law due to coherent and incoherent errors is thus crucial, e.g., in the realization of reliable quantum simulators. In this work, we perform exact numerics and time-dependent perturbation theory to study the dynamics of symmetry violation in quantum many-body systems with slight coherent (at strength λ) or incoherent (at strength γ) breaking of their local and global symmetries. We rigorously prove the symmetry violation to be a divergence measure in Hilbert space. Based on this, we show that symmetry breaking generically leads to a crossover in the divergence growth from diffusive behavior at onset times to ballistic or hyperballistic scaling at intermediate times, before diffusion dominates at long times. More precisely, we show that for local errors the leading coherent contribution to the symmetry violation cannot be of order lower than ∝ λt 2 while its leading-order incoherent counterpart is typically of order ∝ γt. This remarkable interplay between unitary and incoherent gauge-breaking scalings is also observed at higher orders in projectors onto symmetry (super)sectors. Due to its occurrence at short times, the diffusive-to-ballistic crossover is expected to be readily accessible in modern ultracold-atom and NISQ-device experiments.

Robustness of Gauge Digitization to Quantum Noise

“…ZN number of physical qubits can scale from linearly to exponentially with logical qubits [37][38][39][40]. Phase transitions can separate theories with weak and strong gauge violations and different operators [58][59][60][61][62][63][64][65] so one can consider correcting only errors necessary to be in the same phase. For example, QEC that only repairs bit flips on a = 0 to the binary encoding changes the scaling of full symmetry breaking from p to p 2 since at least 2 errors are required.…”

“…Many digitization proposals have been studied (see Sec VI.b of [57]); however a consideration of the behavior of physical hardware is missing. In particular, quantum noise can be connected to gauge-violating operators [58][59][60][61][62][63][64][65]; this insight can determine the robustness of a digitization to noise and extend the lifetime of gauge states in memory.…”

Gauge-Symmetry Violation Quantum Phase Transition in Lattice Gauge Theories

“…2 if G j |ψ = 0, ∀j, the physical sector of the gauge theory coincides with the zero-eigenvalue sector of H G . Even more, ε can rigorously be connected to a mean-square displacement across gauge sectors as well as to the decrease in the overlap between two states that differ only by a gauge transformation [48,49].…”

Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum

“…Alternatively, analog simulations, e.g., in optical lattices, can adopt different strategies, such as a periodic drive to obtain energy terms endowed with the same symmetry characterizing lattice QED [ 43 , 44 ]. In this case, errors can induce gauge-invariance-breaking terms, which can lead to an emergent prethermal behavior [ 45 , 46 , 47 , 48 ].…”