Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy

Protected zero modes in quantum physics traditionally arise in the context of ground states of many-body Hamiltonians. Here we study the case where zero modes exist in the center of a reflection-symmetric many-body spectrum, giving rise to the notion of a protected "infinite-temperature" degeneracy. For a certain class of nonintegrable spin chains, we show that the number of zero modes is determined by a chiral index that grows exponentially with system size. We propose a dynamical protocol, feasible in ongoing experiments in Rydberg atom quantum simulators, to detect these many-body zero modes and their protecting spectral reflection symmetry. Finally, we consider whether the zero energy states obey the eigenstate thermalization hypothesis, as is expected of states in the middle of the many-body spectrum. We find intriguing differences in their eigenstate properties relative to those of nearby nonzero-energy eigenstates at finite system sizes.Comment: 8+1 pages, 5+1 figure

Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model

We demonstrate the existence of exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which generically have finite energy density and are exponentially many in number, are populated by noninteracting excitations. They can exhibit Anderson localization with area-law eigenstate entanglement or, surprisingly, ballistic transport at any disorder strength. These properties differ strikingly from those of typical eigenstates nearby in energy, which we show give rise to diffusive transport as expected in a chaotic quantum system. We discuss how to observe these atypical eigenstates in cold-atom experiments realizing the Fermi-Hubbard model, and comment on the robustness of their properties.Comment: 6+epsilon pages, 4 figures; v2 is published versio

Braiding and Gapped Boundaries in Fracton Topological Phases

We study gapped boundaries of Abelian type-I fracton systems in three spatial dimensions. Using the X-cube model as our motivating example, we give a conjecture, with partial proof, of the conditions for a boundary to be gapped. In order to state our conjecture, we use a precise definition of fracton braiding and show that bulk braiding of fractons has several features that make it \textit{insufficient} to classify gapped boundaries. Most notable among these is that bulk braiding is sensitive to geometry and is "nonreciprocal," that is, braiding an excitation $a$ around $b$ need not yield the same phase as braiding $b$ around $a$. Instead, we define fractonic "boundary braiding," which resolves these difficulties in the presence of a boundary. We then conjecture that a boundary of an Abelian fracton system is gapped if and only if a "boundary Lagrangian subgroup" of excitations is condensed at the boundary, this is a generalization of the condition for a gapped boundary in two spatial dimensions, but it relies on boundary braiding instead of bulk braiding. We also discuss the distinctness of gapped boundaries and transitions between different topological orders on gapped boundaries.Comment: 18 pages, 21 figures. v2: Typo fixes, added references. v3: Published version. Some corrections to figure

Floquet Supersymmetry

We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical sypersymmetry. In particular, we find Floquet analogues of the Witten index that place lower bounds on the degeneracies of states with quasienergies $0$ and $\pi$. Moreover, we show that in some cases time reflection symmetry can also interchange fermions and bosons, leading to fermion/boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies $0$ and $\pi$, which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.Comment: 5+4 pages, 3+1 figures. v2 includes additional connections with SUSY and a new Appendix containing a discussion of robustness to time-reflection-breaking perturbations. This version accepted to PR

Non-Abelian braiding of light

Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially-fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.Comment: 5+13 pages, 2+3 figures; v4 has stylistic revisions to the main text and expanded SM featuring new numerical results providing direct confirmation of non-Abelian braiding, as well as a discussion of the relationship to Majorana zero modes. Accepted in PR

Occupation of topological Floquet bands in open systems

Floquet topological insulators are noninteracting quantum systems that, when driven by a time-periodic field, are described by effective Hamiltonians whose bands carry nontrivial topological invariants. A longstanding question concerns the possibility of selectively populating one of these effective bands, thereby maximizing the system's resemblance to a static topological insulator. We study such Floquet systems coupled to a zero-temperature thermal reservoir that provides dissipation. We find that the resulting electronic steady states are generically characterized by a finite density of excitations above the effective ground state, even when the driving has a small amplitude and/or large frequency. We discuss the role of reservoir engineering in mitigating this problem.Comment: 10 pages, 3 figures; v2 contains updated references; v3 is revised and expande

Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation

We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system was initialized in a particular product state. This pronounced coherence has been attributed to the presence of special "scarred" eigenstates with nearly equally-spaced energies and putative nonergodic properties despite their finite energy density. In this paper we uncover a surprising connection between these scarred eigenstates and low-lying quasiparticle excitations of the spin chain. In particular, we show that these eigenstates can be accurately captured by a set of variational states containing a macroscopic number of magnons with momentum $\pi$. This leads to an interpretation of the scarred eigenstates as finite-energy-density condensates of weakly interacting $\pi$-magnons. One natural consequence of this interpretation is that the scarred eigenstates possess long-range order in both space and time, providing a rare example of the spontaneous breaking of continuous time-translation symmetry. We verify numerically the presence of this space-time crystalline order and explain how it is consistent with established no-go theorems precluding its existence in ground states and at thermal equilibrium.Comment: 13 pages, 8 figures; v2 updated reference

Topological gaps without masses in driven graphene-like systems

We illustrate the possibility of realizing band gaps in graphene-like systems that fall outside the existing classification of gapped Dirac Hamiltonians in terms of masses. As our primary example we consider a band gap arising due to time-dependent distortions of the honeycomb lattice. By means of an exact, invertible, and transport-preserving mapping to a time-independent Hamiltonian, we show that the system exhibits Chern-insulating phases with quantized Hall conductivities $\pm e^2/h$. The chirality of the corresponding gapless edge modes is controllable by both the frequency of the driving and the manner in which sublattice symmetry is broken by the dynamical lattice modulations. Finally, we discuss a promising possible realization of this physics in photonic lattices.Comment: 8 pages, 3 figures; added discussion of distinctness from Haldane model; corrected reference

Stroboscopic Symmetry-Protected Topological Phases

Symmetry-protected topological (SPT) phases of matter have been the focus of many recent theoretical investigations, but controlled mechanisms for engineering them have so far been elusive. In this work, we demonstrate that by driving interacting spin systems periodically in time and tuning the available parameters, one can realize lattice models for bosonic SPT phases in the limit where the driving frequency is large. We provide concrete examples of this construction in one and two dimensions, and discuss signatures of these phases in stroboscopic measurements of local observables.Comment: 6+6 pages, 4+2 figures; v2 includes revised discussion of measurement protocol; v3 is expanded, with plots from additional numerical simulations including all Magnus corrections; v4 is version accepted to PR

Configuration-Controlled Many-Body Localization and the Mobility Emulsion

We uncover a new non-ergodic phase, distinct from the many-body localized (MBL) phase, in a disordered two-leg ladder of interacting hardcore bosons. The dynamics of this emergent phase, which has no single-particle analog and exists only for strong disorder and finite interaction, is determined by the many-body configuration of the initial state. Remarkably, this phase features the $\textit{coexistence}$ of localized and extended many-body states at fixed energy density and thus does not exhibit a many-body mobility edge, nor does it reduce to a model with a single-particle mobility edge in the noninteracting limit. We show that eigenstates in this phase can be described in terms of interacting emergent Ising spin degrees of freedom ("singlons") suspended in a mixture with inert charge degrees of freedom ("doublons" and "holons"), and thus dub it a $\textit{mobility emulsion}$ (ME). We argue that grouping eigenstates by their doublon/holon density reveals a transition between localized and extended states that is invisible as a function of energy density. We further demonstrate that the dynamics of the system following a quench may exhibit either thermalizing or localized behavior depending on the doublon/holon density of the initial product state. Intriguingly, the ergodicity of the ME is thus tuned by the initial state of the many-body system. These results establish a new paradigm for using many-body configurations as a tool to study and control the MBL transition. The ME phase may be observable in suitably prepared cold atom optical lattices.Comment: 20 pages, 12 figure