Role of flavor degrees of freedom in quantum simulations of disorder-free localization

Many-body localization (MBL) is a phenomenon where quenched disorder prevents a system from reaching thermal equilibrium. Recent experiments have used quantum parallelism to simulate disorder-averaged dynamics without explicit sampling, using conserved local degrees of freedom to generate effective disorder. This paper investigates whether the specific local spectrum of these conserved variables—specifically binary versus multilevel disorder—fundamentally changes the nature of the resulting localization.

The authors analyze a flavor-extended Z2 lattice gauge theory that maps onto a mixed-field Ising chain with n-level bond disorder. By varying the number of levels (n), they compare binary (n=2) disorder with multilevel (n=4, 8) and continuous disorder. They employ a combination of exact diagonalization for finite-size spectral and entanglement diagnostics and infinite matrix-product state (iMPS) dynamics to observe the system's behavior in the thermodynamic limit.

The study reveals a qualitative distinction between binary and multilevel disorder. For n=2, the system exhibits apparent localization at intermediate times and small system sizes, but this is a transient effect caused by energy-scale separation and approximate Hilbert-space fragmentation. These systems eventually thermalize. Conversely, for n=4 and higher, the system displays robust MBL signatures, including Poissonian level statistics, area-law eigenstate entanglement, and persistent local memory. The authors conclude that binary disorder lacks the necessary amplitude diversity to suppress resonances, meaning that localization is governed not just by disorder strength, but by the local disorder spectrum itself.

This work provides a critical warning for quantum simulation protocols. It shows that using simple binary ancilla qubits to emulate disorder may lead to misleading experimental results, as the observed nonergodicity may be a finite-time transient rather than a true localized phase. Researchers must account for the local spectrum of their conserved variables to ensure that their simulations accurately capture the physics of many-body localization.