We present a mathematically controlled, sharply falsifiable framework that tests whether many-body localization (MBL) can protect quantum information against local Markovian dephasing. Using the standard phenomenology of quasi-local l-bits, a Schrieffer-Wolff transformation yields an effective classical rate equation with transition rates ~γ (J/W)² e^{-d_H/ξ}. This implies a central bound on the von Neumann entropy production: Φ ≤ C γ N (J/W)² (W ≫ J, γ ≪ J). A variational argument provides an upper bound for the Liouvillian gap. The hypothesis is subjected to a five-point falsification matrix; any single violation disproves it. We provide an open-source QuTiP implementation and numerical results for N=6, confirming the predicted scaling exponent ≈ −2 and persistent Néel imbalance. The framework is compatible with a long-lived prethermal regime and offers a concrete realization of the VES (information degradation minima) hypothesis in open many-body quantum systems. The repository contains the manuscript, executable code (QuTiP, ITensor skeleton), and all figures.
We present a mathematically controlled, sharply falsifiable framework that tests whether many-body localization (MBL) can protect quantum information against local Markovian dephasing. Using the standard phenomenology of quasi-local l-bits, a Schrieffer-Wolff transformation yields an effective classical rate equation with transition rates ~γ (J/W)² e^{-d_H/ξ}. This implies a central bound on the von Neumann entropy production: Φ ≤ C γ N (J/W)² (W ≫ J, γ ≪ J). A variational argument provides an upper bound for the Liouvillian gap. The hypothesis is subjected to a five-point falsification matrix; any single violation disproves it. We provide an open-source QuTiP implementation and numerical results for N=6, confirming the predicted scaling exponent ≈ −2 and persistent Néel imbalance. The framework is compatible with a long-lived prethermal regime and offers a concrete realization of the VES (information degradation minima) hypothesis in open many-body quantum systems. The repository contains the manuscript, executable code (QuTiP, ITensor skeleton), and all figures.
Abstract Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase , in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. The last decades of research have brought an unprecedented new variety of tools and indicators to study the breakdown of ergodicity, ranging from spectral and wave function measures, matrix elements of observables, through quantities probing unitary quantum dynamics, to transport and quantum information measures. We give a comprehensive overview of these approaches and attempt to provide a unified understanding of their main features. We emphasize general trends towards ergodicity with increasing length and time scales, which exclude naive single-parameter scaling hypothesis, necessitate the use of more refined scaling procedures, and prevent unambiguous extrapolations of numerical results to the asymptotic limit. Providing a concise description of numerical methods for studying ETH and MBL, we explore various approaches to tackle the question of the MBL phase. Persistent finite size drifts towards ergodicity consistently emerge in quantities derived from eigenvalues and eigenvectors of disordered many-body systems. The drifts are related to continuous inching towards ergodicity and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede the understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength provides premises suggesting the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.
We demonstrate that the topological entanglement entropy (γ = log D) is a pure universal number that strictly requires a hard gap (s=0) to exist. Building on the Hard Gap Criterion established in "The Hard Gap Criterion: Universality Classes and Thermodynamic Scaling in Gapped Dephasing Baths", we prove that a soft gap (s ≥ 1) induces anyon proliferation, destroys the topological order, and drives γ → 0. This establishes that the conservation of many-body quantum information is not just a property of the Hamiltonian, but a direct consequence of the infrared spectral structure of the environment. We show that γ is the many-body analogue of the entanglement concurrence C in the conservation law V² + C² = 1 established in "Conservation of Quantum Information in Gapped Baths: The Duality-Depleted Regime". The area law term represents local decoherence, while the topological constant represents globally protected information. The derivation uses only established theorems (the area law of entanglement entropy, the Kitaev-Preskill topological correction, and the algebraic theory of anyons) and contains no fitting, no adjustment, and no circularity. We provide exact numerical validation via the stabilizer formalism, computing the exact pure numbers for the Toric code (log 2 ≈ 0.693147), the Ising model (log 2), and the Fibonacci model (≈ 0.642965). The exact diagonalization confirms that the topological ground state is exactly pure (total stabilizer rank equals the number of qubits), validating the perfect delocalization of quantum information. We state four falsifiable predictions and provide a complete, reproducible Python script.
Understanding under which conditions physical systems thermalize is a long-standing question in many-body physics. While generic quantum systems thermalize, there are known instances where thermalization is hindered, for example in many-body localized (MBL) systems. Here we introduce a class of stochastic collision models coupling a many-body system out of thermal equilibrium to an external heat bath. We derive upper and lower bounds on the size of the bath required to thermalize the system via such models, under certain assumptions on the Hamiltonian. We use these bounds, expressed in terms of the max-relative entropy, to characterize the robustness of MBL systems against externally-induced thermalization. Our bounds are derived within the framework of resource theories using the convex split lemma, a recent tool developed in quantum information. We apply our results to the disordered Heisenberg chain, and numerically study the robustness of its MBL phase in terms of the required bath size. The thermalization of many-body localization phases poses a number of open questions related to our understanding of thermalization in quantum systems. Here, the authors aim to demonstrate that a quantum information approach can be used to investigate the mechanisms of thermalization in a quantum many-body system when coupled to an external system.
We derive testable consequences of the hypothesis that quantum decoherence is subject to a global compression bound. Starting from the bounded compression condition, we show that simultaneous decoherence across multiple channels of a quantum system must satisfy a trade-off relation. We formulate this bound in terms of three representation-invariant measures—the purity loss rate, the dissipative entropy production rate, and the Kossakowski eigenvalue sum—ensuring that all predictions are independent of the non-unique Lindblad decomposition. We derive the bound from two independent physical principles: the finite quantum channel capacity of the environment as an information sink, and the thermodynamic cost of irreversible decoherence via the Landauer principle. For multi-qubit systems, we predict that the decoherence rate of maximally entangled (GHZ) states saturates for sufficiently large qubit number N, deviating from the linear scaling predicted by standard Lindblad theory. We identify the transition regime between weak and strong system–environment coupling as the natural domain where the bound becomes experimentally accessible, and propose concrete protocols using superconducting qubits, trapped ions, and mesoscopic systems. The predictions are falsifiable and independent of any specific interpretive framework for quantum mechanics.
Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system-an interacting fermionic chain subject to quenched disorder-in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.