Entanglement Entropy and Entanglement Growth in Gauge Theory

P. V. Buividovich, M. I. Polikarpov

Anber, Mohamed M., Kolligs, Benjamin J.

Jared Jeyaretnam, Tanmay Bhore, Jesse J. Osborne +2 more

Lattice gauge theories, the discrete counterparts of continuum gauge theories, provide a rich framework for studying non-equilibrium quantum dynamics. Recent studies suggest disorder-free localization in the lattice Schwinger model, but its origin remains unclear. Using a combination of analytical and numerical methods, we show that Hilbert space fragmentation emerges in the strong coupling limit, constraining particle dynamics and causing sharp jumps in entanglement entropy growth within charge sectors. By analyzing jump statistics, we find that entanglement growth follows a single-logarithmic or weak power-law dependence on time, rather than a double-logarithmic form. This suggests a single ergodicity-breaking regime that mimics many-body localization in finite systems due to fragmentation effects. Our findings clarify the nature of disorder-free localization and its distinction from conventional many-body localization, highlighting how gauge constraints influence thermalization in lattice gauge theories.

Sinya Aoki A, Takumi Iritani, Masahiro Nozaki A +3 more

We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the Z N gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the Z N gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.

Christopher Eling, Yaron Oz, Stefan Theisen

Alexander Velytsky

We consider the entanglement entropy for a subsystem in $d+1$ dimensional $SU(N)$ lattice gauge theory. The $1+1$ gauge theory is treated exactly and shows trivial behavior. Gauge theories in higher dimensions are treated within Migdal-Kadanoff approximation. We consider the gauge theory in the confinement phase. We demonstrate the existence of a nonanalytical change from the short distance to long distance form in the entanglement entropy in such systems ($d>2$) reminiscent of phase transition. The transition is manifested in nontrivial change in the renormalization group flow of character expansion coefficients defining the partition function.