The Deep Web, i.e., content hidden behind HTML forms, has long been acknowledged as a significant gap in search engine coverage. Since it represents a large portion of the structured data on the Web, accessing Deep-Web content has been a long-standing challenge for the database community. This paper describes a system for surfacing Deep-Web content, i.e., pre-computing submissions for each HTML form and adding the resulting HTML pages into a search engine index. The results of our surfacing have been incorporated into the Google search engine and today drive more than a thousand queries per second to Deep-Web content. Surfacing the Deep Web poses several challenges. First, our goal is to index the content behind many millions of HTML forms that span many languages and hundreds of domains. This necessitates an approach that is completely automatic, highly scalable, and very efficient. Second, a large number of forms have text inputs and require valid inputs values to be submitted. We present an algorithm for selecting input values for text search inputs that accept keywords and an algorithm for identifying inputs which accept only values of a specific type. Third, HTML forms often have more than one input and hence a naive strategy of enumerating the entire Cartesian product of all possible inputs can result in a very large number of URLs being generated. We present an algorithm that efficiently navigates the search space of possible input combinations to identify only those that generate URLs suitable for inclusion into our web search index. We present an extensive experimental evaluation validating the effectiveness of our algorithms.

In this paper we systematically classify and describe bosonic symmetry protected topological (SPT) phases in all physical spatial dimensions using semiclassical nonlinear Sigma model (NLSM) field theories. All the SPT phases on a d−dimensional lattice discussed in this paper can be described by the same NLSM, which is an O(d+2) NLSM in (d+1)−dimensional space-time, with a topological Θ−term. The field in the NLSM is a semiclassical Landau order parameter with a unit length constraint. The classification of SPT phases discussed in this paper based on their NLSMs is Completely Identical to the more mathematical classification based on group cohomology given in Ref. 1,2. Besides the classification, the formalism used in this paper also allows us to explicitly discuss the physics at the boundary of the SPT phases, and it reveals the relation between SPT phases with different symmetries. For example, it gives many of these SPT states a natural "decorated defect" construction.

We demonstrate the following conclusion: If |Ψ is a 1d or 2d nontrivial short range entangled state, and |Ω is a trivial disordered state defined on the same Hilbert space, then the following quantity (so called strange correlator) C(r, r ) = Ω|φ(r)φ(r )|Ψ Ω|Ψ either saturates to a constant or decays as a power-law in the limit |r − r | → +∞, even though both |Ω and |Ψ are quantum disordered states with short-range correlation. φ(r) is some local operator in the Hilbert space. This result is obtained based on both field theory analysis, and also an explicit computation of C(r, r ) for four different examples: 1d Haldane phase of spin-1 chain, 2d quantum spin Hall insulator with a strong Rashba spin-orbit coupling, 2d spin-2 AKLT state on the square lattice, and the 2d bosonic symmetry protected topological phase with Z2 symmetry. This result can be used as a diagnosis for short range entangled states in 1d and 2d. PACS numbers:A short range entangled (SRE) state is a ground state of a quantum many-body system that does not have ground state degeneracy or bulk topological entanglement entropy. But a SRE state (for example the integer quantum Hall state) can still have protected stable gapless edge states. Thus it appears that the bulk of all the SRE states are identically trivial, and a nontrivial SRE state is usually characterized by its edge states. In this paper we propose a diagnosis to determine whether a given many-body wave function defined on a lattice without boundary is a nontrivial SRE state or a trivial one. This diagnosis is based on the following quantity called "strange correlator" [36]:Here |Ψ is the wave function that needs diagnosis, |Ω is a direct product trivial disordered state defined on the same Hilbert space. Our conclusion is that if |Ψ is a nontrivial SRE state in one or two spatial dimensions, then for some local operator φ(r), C(r, r ) will either saturate to a constant or decay as a power-law in the limit |r − r | → +∞, even though both |Ω and |Ψ are disordered states with short-range correlation. Another possible way of diagnosing a SRE wave function is through its entanglement spectrum [1]. If a SRE state has nontrivial edge states, an analogue of its edge states should also exist in its entanglement spectrum [2]. However, many SRE states are protected by certain symmetry, some SRE states are protected by lattice symmetries (for example the spin-2 AKLT state on the square lattice requires translation symmetry). If the cut we make to compute the entanglement spectrum breaks such lattice symmetry, then the entanglement spectrum would be trivial, even if the original state is a nontrivial SRE state. By contrast, the strange correlator in Eq. (1) is defined on a lattice without edge, thus it already preserves all the symmetries of the system, including all the lattice symmetries. Thus the strange correlator can reliably diagnose SRE states protected by lattice symmetries as well.The strange correlator can be roughly understood as follows: |Ψ can be viewed as a generic initial state evol...

In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard " √ 3 × √ 3" noncollinear antiferromagnetic order (or the so-called 120• state) and the " √ 12 × √ 12" valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the "intertwinement" between the √ 3 × √ 3 antiferromagnetic order and the √ 12 × √ 12 VBS order. Then using a controlled renormalizationgroup calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the N f = 4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z 4 symmetry only at the critical point. The aforementioned topological term is also naturally derived from the N f = 4 QED. We also point out that physics around this DQCP is analogous to the boundary of a 3d bosonic symmetry-protected topological state with only on-site symmetries.

In this paper we construct bosonic short range entangled (SRE) states in all spatial dimensions by coupling a 2  gauge field to fermionic SRE states with the same symmetries, and driving the 2  gauge field to its confined phase. We demonstrate that this approach allows us to construct many examples of bosonic SRE states, and we demonstrate that the previous descriptions of bosonic SRE states such as the semiclassical nonlinear sigma model field theory and the Chern-Simons field theory can all be derived using the fermionic SRE states.

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Motivated by the recent discovery of higher-order topological insulators, we study their counterparts in strongly interacting bosons: "higher-order symmetry protected topological (HOSPT) phases". While the usual (1st-order) SPT phases in d spatial dimensions support anomalous (d − 1)dimensional surface states, HOSPT phases in d dimensions are characterized by topological boundary states of dimension (d−2) or smaller, protected by certain global symmetries and robust against disorders. Based on a dimensional reduction analysis, we show that HOSPT phases can be built from lower-dimensional SPT phases in a way that preserves the associated crystalline symmetries. When the total symmetry is a direct product of global and crystalline symmetry groups, we are able to classify the HOSPT phases using the Künneth formula of group cohomology. Based on a decorated domain wall picture of the Künneth formula, we show how to systematically construct the HOSPT phases, and demonstrate our construction with many examples in two and three dimensions. PACS numbers:arXiv:1809.07325v2 [cond-mat.str-el]