Publications

Recent quantum Hall experiments have observed "daughter states"next to several plateaus at half-integer filling factors in various platforms. These states were first proposed based on model wave functions for the Moore-Read state by Levin and Halperin. We show that these daughters and their parents belong to an extensive family tree that encompasses all pairing channels and permits a unified description in terms of weakly interacting composite fermions. Each daughter represents a bosonic integer quantum Hall state formed by composite-fermion pairs. The pairing of the parent dictates an additional number of filled composite-fermion Landau levels. We support our field-theoretic composite-fermion treatment by using the K-matrix formalism, analysis of trial wave functions, and a coupled-wire construction. Our analysis yields the topological orders, quantum numbers, and experimental signatures of all daughters of paired states at half-filling and "next-generation"even denominators. Crucially, no two daughters share the same two parents. The unique parentage implies that Hall conductance measurements alone could pinpoint the topological order of even-denominator plateaus. Additionally, we propose a numerically suitable trial wave function for one daughter of the SU(2)2 topological order, which arises at filling factor ν=611. Finally, our insights explain experimentally observed features of transitions in wide-quantum wells, such as suppression of the Jain states with the simultaneous development of half-filled and daughter states.

Non-Abelian phases are among the most highly sought states of matter, with those whose anyons permit universal quantum gates constituting the ultimate prize. The most promising candidate of such a phase is the fractional quantum Hall plateau at filling factors ν=125, which putatively facilitates Fibonacci anyons. Experimental validation of this assertion poses a major challenge and remains elusive. We present a measurement protocol that could achieve this goal with already-demonstrated experimental techniques. Interfacing the ν=125 state with any readily available Abelian state yields a binary outcome of upstream noise or no noise. Judicious choices of the Abelian states can produce a sequence of yes-no outcomes that fingerprint the possible non-Abelian phase by ruling out its competitors. Crucially, this identification is insensitive to the precise value of the measured noise and can uniquely identify the anyon type at filling factors ν=125. In addition, it can distinguish any non-Abelian candidates at half-filling in graphene and semiconductor heterostructures.

Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure of vortices when the microscopic particles - electrons or spinful bosons - are near half-filling. These conditions lead to a compact gauge theory of spinons and chargons, which arise as the fundamental topological defects of the low-energy vortices. The gauge theory formulation is particularly suitable for studying numerous exotic phases and transitions. We support the general analysis by an exact implementation of the duality on a coupled-wire array. Finally, we demonstrate how the latter can be exploited to construct parent Hamiltonians for fractional phases and their transitions.

The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum many-body systems. Analytical studies of this phenomenon are primarily based on two distinct frameworks: field theories of partons and emergent gauge fields, or coupled arrays of one-dimensional quantum wires. We unify these approaches for two-dimensional spin systems. Via exact manipulations, we demonstrate how parton gauge theories arise in microscopic wire arrays and explicitly relate spin operators to emergent quasiparticles and gauge-field monopoles. This correspondence allows us to compute physical correlation functions within both formulations and leads to a straightforward algorithm for constructing parent Hamiltonians for a wide range of exotic phases. We exemplify this technique for several chiral and nonchiral quantum spin liquids.

We introduce (3+1)-dimensional models of short-range-interacting electrons that form a strongly correlated many-body state whose low-energy excitations are relativistic neutral fermions coupled to an emergent gauge field, QED4. We discuss the properties of this critical state and its instabilities towards exotic phases such as a gapless "composite" Weyl semimetal and fully gapped topologically ordered phases that feature anyonic pointlike as well as linelike excitations. These fractionalized phases describe electronic insulators. They may be further enriched by symmetries which result in the formation of nontrivial surface states.

We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2π Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state—distinct in the presence of inversion symmetry—without Berry flux. As in the Dirac composite Fermi liquid introduced by Son [Phys. Rev. X 5, 031027 (2015)], breaking particle-hole symmetry recovers the familiar Chern-Simons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.

Spontaneous breaking of translational symmetry, known as density-wave order, is common in nature. However, such states are strongly sensitive to impurities or other forms of frozen disorder leading to fascinating glassy phenomena. We analyze impurity effects on a particularly ubiquitous form of broken translation symmetry in solids: a spin-density wave (SDW) with spatially modulated magnetic order. Related phenomena occur in pair-density-wave (PDW) superconductors where the superconducting order is spatially modulated. For weak disorder, we find that the SDW or PDW order can generically give way to a SDW or PDW glass—new phases of matter with a number of striking properties, which we introduce and characterize here. In particular, they exhibit an interesting combination of conventional (symmetry-breaking) and spin-glass (Edwards-Anderson) order. This is reflected in the dynamic response of such a system, which—as expected for a glass—is extremely slow in certain variables, but, surprisingly, is fast in others. Our results apply to all uniaxial metallic SDW systems where the ordering vector is incommensurate with the crystalline lattice. In addition, the possibility of a PDW glass has important consequences for some recent theoretical and experimental work on La_2−xBa_xCu₂O₄.

We study theoretically quantum melting transitions of stripe order in a metallic environment, and the associated reconstruction of the electronic Fermi surface. We show that such quantum phase transitions can be continuous in situations where the stripe melting occurs by proliferating pairs of dislocations in the stripe order parameter without proliferating single dislocations. We develop an intuitive picture of such phases as “stripe loop metals” where the fluctuating stripes form closed loops of arbitrary size at long distances. We obtain a controlled critical theory of a few different continuous quantum melting transitions of stripes in metals. At such a (deconfined) critical point, the fluctuations of the stripe order parameter are strongly coupled, yet tractable. They also decouple dynamically from the Fermi surface. We calculate many universal properties of these quantum critical points. In particular, we find that the full Fermi surface and the associated Landau quasiparticles remain sharply defined at the critical point. We discuss the phenomenon of Fermi surface reconstruction across this transition and the effect of quantum critical stripe fluctuations on the superconducting instability. We study possible relevance of our results to several phenomena in the cuprates.

We present a theoretical approach to describing the Mott transition of electrons on a two-dimensional lattice that begins with the low-energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations that correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a priori assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low-energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon Fermi surface coupled to a U(1) gauge field, which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin antisymmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.