Universal Error Bound for Constrained Quantum Dynamics.

It is well known in quantum mechanics that a large energy gap between a Hilbert subspace of specific interest and the remainder of the spectrum can suppress transitions from the quantum states inside the subspace to those outside due to additional couplings that mix these states, and thus approximately lead to a constrained dynamics within the subspace. While this statement has widely been used to approximate quantum dynamics in various contexts, a general and quantitative justification stays lacking. Here we establish an observable-based error bound for such a constrained-dynamics approximation in generic gapped quantum systems. This universal bound is a linear function of time that only involves the energy gap and coupling strength, provided that the latter is much smaller than the former. We demonstrate that either the intercept or the slope in the bound is asymptotically saturable by simple models. We generalize the result to quantum many-body systems with local interactions, for which the coupling strength diverges in the thermodynamic limit while the error is found to grow no faster than a power law t^{d+1} in d dimensions. Our work establishes a universal and rigorous result concerning nonequilibrium quantum dynamics.

Onsager's Scars in Disordered Spin Chains.

We propose a class of nonintegrable quantum spin chains that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct scarred models for arbitrary spin quantum number S. There are two types of scar states, namely, coherent states associated with an Onsager-algebra element and one-magnon scar states. While both of them are highly excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also investigate the dynamics of the fidelity and entanglement entropy for several initial states. The results clearly show that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly. To our knowledge, our model is the first explicit example of disordered quantum many-body scarred models.

S-((phenylsulfonyl)difluoromethyl)thiophenium salts: carbon-selective electrophilic difluoromethylation of ß-ketoesters, ß-diketones, and dicyanoalkylidenes.

S-((Phenylsulfonyl)difluoromethyl)thiophenium salts were designed and prepared by a triflic acid catalyzed intramolecular cyclization of ortho-ethynyl aryldifluoromethyl sulfanes. The thiophenium salts were found to be efficient as electrophilic difluoromehtylating reagents for introduction of a CF2 H group to sp(3) -hybridized carbon nucleophiles such as of ß-ketoesters and dicyanoalkylidenes. The (phenylsulfonyl)difluoromethyl group can be readily transformed into CF2 H under mild reaction conditions. Enantioselective electrophilic difluoromethylation was also achieved in the presence of bis(cinchona) alkaloids.

Asymmetric Mannich reaction between (S)-N-(tert-butanesulfinyl)-3,3,3-trifluoroacetaldimine and malonic acid derivatives. Stereodivergent synthesis of (R)- and (S)-3-amino-4,4,4-trifluorobutanoic acids.

Inorganic as well as organic base catalysis was found to be effective for diastereoselective Mannich additions of malonic acid derivatives to (SS)-N-(tert-butanesulfinyl)-3,3,3-trifluoroacetaldimine. In the presence of catalytic amounts of inorganic bases, n-BuLi or DMAP, the reaction gives the corresponding (R,SS)-ß-aminomalonates in good yield and with diastereoselectivity up to 9/1 dr. In contrast, phosphazene bases favour the formation of the (S,SS)-diastereomer with selectivities as high as 99/1. Simple choosing of an appropriate base catalyst for the Mannich addition reaction allowed us to obtain enantiomerically pure (R)- or (S)-configured 3-amino-4,4,4-trifluorobutanoic acids after hydrolysis and decarboxylation of the corresponding ß-aminomalonates.

Kinetic resolution of allyl fluorides by enantioselective allylic trifluoromethylation based on silicon-assisted C-F bond cleavage.

Two birds, one stone! The first kinetic resolution of allyl fluorides was achieved by the development of an organocatalyzed enantioselective allylic trifluoromethylation. Two kinds of chiral fluorinated compounds, which incorporate C*F and C*CF3 units, respectively, can thus be accessed by a single transformation.

Organic base-catalyzed stereodivergent synthesis of (R)- and (S)-3-amino-4,4,4-trifluorobutanoic acids.

Organic base-catalyzed reaction of (S)-N-tert-butanesulfinyl (3,3,3)-trifluoroacetaldimine with dialkyl malonates was found to be effective for synthesis of both (S,S(S)) and (R,S(S)) ß-aminomalonates in high yield with good to excellent diastereoselectivity (76-98% de). The products of this Mannich reaction provide direct access to ß-trifluoromethyl-ß-alanine of either (R) or (S) absolute configuration.