Correlations and commuting transfer matrices in integrable unitary circuits

We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.

Topological Edge Transport in Twisted Double-Bilayer Graphene

Topological insulators realized in materials with strong spin-orbit interactions challenged the long-held view that electronic materials are classified as either conductors or insulators. The emergence of controlled, two-dimensional moire patterns has opened new vistas in the topological materials landscape. Here we report on evidence, obtained by combining thermodynamic measurements, local and non-local transport measurements, and theoretical calculations, that robust topologically non-trivial, valley Chern insulators occur at charge neutrality in twisted double-bilayer graphene (TDBG). These time reversal-conserving valley Chern insulators are enabled by valley-number conservation, a symmetry that emerges from the moire pattern. The thermodynamic gap extracted from chemical potential measurements proves that TDBG is a bulk insulator under transverse electric field, while transport measurements confirm the existence of conducting edge states. A Landauer-Buttiker analysis of measurements on multi-terminal samples allows us to quantitatively assess edge state scattering and demonstrate that it does not destroy the edge states, leaving the bulk-boundary correspondence largely intact.

Symmetry broken Chern insulators and magic series of Rashba-like Landau level crossings in magic angle bilayer graphene

Flat-bands in magic angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations, superconductivity and mag-netism. However, the phases of MATBG in magnetic field, and what they reveal about the zero-field phase diagram remain relatively unchartered. Here we use magneto-transport and Hall measurements to reveal a rich sequence of wedge-like regions of quantized Hall conductance with Chern numbers C = +(-)1, +(-)2, +(-)3, +(-)4 which nucleate from integer fillings of the moire unit cell v = +(-)3, +(-)2, +(-)1, 0 correspondingly. We interpret these phases as spin and valley polarized Chern insulators, equivalent to quantum Hall ferro-magnets. The exact sequence and correspondence of Chern numbers and filling factors suggest that these states are driven directly by electronic interactions which specifically break time-reversal symmetry in the system. We further study quantum magneto-oscillation in the yet unexplored higher energy dispersive bands with a Rashba-like dis-persion. Analysis of Landau level crossings enables a parameter-free comparison to a newly derived magic series of level crossings in magnetic field and provides constraints on the parameters w0 and w1 of the Bistritzer-MacDonald MATBG Hamiltonian. Over-all, our data provides direct insights into the complex nature of symmetry breaking in MATBG and allows for quantitative tests of the proposed microscopic scenarios for its electronic phases.

Hofstadter Topology: Non-crystalline Topological Materials at High Flux

The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding $sim 10^4$ T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of remarkable possible phases emerges. Remarkably, we find topological phases which cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with nonzero Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with nontrivial Kane-Mele invariant produces a 3D TI or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of two-fold rotation and time-reversal and show that there exists a 3D higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group which exists at rational values of the flux. The advent of Moire lattices also renders our work relevant experimentally. In Moire lattices, it is possible for fields of order $1-30$ T to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

Solving the quantum dimer and six vertex models one electric field line at a time

The nature and the very existence of the resonant plaquette valence bond state that separates the classical columnar phase and the Rokhsar and Kivelson point in the quantum dimer model remains unsettled. Here we take a different line of attack on this model, and on the closely related six vertex model, by exploiting the global conservation law of the number of electric field lines. This allows us to study a single fluctuating electric field line which we show maps exactly onto a one dimensional spin chain. In the case of the six vertex model, the electric field line maps onto the celebrated spin 1/2 XXZ model which can be solved exactly. In the quantum dimer model, the electric field line is mapped onto a two-leg spin 1/2 ladder, which we study using numerical exact diagonalization. Our findings are consistent with the existence of three distinct phases including a Luttinger liquid phase, the one-dimensional precursor to the two-dimensional plaquette valence bond solid. The uncanny resemblance of our quasi-one-dimensional electric field line problem to the full two-dimensional problem suggests that much of the behavior of the latter might be understood by thinking of it as a closely packed array of field lines which themselves are undergoing non-trivial phase transitions.

The Metal-Poor Stellar Halo in RAVE-TGAS and its Implications for the Velocity Distribution of Dark Matter

The local velocity distribution of dark matter plays an integral role in interpreting the results from direct detection experiments. We previously showed that metal-poor halo stars serve as excellent tracers of the virialized dark matter velocity distribution using a high-resolution hydrodynamic simulation of a Milky Way--like halo. In this paper, we take advantage of the first textit{Gaia} data release, coupled with spectroscopic measurements from the RAdial Velocity Experiment (RAVE), to study the kinematics of stars belonging to the metal-poor halo within an average distance of $sim 5$ kpc of the Sun. We study stars with iron abundances [Fe/H]$ < -1.5$ and $-1.8$ that are located more than $1.5$ kpc from the Galactic plane. Using a Gaussian mixture model analysis, we identify the stars that belong to the halo population, as well as some kinematic outliers. We find that both metallicity samples have similar velocity distributions for the halo component, within uncertainties. Assuming that the stellar halo velocities adequately trace the virialized dark matter, we study the implications for direct detection experiments. The Standard Halo Model, which is typically assumed for dark matter, is discrepant with the empirical distribution by $sim6sigma$ and predicts fewer high-speed particles. As a result, the Standard Halo Model overpredicts the nuclear scattering rate for dark matter masses below $sim 10$ GeV. The kinematic outliers that we identify may potentially be correlated with dark matter substructure, though further study is needed to establish this correspondence.

Empirical Determination of Dark Matter Velocities using Metal-Poor Stars

The Milky Way dark matter halo is formed from the accretion of smaller subhalos. These sub-units also harbor stars---typically old and metal-poor---that are deposited in the Galactic inner regions by disruption events. In this Letter, we show that the dark matter and metal-poor stars in the Solar neighborhood share similar kinematics due to their common origin. Using the high-resolution Eris simulation, which traces the evolution of both the dark matter and baryons in a realistic Milky-Way analog galaxy, we demonstrate that metal-poor stars are indeed effective tracers for the local, virialized dark matter velocity distribution. The local dark matter velocities can therefore be inferred from observations of the stellar halo made by the Sloan Digital Sky Survey within 4 kpc of the Sun. This empirical distribution differs from the Standard Halo Model in important ways and suggests that the bounds on the spin-independent scattering cross section may be weakened for dark matter masses below $sim$10 GeV. Data from Gaia will allow us to further refine the expected distribution for the smooth dark matter component, and to test for the presence of local substructure.