Dissipation-Stabilized Quantum Revivals in a Non-Hermitian Lattice Gauge Theory

Abstract

With the advent of quantum simulation experiments of lattice gauge theories (LGTs), an open question is the effect of non-Hermiticity on their rich physics. The well-known PXP model, a U$(1)$ LGT with a two-level electric field in one spatial dimension, has become a paradigm of exotic physics in and out of equilibrium. Here, we introduce a non-Hermitian version in which the spin-flip rate differs between the two spin directions. While the naive expectation is that non-Hermiticity might suppress coherent phenomena such as quantum many-body scars, we find that when the facilitating direction of the spin is disfavored, the oscillations are instead \emph{enhanced}, decaying much slower than in the PXP limit. We demonstrate that this can be understood through a similarity transformation that maps our model to the standard PXP model, revealing that the oscillations are enhanced versions of the PXP scars. Our work provides an analytically tractable and conceptually simple example where non-Hermiticity enhances the stability of dynamically non-trivial coherent many-body modes.

Figures (4)

• Figure 1: Hilbert subspace of $L=4$ system, which includes the Néel states, $\mathbb{Z}_{2}$ and $\overline{\mathbb{Z}}_{2}$. The columns indicates the number of up spins, $n_{\uparrow}$, and the corresponding weight of these states, $V_{\uparrow}$ (see Eq. \ref{['eq:similarity_transformation']}). The red (blue) arrows indicate transitions which raise (lower) $n_{\uparrow}$ and have the strength $e^{g}$$\left(e^{-g}\right)$.
• Figure 2: Probability $P_{\mathbb{Z}{}_{2}/\bar{\mathbb{Z}}_{2}}\left(t\right)$ of finding the system in $\mathbb{Z}{}_{2}$ or $\bar{\mathbb{Z}}{}_{2}$ states as a function of time. The plots display results for $g=-1,0,1$ and $L=18$ and initial state of $\bar{\mathbb{Z}}{}_{2}$.
• Figure 3: Probability distribution $p_{N_{\uparrow}}$ to measure $N_{\uparrow}$ spins up in quantum scars (left column) and thermal states (right column) computed for $L=16$ and $g=-1$ (top row), $g=0$ (middle row) and $g=1$ (bottom row). In the left column, only scars with negative energies are plotted; darker colors correspond to eigenvalues closer to zero.
• Figure 4: Bipartite entanglement entropy of all the right-eigenvectors for $L=16$ and $g=-1,0,1$.