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Register a new userObservation of a transition from a topologically ordered to a spontaneously broken symmetry phase
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Until the late 1980s, phases of matter were understood in terms of Landaus symmetry breaking theory. Following the discovery of the quantum Hall effect the introduction of a second class of phases, those with topological order, was necessary. Phase transitions within the first class of phases involve a change in symmetry, whereas those between topological phases require a change in topological order. However, in rare cases transitions may occur between the two classes in which the vanishing of the topological order is accompanied by the emergence of a broken symmetry. Here, we report the existence of such a transition in a two-dimensional electron gas hosted by a GaAs/AlGaAs crystal. When tuned by hydrostatic pressure, the $ u=5/2$ fractional quantum Hall state, believed to be a prototype non-Abelian topological phase, gives way to a quantum Hall nematic phase. Remarkably, this nematic phase develops spontaneously, in the absence of any externally applied symmetry breaking fields.
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We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with emergent symmetries of the edge, which play a crucial role in the structure of its phase diagram. Using this symmetry principle, transitions between distinct gapped phases at the boundaries of Abelian states can be understood in terms of symmetry breaking transitions or transitions between symmetry protected topological phases. Yet more exotic phenomena occur when the bulk hosts non-Abelian anyons. To demonstrate these principles, we explore the phase diagrams of the edges of a single and a double layer of the toric code, as well as those of domain walls in a single and double-layer Kitaev spin liquid (KSL). In the case of the KSL, we find that the presence of a non-Abelian anyon in the bulk enforces Kramers-Wannier self-duality as a symmetry of the effective boundary theory. These examples illustrate a number of surprising phenomena, such as spontaneous duality-breaking, two-sector phase transitions, and unfreezing of marginal operators at a transition between different gapless phases.
We present an approach to identify topological order based on unbiased infinite projected entangled-pair states (iPEPS) simulations, i.e. where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network ansatz. As an example we consider the ground state of the toric code model in a magnetic field exhibiting $Z_2$ topological order. The optimization is done by an efficient energy minimization approach based on a summation of tensor environments to compute the gradient. We show that the optimized tensors, when brought into the right gauge, are approximately $Z_2$ symmetric, and they can be fully symmetrized a posteriori to generate a stable topologically ordered state, yielding the correct topological entanglement entropy and modular S and U matrices. To compute the latter we develop a variant of the corner-transfer matrix method which is computationally more efficient than previous approaches based on the tensor renormalization group.
We discuss renormalization in a toy model with one fermion field and one real scalar field phi, featuring a spontaneously broken discrete symmetry which forbids a fermion mass term and a phi^3 term in the Lagrangian. We employ a renormalization scheme which uses the MSbar scheme for the Yukawa and quartic scalar couplings and renormalizes the vacuum expectation value of phi by requiring that the one-point function of the shifted field is zero. In this scheme, the tadpole contributions to the fermion and scalar selfenergies are canceled by choice of the renormalization parameter delta_v of the vacuum expectation value. However, delta_v and, therefore, the tadpole contributions reenter the scheme via the mass renormalization of the scalar, in which place they are indispensable for obtaining finiteness. We emphasize that the above renormalization scheme provides a clear formulation of the hierarchy problem and allows a straightforward generalization to an arbitrary number of fermion and scalar fields.
We generalize the formalism of the dynamical vertex approximation (D$Gamma$A) -- a diagrammatic extension of the dynamical mean-field theory (DMFT)-- to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2)-symmetry, associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which defines the ladder implementation of D$Gamma$A for magnetic systems. The relation of this assumption with the DMFT limit of large coordination-number/ high-dimensions is explicitly discussed. As a last step, we derive the expression for the ladder D$Gamma$A self-energy in the FM- and AF-ordered phases of the Hubbard model. The physics emerging in the AF-ordered case is explicitly illustrated by means of approximated calculations based on a static mean-field input for the D$Gamma$A equations. The results obtained capture fundamental aspects of both metallic and insulating ground states of two-dimensional antiferromagnets, providing a reliable compass for future, more extensive applications of our approach. Possible routes to further develop diagrammatic-based treatments of magnetic phases in correlated electron systems are briefly outlined in the conclusions.
Spontaneous C4-symmetry breaking phases are ubiquitous in layered quantum materials and compete with other phases such as superconductivity. Phenomena like light induced superconductivity and metallicity are believed to arise from optical excitations selectively melting the C4-symmetry breaking phase, enabling competing phases to emerge. Phenomenological models suggest that light directly modifies the order parameter or its potential. However, clear evidence for such a process is lacking. Here, we measure the order parameter dynamics of the C4 symmetry breaking transition in the prototypical manganite La0.5Sr1.5MnO4. Despite some degrees of freedom appearing to show a coherent response and critical slowing, consistent with previous measurements, we find the order-parameter is overdamped and incoherent. Concomitant changes in the lattice potential of the entire system in under ~25 fs show rapid energy redistribution and lack of selectivity in photoexcitation, suggesting a disorder-driven transition where the order parameter potential plays a minimal role, in contrast to previous models.
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