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A catalyst is a substance that enables otherwise impossible transformations between states of a system, without being consumed in the process. In this work, we apply the notion of catalysts to many-body quantum physics. In particular, we construct catalysts that enable transformations between different symmetry-protected topological (SPT) phases of matter using symmetric finite-depth quantum circuits. We discover a wide variety of catalysts, including GHZ-like states which spontaneously break the symmetry, gapless states with critical correlations, topological orders with symmetry fractionalization, and spin-glass states. These catalysts are all united under a single framework which has close connections to the theory of quantum anomalies, and we use this connection to put strong constraints on possible pure- and mixed-state catalysts. We also show how the catalyst approach leads to new insights into the structure of certain phases of matter, and to new methods to efficiently prepare SPT phases with long-range interactions or projective measurements.

We propose new physically reasonable systems capable of avoiding ergodicity at infinite time in the thermodynamic limit, even with generic perturbations and when coupled to a heat bath. In two dimensions, the rainbow loop soup has (stretched) exponentially numerous absolutely stable nonergodic states with diverging energy but vanishing energy density. In three dimensions the rainbow membrane soup has (stretched) exponentially numerous nonergodic states with diverging energy barriers, leading to infinite-time robust ergodicity breaking that even survives coupling to a nonzero temperature heat bath. We describe our results in the language of exact emergent symmetries and demonstrate how the systems avoid common instabilities. Our construction naturally connects to quantum dimer models, topologically ordered systems, the group word construction, and Hamiltonians whose low-energy eigenstates exhibit anomalous entanglement entropy., Comment: 4.25+2 pages, 3 figures

We introduce a framework that allows for the exact analytic treatment of quantum dynamics subject to coherent noise. The noise is modeled via unitary evolution under a Hamiltonian drawn from a random-matrix ensemble for arbitrary Hilbert-space dimension $N$. While the methods we develop apply to generic such ensembles with a notion of rotation invariance, we focus largely on the Gaussian unitary ensemble (GUE). Averaging over the ensemble of ''noisy'' Hamiltonians produces an effective quantum channel, the properties of which are analytically calculable and determined by the spectral form factors of the relevant ensemble. We compute spectral form factors of the GUE exactly for any finite $N$, along with the corresponding GUE quantum channel, and its variance. Key advantages of our approach include the ability to access exact analytic results for any $N$ and the ability to tune to the noise-free limit (in contrast, e.g., to the Haar ensemble), and analytic access to moments beyond the variance. We also highlight some unusual features of the GUE channel, including the nonmonotonicity of the coefficients of various operators as a function of noise strength and the failure to saturate the Haar-random limit, even with infinite noise strength., Comment: 18 pages, 5 figures

The 4d-electron trimer lattice Ba4Nb1-xRu3+xO12 is believed to feature a heavy spinon Fermi surface that underpins both a quantum spin liquid (QSL) and an adjacent heavy-fermion strange metal (HFSM) phase, depending on Nb content. Itinerant spinons act as heat carriers that render the charge-insulating QSL a much better thermal conductor than the HFSM [1]. We find application of magnetic fields up to 14 T below 150 mK induces an abrupt rise in the heat capacity by as much as 5000% and breaks the signature linear temperature dependences of the heat capacity of both phases. In contrast, the AC magnetic susceptibility and the electrical resistivity are insensitive to applied fields up to 14 T over the same milli-Kelvin temperature range, whereas field depresses the thermal conductivity by up to 40% at temperatures below 4 K. These complex phenomena imply applied magnetic field drastically alters the spinons at low temperatures and demand new physics: We propose the steep rise in the heat capacity (and thus entropy) at milli-Kelvin temperatures and strong magnetic fields announces a field-induced localization of spinons., Comment: 4 figures

We introduce a large class of models exhibiting robust ergodicity breaking in quantum dynamics. Our work is inspired by recent discussions of "topologically robust Hilbert space fragmentation," but massively generalizes in two directions: firstly from states describable as "loop-soups" to a broader class of states reminiscent of string-nets and sponges, and secondly from models restricted to square or cubic lattices, to models defined on arbitrary lattices (and even arbitrary graphs without translation invariance). Our constructions leverage a recently proposed group-theory framework [PRX 14, 021034 (2024)], and identify a host of new phenomena arising from the interplay of "group-model dynamics" and lattice structure. We make crisp connections to gauge theories, and our construction generalizes Kitaev's quantum double to infinite groups., Comment: 44 pages, 10 figures, to be submitted to SciPost Physics

We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed configurations" within Hilbert space. Our construction is based on quantum perturbations to a classical low-density parity check code. In principle, it is possible to detect this eigenstate localization by measuring few-body correlation functions in efficiently preparable mixed states., Comment: 5+8 pages, 1+0 figures. Published version

Many-body quantum games provide a natural perspective on phases of matter in quantum hardware, crisply relating the quantum correlations inherent in phases of matter to the securing of quantum advantage at a device-oriented task. In this paper we introduce a family of multiplayer quantum games for which topologically ordered phases of matter are a resource yielding quantum advantage. Unlike previous examples, quantum advantage persists away from the exactly solvable point and is robust to arbitrary local perturbations, irrespective of system size. We demonstrate this robustness experimentally on Quantinuum's H1-1 quantum computer by playing the game with a continuous family of randomly deformed toric code states that can be created with constant-depth circuits leveraging mid-circuit measurements and unitary feedback. We are thus able to tune through a topological phase transition - witnessed by the loss of robust quantum advantage - on currently available quantum hardware. This behavior is contrasted with an analogous family of deformed GHZ states, for which arbitrarily weak local perturbations destroy quantum advantage in the thermodynamic limit. Finally, we discuss a topological interpretation of the game, which leads to a natural generalization involving an arbitrary number of players., Comment: 4.5 pages, 3 figures