Crystalline topological insulator nanowires with a magnetic flux threaded through their cross section display Aharanov-Bohm conductance oscillations. A characteristic of these oscillations is the perfectly transmitted mode present at certain values of the magnetic flux, due to the appearance of an effective time-reversal symmetry combined with the topological origin of the nanowire surface states. In contrast, amorphous nanowires display a varying cross section along the wire axis that breaks the effective time-reversal symmetry. In this work, we use transport calculations to study the stability of the Aharanov-Bohm oscillations and the perfectly transmitted mode in amorphous topological nanowires. We observe that at low energies and up to moderate amorphicity the transport is dominated, as in the crystalline case, by the presence of a perfectly transmitted mode. In an amorphous nanowire the perfectly transmitted mode is protected by chiral symmetry or, in its absence, by a statistical time-reversal symmetry. At high amorphicities the Aharanov-Bohm oscillations disappear and the conductance is dominated by nonquantized resonant peaks. We identify these resonances as bound states and relate their appearance to a topological phase transition that brings the nanowires into a trivial insulating phase.

Correlation functions and correlation lengths are frequently used to describe phase transitions in quantum systems, but they require an explicit choice of observables. The recently introduced information lattice instead provides an observable-independent way to identify where and at which scale information is contained in quantum lattice models. Here, we use it to study the difference between the metallic and insulating regimes of one-dimensional noninteracting tight-binding chains. We find that the information per scale follows a power law in metals at low temperature and that Friedel-like oscillations are visible in the information lattice. At high temperature or in insulators at low temperature, the information per scale decays exponentially. Thus, the information lattice is a useful tool for analyzing the metal-insulator transition.

We investigate the out-of-equilibrium dynamics of quantum information in one-dimensional systems undergoing a quantum quench using a local perspective based on the information lattice. This framework provides a scale- and space-resolved decomposition of quantum correlations, enabling a hydrodynamic description of the information flow through well-defined local densities—termed local information—and currents. We apply this framework to three local quenches in noninteracting fermionic chains: (i) the release of a single particle into an empty tight-binding chain, (ii) the connection of two critical chains via the removal of a central barrier, and (iii) the coupling of a topological Kitaev chain to a critical chain. In each case, the information lattice reveals the local structure of correlation buildup and information interface effects, going beyond global measures such as the von Neumann entropy. In particular, through the information lattice, we uncover the signatures in the local information flow associated with topological edge modes and analytically explain the fractional von Neumann entropy values observed in Majorana quench protocols. Our approach is general and applicable to interacting, disordered, and open systems, providing a powerful tool for characterizing quantum information dynamics.

Disorder can prevent many-body quantum systems from reaching thermal equilibrium, leading to a many-body localized phase. Recent works suggest that nonperturbative effects caused by rare regions of low disorder may destabilize the localized phase. However, numerical simulations of interacting systems are generically possible only for small system sizes, where finite-size effects might dominate. Here we perform a numerical investigation of noninteracting disordered spin chains coupled to a local Lindblad bath at the boundary. Our results reveal strong finite-size effects in the Lindbladian gap in both bath-coupled Anderson and Aubry-Andr & eacute;-Harper models, leading to a non-monotonic behavior with the system size. We discuss the relaxation properties of a simple toy model coupled to local Lindblad baths, connecting its features to those of noninteracting localized chains. We comment on the implications of our findings for many-body systems.

We investigate the gauging of higher-form finite Abelian symmetries and their sub-groups in quantum spin models in spatial dimensions d = 2 and 3. Doing so, we naturally uncover gauged models with dual higher-group symmetries and potential mixed ‘t Hooft anomalies. We demonstrate that the mixed anomalies manifest as the symmetry fractionalization of higher-form symmetries participating in the mixed anomaly. Gauging is realized as an isomorphism or duality between the bond algebras that generate the space of quantum spin models with the dual generalized symmetry structures. We explore the mapping of gapped phases under such gauging related dualities for 0-form and 1-form symmetries in spatial dimension d = 2 and 3. In d = 2, these include several non-trivial dualities between short-range entangled gapped phases with 0-form symmetries and 0-form symmetry enriched Higgs and (twisted) deconfined phases of the gauged theory with possible symmetry fractionalizations. Such dualities also imply strong constraints on several unconventional, i.e., deconfined or topological transitions. In d = 3, among others, we find, dualities between topological orders via gauging of 1-form symmetries. Hamiltonians self-dual under gauging of 1-form symmetries host emergent non-invertible symmetries, realizing higher-categorical generalizations of the Tambara-Yamagami fusion category.

We propose a universal framework for classifying quantum states based on their scale-resolved correlation structure. Using the recently introduced information lattice, which provides an operational definition of the total amount of correlations at each scale, we define intrinsic characteristic length scales of quantum states. We analyze ground and midspectrum eigenstates of the disordered interacting Kitaev chain, showing that our framework provides a novel unbiased approach to quantum matter.

The surface of a three-dimensional topological insulator (TI) hosts surface states whose properties are determined by a Dirac-like equation. The electronic system on the surface of TI nanowires with a polygonal cross-sectional shape adopts the corresponding polygonal shape. In a constant transverse magnetic field, such an electronic system exhibits rich properties because different facets of the polygon experience different values of the magnetic field due to the changing magnetic field projection between facets. We investigate the energy spectrum and transport properties of nanowires, where we consider three different polygonal shapes, all showing distinct properties visible in the energy spectrum and transport properties. Here we propose that the wire conductance can be used to establish the presence of nanowire surface states by rotating the magnetic field and observing a variation in agreement with the cross-sectional shape of the nanowire. Distinguishing between the different shapes also works in the presence of impurities as long as conductance steps are discernible, thus revealing the subband structure.

During time evolution of many-body systems entanglement grows rapidly, limiting exact simulations to small-scale systems or small timescales. Quantum information tends, however, to flow towards larger scales without returning to local scales, such that its detailed large-scale structure does not directly affect local observables. This allows for the removal of large-scale quantum information in a way that preserves all local observables and gives access to large-scale and large-time quantum dynamics. To this end, we use the recently introduced information lattice to organize quantum information into different scales, allowing us to define local information and information currents that we employ to systematically discard long-range quantum correlations in a controlled way. Our approach relies on decomposing the system into subsystems up to a maximum scale and time evolving the subsystem density matrices by solving the subsystem von Neumann equations in parallel. Importantly, the information flow needs to be preserved during the discarding of large-scale information. To achieve this without the need to make assumptions about the microscopic details of the information current, we introduce a second scale at which information is discarded, while using the state at the maximum scale to accurately obtain the information flow. The resulting algorithm, which we call local-information time evolution, is highly versatile and suitable for investigating many-body quantum dynamics in both closed and open quantum systems with diverse hydrodynamic behaviors. We present results for the energy transport in the mixed-field Ising model and the magnetization transport in the XX spin chain with onsite dephasing where we accurately determine the power-law exponent and the diffusion coefficients. Furthermore, the information lattice framework employed here promises to offer insightful results about the spatial and temporal behavior of entanglement in many-body systems.

While topology is a property of a quantum state itself, most existing methods for characterizing the topology of interacting phases of matter require direct knowledge of the underlying Hamiltonian. We offer an alternative by utilizing the one-particle density matrix formalism to extend the concept of the Chern, chiral, and Chern-Simons markers to include interactions. The one-particle density matrix of a free-fermion state is a projector onto the occupied bands, defining a Brillouin zone bundle of the given topological class. This is no longer the case in the interacting limit, but as long as the one-particle density matrix is gapped, its spectrum can be adiabatically flattened, connecting it to a topologically equivalent projector. The corresponding topological markers thus characterize the topology of the interacting phase. Importantly, the one-particle density matrix is defined in terms of a given state alone, making the local markers numerically favorable, and providing a valuable tool for characterizing topology of interacting systems when only the state itself is available. To demonstrate the practical use of the markers we use the chiral marker to identify the topology of midspectrum eigenstates of the Ising-Majorana chain across the transition between the ergodic and many-body localized phases. We also apply the chiral marker to random states with a known topology, and compare it with the entanglement spectrum degeneracy.

The eigenstate thermalization hypothesis describes how most isolated many-body quantum systems reach thermal equilibrium. However, the hypothesis is violated by phenomena such as many-body localization and quantum many-body scars. In this work, we study a finite, two-dimensional, disordered model hosting a tower of scar states. This construction is a particular instance of a general framework and we demonstrate its generality by constructing two disordered models hosting a different tower of scar states. At weak disorder, we find numerically that the spectra are nonthermal, and the scar states appear as exact eigenstates with high entropy for certain bipartitions. At strong disorder, the spectra localize and the scar states are identified as inverted scars since the scar states are embedded in a localized background as opposed to a thermal background. We argue that, for the considered type of models, the localization is stronger than what would be naively expected, and we show this explicitly for one of the models. The argument also provides guidelines for obtaining similarly strong localization in other scarred models. We study the transition from the thermal phase to localization by observing the adjacent gap ratio shifting from the Wigner surmise to the Poisson distribution with increasing disorder strength. Moreover, the entanglement entropy transitions from volume-law scaling with system size at weak disorder to area-law scaling at strong disorder. Finally, we demonstrate that localization protects scar revivals for initial states with partial support in the scar subspace.