Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators $({\mathrm{l}}^{*}\text{-bits})$ underlie localization in such systems. In dimensions $d>1$ , we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to ${\mathrm{l}}^{*}\text{-bits}$ . Physical consequences of ${\mathrm{l}}^{*}\text{-bits}$ include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in $d=1$ and thermal eigenstates at all parameters in $d>1$ . Near-term experiments in ultracold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of ${\mathrm{l}}^{*}\text{-bits}$ .Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators $({\mathrm{l}}^{*}\text{-bits})$ underlie localization in such systems. In dimensions $d>1$, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to ${\mathrm{l}}^{*}\text{-bits}$. Physical consequences of ${\mathrm{l}}^{*}\text{-bits}$ include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in $d=1$ and thermal eigenstates at all parameters in $d>1$. Near-term experiments in ultracold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of ${\mathrm{l}}^{*}\text{-bits}$.

arXiv:1605.00655Physical review. B./Physical review. BOct 7, 201675 citations

Many-body localization and quantum thermalization

Ehud Altman

Nature PhysicsSep 25, 201892 citations

Quantum versus classical thermalization in many-body isolated systems

Felix M. Izrailev

Bulletin of the American Physical SocietyMar 5, 20190 citations

Thermal avalanches in isolated many-body localized systems

Muhammad Sajid, Rozhin Yousefjani, Abolfazl Bayat

Many-body localization is a profound phase of matter affecting the entire spectrum which emer ges in the presence of disorder in interacting many-body systems. Recently, the stability of many-body localization has been challenged by the avalanche mechanism, in which a small thermal region can spread, destabilizing localization and leading to global thermalization of the system. A key unresolved question is the critical competition between the thermal region's influence and the disorder strength required to trigger such an avalanche. Here, we numerically investigate many-body localization stability in an isolated Heisenberg spin chain of size $L$ subjected to a disordered magnetic field. By embedding a tunable thermal region of size $P$ , we analyze the system's behavior in both static and dynamical regimes using entanglement entropy and the gap ratio. Our study yields two main findings. Firstly, for strong disorder, the avalanche only occurs if the thermal region scales with system size, specifically when $P/L$ exceeds a threshold value. Secondly, at strong disorder, we identify an intermediate phase between many-body localization and ergodic behavior as $P$ increases. This intermediate phase leaves its fingerprint in both static and dynamic properties of the system and tends to vanish in the thermodynamic limit. Although our simulations are restricted to finite system sizes, the analysis suggests that these results hold in the thermodynamic limit for isolated many-body systems.Many-body localization is a profound phase of matter affecting the entire spectrum which emer ges in the presence of disorder in interacting many-body systems. Recently, the stability of many-body localization has been challenged by the avalanche mechanism, in which a small thermal region can spread, destabilizing localization and leading to global thermalization of the system. A key unresolved question is the critical competition between the thermal region's influence and the disorder strength required to trigger such an avalanche. Here, we numerically investigate many-body localization stability in an isolated Heisenberg spin chain of size $L$ subjected to a disordered magnetic field. By embedding a tunable thermal region of size $P$, we analyze the system's behavior in both static and dynamical regimes using entanglement entropy and the gap ratio. Our study yields two main findings. Firstly, for strong disorder, the avalanche only occurs if the thermal region scales with system size, specifically when $P/L$ exceeds a threshold value. Secondly, at strong disorder, we identify an intermediate phase between many-body localization and ergodic behavior as $P$ increases. This intermediate phase leaves its fingerprint in both static and dynamic properties of the system and tends to vanish in the thermodynamic limit. Although our simulations are restricted to finite system sizes, the analysis suggests that these results hold in the thermodynamic limit for isolated many-body systems.

arXiv:2506.04834Physical review. B./Physical review. BOct 1, 20252 citations

({\mathrm{l}}^{*}\text{-bits})

underlie localization in such systems. In dimensions

d>1

, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to

{\mathrm{l}}^{*}\text{-bits}

. Physical consequences of

{\mathrm{l}}^{*}\text{-bits}

include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in

d=1

and thermal eigenstates at all parameters in

d>1

. Near-term experiments in ultracold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of

{\mathrm{l}}^{*}\text{-bits}

L

subjected to a disordered magnetic field. By embedding a tunable thermal region of size

P

, we analyze the system's behavior in both static and dynamical regimes using entanglement entropy and the gap ratio. Our study yields two main findings. Firstly, for strong disorder, the avalanche only occurs if the thermal region scales with system size, specifically when

P/L

exceeds a threshold value. Secondly, at strong disorder, we identify an intermediate phase between many-body localization and ergodic behavior as

P

increases. This intermediate phase leaves its fingerprint in both static and dynamic properties of the system and tends to vanish in the thermodynamic limit. Although our simulations are restricted to finite system sizes, the analysis suggests that these results hold in the thermodynamic limit for isolated many-body systems.