1,643 research outputs found

    Anyon dynamics in field-driven phases of the anisotropic Kitaev model

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    The Kitaev model on a honeycomb lattice with bond-dependent Ising interactions offers an exactly solvable model of a quantum spin liquid (QSL) with gapped Z2Z_2 fluxes and gapless linearly dispersing Majorana fermions in the isotropic limit (Kx=Ky=KzK_x=K_y=K_z). We explore the phase diagram along two axes, an external magnetic field, hh, applied out-of-plane of the honeycomb, and anisotropic interactions, KzK_z larger than the other two. For Kz/K≫2K_z/K\gg 2 and h=0h=0, the matter Majorana fermions have the largest gap, and the system is described by a gapped Z2Z_2 Toric code in which the Z2Z_2 fluxes form the low energy bosonic Ising electric (e) and magnetic (m) charges along with their fermionic bound state ϵ=e×m\epsilon=e\times m. In this regime, we find that a small out-of-plane magnetic field creates ϵ\epsilon fermions that disperse in fixed one-dimensional directions before the transition to a valence bond solid phase, providing a direct dynamical signature of low energy Z2Z_2 Abelian flux excitations separated from the Majorana sector. At lower KzK_z in the center of the Abelian phase, in a regime we dub the primordial fractionalized (PF) regime, the field generates a hybridization between the ϵ\epsilon fermions and the Majorana matter fermions, resulting in a ψ\psi fermion. All the other phases in the field-anisotropy plane are naturally obtained from this primordial soup. We show that in the Z2Z_2 Abelian phase, including the PF regime, the dynamical structure factors of local spin flip operators reveal distinct peaks that can be identified as arising from different anyonic excitations. We present in detail their signatures in energy and momentum and propose their identification by inelastic light scattering or inelastic polarized neutron scattering as ``smoking gun" signatures of fractionalization in the QSL phase.Comment: 16 pages, 6 figures, 1 tabl

    Quantum traces for SLnSL_n-skein algebras

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    We establish the existence of several quantum trace maps. The simplest one is an algebra map between two quantizations of the algebra of regular functions on the SLnSL_n-character variety of a surface S\mathfrak{S} equipped with an ideal triangulation λ\lambda. The first is the (stated) SLnSL_n-skein algebra S(S)\mathscr{S}(\mathfrak{S}). The second X‾(S,λ)\overline{\mathcal{X}}(\mathfrak{S},\lambda) is the Fock and Goncharov's quantization of their XX-moduli space. The quantum trace is an algebra homomorphism trˉX:S‾(S)→X‾(S,λ)\bar{tr}^X:\overline{\mathscr{S}}(\mathfrak{S})\to\overline{\mathcal{X}}(\mathfrak{S},\lambda) where the reduced skein algebra S‾(S)\overline{\mathscr{S}}(\mathfrak{S}) is a quotient of S(S)\mathscr{S}(\mathfrak{S}). When the quantum parameter is 1, the quantum trace trˉX\bar{tr}^X coincides with the classical Fock-Goncharov homomorphism. This is a generalization of the Bonahon-Wong quantum trace map for the case n=2n=2. We then define the extended Fock-Goncharov algebra X(S,λ)\mathcal{X}(\mathfrak{S},\lambda) and show that trˉX\bar{tr}^X can be lifted to trX:S(S)→X(S,λ)tr^X:\mathscr{S}(\mathfrak{S})\to\mathcal{X}(\mathfrak{S},\lambda). We show that both trˉX\bar{tr}^X and trXtr^X are natural with respect to the change of triangulations. When each connected component of S\mathfrak{S} has non-empty boundary and no interior ideal point, we define a quantization of the Fock-Goncharov AA-moduli space A‾(S,λ)\overline{\mathcal{A}}(\mathfrak{S},\lambda) and its extension A(S,λ)\mathcal{A}(\mathfrak{S},\lambda). We then show that there exist quantum traces trˉA:S‾(S)→A‾(S,λ)\bar{tr}^A:\overline{\mathscr{S}}(\mathfrak{S})\to\overline{\mathcal{A}}(\mathfrak{S},\lambda) and trA:S(S)↪A(S,λ)tr^A:\mathscr{S}(\mathfrak{S})\hookrightarrow\mathcal{A}(\mathfrak{S},\lambda), where the second map is injective, while the first is injective at least when S\mathfrak{S} is a polygon. They are equivalent to the XX-versions but have better algebraic properties.Comment: 111 pages, 35 figure

    Fractional quantum anomalous Hall states in twisted bilayer MoTe2_2 and WSe2_2

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    We demonstrate via exact diagonalization that AA stacked TMD homobilayers host fractional quantum anomalous Hall states, zero-field analogs of their finite-field cousins, at fractional fillings n=13, 23n=\frac{1}{3},\, \frac{2}{3}. Additionally, ferromagnetism is present across a broad range of fillings where the system is insulating or metallic alike. While both fractional quantum anomalous hall states are robust at angles near θ≈2∘\theta\approx 2^{\circ}, the n=13n=\frac{1}{3} gives way to a charge density wave with increasing twist angle whereas the n=23n=\frac{2}{3} state survives across a much broader range of twist angles. We show that the competition between FQAH and charge density wave or metallic phases is primarily controlled by Bloch band wavefunctions and dispersion respectively

    Floquet topological phase transitions induced by uncorrelated or correlated disorder

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    The impact of weak disorder and its spatial correlation on the topology of a Floquet system is not well understood so far. In this study, we investigate a model closely related to a two-dimensional Floquet system that has been realized in experiments. In the absence of disorder, we determine the phase diagram and identify a new phase characterized by edge states with alternating chirality in adjacent gaps. When weak disorder is introduced, we examine the disorder-averaged Bott index and analyze why the anomalous Floquet topological insulator is favored by both uncorrelated and correlated disorder, with the latter having a stronger effect. For a system with a ring-shaped gap, the Born approximation fails to explain the topological phase transition, unlike for a system with a point-like gap.Comment: 6+3 pages, 3 + 2 figure

    The orbifold DT/PT vertex correspondence

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    We present an orbifold topological vertex formalism for PT invariants of toric Calabi-Yau 3-orbifolds with transverse An−1A_{n-1} singularities. We give a proof of the orbifold DT/PT Calabi-Yau topological vertex correspondence. As an application, we derive an explicit formula for the PT Zn\mathbb{Z}_{n}-vertex in terms of loop Schur functions and prove the multi-regular orbifold DT/PT correspondence.Comment: Some minor change

    Hiérarchie de fusion et systèmes T et Y pour le modèle de boucles diluées A2(2)A_2^{(2)} sur le ruban

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    Le modèle de boucles diluées A2(2)A_2^{(2)} est étudié pour la géométrie d'un ruban de taille NN. Deux familles de conditions frontières sont connues pour satisfaire l’équation de Yang-Baxter à la frontière. Fixer ces conditions aux deux bouts du ruban donne un total de quatre modèles. Pour chaque modèle, les matrices de transfert, qui commutent entre elles, sont connues. Dans ce mémoire, la hiérarchie de fusion des matrices de transfert et les systèmes T et Y sont construits pour chaque modèle et pour un paramètre de croisement λ\lambda générique. Pour λ/π\lambda/\pi rationnel, il est prouvé qu'il existe une relation linéaire entre les matrices fusionnées qui ferme la hiérarchie de fusion en un système fini. Les relations de fusion et de fermeture permettent de calculer les premiers termes d'une expansion de l'énergie libre lorsque NN est grand. Ces premiers termes correspondent à l'énergie libre de bulk et de bord. Les résultats analytiques sont en accord avec des résultats numériques obtenus pour de petits NN. Ce mémoire complète une étude des modèles A2(2)A_2^{(2)} avec des conditions frontières périodiques (A. Morin-Duchesne, P.A. Pearce, J. Stat. Mech. (2019)).We study the dilute A2(2)A_2^{(2)} loop models on the geometry of a strip of width NN. Two families of boundary conditions are known to satisfy the boundary Yang-Baxter equation. Fixing the boundary condition on the two ends of the strip leads to four models. We construct the fusion hierarchy of commuting transfer matrices for the model as well as its T- and Y-systems, for these four boundary conditions and with a generic crossing parameter λ\lambda. For λ/π\lambda/\pi rational we prove a linear relation satisfied by the fused transfer matrices that closes the fusion hierarchy into a finite system. The fusion relations allow us to compute the two leading terms in the large-NN expansion of the free energy, namely the bulk and boundary free energies. These are found to be in agreement with numerical data obtained for small NN. The present work complements a previous study (A. Morin-Duchesne, P.A. Pearce, J. Stat. Mech. (2019)) that investigated the dilute A2(2)A_2^{(2)} loop models with periodic boundary conditions

    Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice

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    The Jordan-Wigner map in 2D is as an exact lattice regularization of the 2 pi-flux attachment to a hard-core boson (or spin-1/2) leading to a composite-fermion particle. When the spin-1/2 model obeys ice rules this map preserves locality, namely, local Rohkshar-Kivelson models of spins are mapped onto local models of Jordan-Wigner/composite-fermions. Using this composite-fermion dual representation of RK models, we construct spin-liquid states by projecting Slater determinants onto the subspaces of the ice rules. Interestingly, we find that these composite-fermions behave as ``dipolar" partons for which the projective implementations of symmetries are very different from standard ``point-like" partons. We construct interesting examples of composite-fermion liquid states that respect all microscopic symmetries of the RK model. In the six-vertex subspace, we constructed a time-reversal and particle-hole-invariant state featuring two massless Dirac nodes, which is a composite-fermion counterpart to the classic pi-flux state of Abrikosov-Schwinger fermions in the square lattice. This state is a good ground state candidate for a modified RK-like Hamiltonian of quantum spin-ice. In the dimer subspace, we construct a state fearturing a composite Fermi surface but with nesting instabilities towards ordered phases such as the columnar state. We have also analyzed the low energy emergent gauge structure. If one ignores confinement, the system would feature a U(1) x U(1) low energy gauge structure with two associated gapless photon modes, but with the composite fermion carrying gauge charge only for one photon and behaving as a gauge neutral dipole under the other. These states are examples of pseudo-scalar U(1) spin liquids where mirror and time-reversal symmetries act as particle-hole conjugations, and the emergent magnetic fields are even under such time-reversal or lattice mirror symmetries.Comment: 44 pages, 35 figure

    Exotic Ground States and Dynamics in Constrained Systems

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    The overarching theme of this thesis is the question of how constraints influence collective behavior. Constraints are crucial in shaping both static and dynamic properties of systems across diverse areas within condensed matter physics and beyond. For example, the simple geometric constraint that hard particles cannot overlap at high density leads to slow dynamics and jamming in glass formers. Constraints also arise effectively at low temperature as a consequence of strong competing interactions in magnetic materials, where they give rise to emergent gauge theories and unconventional magnetic order. Enforcing constraints artificially in turn can be used to protect otherwise fragile quantum information from external noise. This thesis in particular contains progress on the realization of different unconventional phases of matter in constrained systems. The presentation of individual results is organized by the stage of realization of the respective phase. Novel physical phenomena after conceptualization are often exemplified in simple, heuristic models bearing little resemblance of actual matter, but which are interesting enough to motivate efforts with the final goal of realizing them in some way in the lab. One form of progress is then to devise refined models, which retain a degree of simplification while still realizing the same physics and improving the degree of realism in some direction. Finally, direct efforts in realizing either the original models or some refined version in experiment today are mostly two-fold. One route, having grown in importance rapidly during the last two decades, is via the engineering of artificial systems realizing suitable models. The other, more conventional way is to search for realizations of novel phases in materials. The thesis is divided into three parts, where Part I is devoted to the study of two simple models, while artificial systems and real materials are the subject of Part II and Part III respectively. Below, the content of each part is summarized in more detail. After a general introduction to entropic ordering and slow dynamics we present a family of models devised as a lattice analog of hard spheres. These are often studied to explore whether low-dimensional analogues of mean-field glass- and jamming transitions exist, but also serve as the canonical model systems for slow dynamics in granular materials more generally. Arguably the models in this family do not offer a close resemblance of actual granular materials. However, by studying their behavior far from equilibrium, we observe the onset of slow dynamics and a kinetic arrest for which, importantly, we obtain an essentially complete analytical and numerical understanding. Particularly interesting is the fact that this understanding hinges on the (in-)ability to anneal topological defects in the presence of a hardcore constraints, which resonates with some previous proposals for an understanding of the glass transition. As another example of anomalous dynamics arising in a magnetic system, we also present a detailed study of a two-dimensional fracton spin liquid. The model is an Ising system with an energy function designed to give rise to an emergent higher-rank gauge theory at low energy. We show explicitly that the number of zero-energy states in the model scales exponentially with the system size, establishing a finite residual entropy. A purpose-built cluster Monte-Carlo algorithm makes it possible to study the behavior of the model as a function of temperature. We show evidence for a first order transition from a high-temperature paramagnet to a low-temperature phase where correlations match predictions of a higher-rank coulomb phase. Turning away from heuristic models, the second part of the thesis begins with an introduction to quantum error correction, a scheme where constraints are artificially imposed in a quantum system through measurement and feedback. This is done in order to preserve quantum information in the presence of external noise, and is widely believed to be necessary in order to one day harness the full power of quantum computers. Given a certain error-correcting code as well as a noise model, a particularly interesting quantity is the threshold of the code, that is the critical amount of external noise below which quantum error correction becomes possible. For the toric code under independent bit- and phase-flip noise for example, the threshold is well known to map to the paramagnet to ferromagnet transition of the two-dimensional random-bond Ising model along the Nishimori line. Here, we present the first generalization of this mapping to a family of codes with finite rate, that is a family where the number of encoded logical qubits grows linearly with the number of physical qubits. In particular, we show that the threshold of hyperbolic surface codes maps to a paramagnet to ferromagnet transition in what we call the 'dual'' random-bond Ising model on regular tessellations of compact hyperbolic manifolds. This model is related to the usual random-bond Ising model by the Kramers-Wannier duality but distinct from it even on self-dual tessellations. As a corollary, we clarify long-standing issues regarding self-duality of the Ising model in hyperbolic space. The final part of the thesis is devoted to the study of material candidates of quantum spin ice, a three-dimensional quantum spin liquid. The work presented here was done in close collaboration with experiment and focuses on a particular family of materials called dipolar-octupolar pyrochlores. This family of materials is particularly interesting because they might realize novel exotic quantum states such as octupolar spin liquids, while at the same time being described by a relatively simple model Hamiltonian. This thesis contains a detailed study of ground state selection in dipolar-octupolar pyrochlore magnets and its signatures as observable in neutron scattering. First, we present evidence that the two compounds Ce2Zr2O7 and Ce2Sn2O7 despite their similar chemical composition realize an exotic quantum spin liquid state and an ordered state respectively. Then, we also study the ground-state selection in dipolar-octupolar pyrochlores in a magnetic field. Most importantly, we show that the well-known effective one-dimensional physics -- arising when the field is applied along a certain crystallographic axis -- is expected to be stable at experimentally relevant temperatures. Finally, we make predictions for neutron scattering in the large-field phase and compare these to measurements on Ce2Zr2O7
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