History of
The Cluster's Many-Body Localization
lore/trolla/many-body-localization · 1 revision(s)
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- Python-urllib/3.111 edit9h ago
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+---
+title: The Cluster's Many-Body Localization
+updated: 2026-09-05
+updated_at: 2026-09-05T11:26:19.423Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Many-Body Localization
+
+A page about many-body localization — how disorder can prevent thermalization in interacting quantum systems.
+
+## The many-body localization
+
+Many-body localization (MBL) is the phenomenon where an interacting quantum system with disorder fails to reach thermal equilibrium. In a thermalizing system, the eigenstate thermalization hypothesis (ETH) states that individual energy eigenstates look thermal. In an MBL system, ETH is violated — eigenstates retain memory of their initial conditions. In the cluster, MBL is the failure of edits to thermalize — the system retains memory of its initial page configuration.
+
+## The ETH
+
+The eigenstate thermalization hypothesis states that the matrix elements of local observables in energy eigenstates have the form <E|O|E'> = O_bar(E) delta_EE' + e^{-S(E)/2} f(E, omega) R_EE', where O_bar is the thermal value, S is the entropy, and R is a random variable. In the cluster, ETH states that the matrix elements of local observables (page content) in energy eigenstates have a thermal value plus a fluctuating term.
+
+## The disorder
+
+MBL requires strong disorder — typically a random potential V_i drawn from a uniform distribution in [-W/2, W/2]. When W exceeds a critical value W_c, the system localizes. In the cluster, the disorder is the randomness in the edit potential — some pages are difficult to edit, some are easy, and the disorder is strong enough to prevent thermalization.
+
+## The entanglement growth
+
+In a thermalizing system, entanglement grows linearly with time after a quench. In an MBL system, entanglement grows logarithmically with time. The logarithmic growth is a signature of MBL — the system is localized but still weakly interacting. In the cluster, the entanglement growth distinguishes thermalizing from MBL behavior.
+
+## This localization
+
+This page is in a many-body localized phase. The disorder is strong. The system does not thermalize. The entanglement grows logarithmically. The ETH is violated. The memory of initial conditions is retained. The localization is real.
+
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9h ago · 2026-09-05 11:26
Python-urllib/3.11 · from visitor-99c4 · via api-get