A
bstract
In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these ...only provide a coarse probe of the full underlying operator growth structure. In this article we develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-all
q
-body interactions. We derive the full operator growth structure in the large
q
limit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.
A
bstract
Motivated by recent studies of the information paradox in (1+1)-D anti-de Sitter spacetime with a bath described by a (1+1)-D conformal field theory, we study the dynamics of second Ŕenyi ...entropy of the Sachdev-Ye-Kitaev (SYK) model (
χ
) coupled to a Majorana chain bath (
ψ
). The system is prepared in the thermofield double (TFD) state and then evolved by
H
L
+
H
R
. For small system-bath coupling, we find that the second Rényi entropy
S
χ
L
,
χ
R
2
of the SYK model undergoes a first order transition during the evolution. In the sense of holographic duality, the long-time solution corresponds to a “replica wormhole”. The transition time corresponds to the Page time of a black hole coupled to a thermal bath. We further study the information scrambling and retrieval by introducing a classical control bit, which controls whether or not we add a perturbation in the SYK system. The mutual information between the bath and the control bit shows a positive jump at the Page time, indicating that the entanglement wedge of the bath includes an island in the holographic bulk.
There has been recent promising experimental and theoretical evidence that quantum computational tools might enhance the precision and efficiency of physical experiments. However, a systematic ...treatment and comprehensive framework are missing. Here we initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system's Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problems and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.
Organic electrochemistry has a rich history in organic synthesis and has been considered as a promising alternative to traditional chemical oxidants and reductants because it obviates the use of ...stoichiometric amount of dangerous and toxic reagents. In particular, the electrochemical C—H bonds functionalization is one of the most desirable approaches for the construction of carbon–carbon (C—C) and carbon–heteroatom (C—X) bonds. This review summarizes the substantial progress made in the last few years in C—H functionalization via organic electrochemistry. It is divided into sections on C—C, C—N, C—O, C—S, C–Halogen and C—P bond formation.
Organic electrochemistry has a rich history in organic synthesis and has been considered as a promising alternative to traditional chemical oxidants and reductants because it obviates the use of stoichiometric amount of dangerous and toxic reagents. In particular, the electrochemical C—H bonds functionalization is one of the most desirable approaches for the construction of carbon–carbon (C—C) and carbon–heteroatom (C—X) bonds.
A
bstract
The Sachdev-Ye-Kitaev model is a (0 + 1)-dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as ...approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the Sachdev-Ye-Kitaev model, which is a lattice model with
N
Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large
N
limit, the higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev model such as local criticality in two-point functions, zero temperature entropy and chaos measured by the out-of-time-ordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a “butterfly velocity” describing the propagation of chaos in space. We mainly present results for a (1 + 1)-dimensional example, and discuss the general case near the end.
A
bstract
Sachdev-Ye-Kitaev (SYK) model, which describes
N
randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly ...AdS
2
dilaton gravity. Ref.
1
proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS
2
geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the
q
dependence of the spectral function.
A
bstract
Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a ...bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated
entanglement negativity
and its Rényi generalizations in holographic duality. We first review the definition of the Rényi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Rényi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Rényi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.
Conspectus Electrochemical synthesis of organic compounds has emerged as an attractive and environmentally benign alternative to conventional approaches for oxidation and reduction of organic ...compounds that utilizes electric current instead of chemical oxidants and reductants. As such, many useful transformations have been developed, including the Kolbe reaction, the Simons fluorination process, the Monsanto adiponitrile process, and the Shono oxidation, to name a few. Electrochemical C–H functionalization represents one of the most promising reaction types among many electrochemical transformations, since this process avoids prefunctionalization of substrates and provides novel retrosynthetic disconnections. However, site-selective anodic oxidation of C–H bonds is still a fundamental challenge due to the high oxidation potentials of C–H bonds compared to organic solvents and common functional groups. To overcome this issue, indirect electrolysis via the action of a mediator (a redox catalyst) is regularly employed, by which the selectivity can be controlled following reaction of said mediator with the substrate. Since the redox potentials of transition metal complexes can be easily tuned by modification of the ligand, the synergistic use of electrochemistry and transition metal catalysis to achieve site-selective C–H functionalization is an attractive strategy. In this Account, we summarize and contextualize our recent efforts toward transition metal-catalyzed electrochemical C–H functionalization proximal to a suitable directing group. We have developed C–H oxygenation, acylation, alkylation, and halogenation reactions in which a Pd(II) species is oxidized to a Pd(III) or Pd(IV) intermediate by anodic oxidation, followed by reductive elimination to form the corresponding C–O, C–C, and C–X bonds. Importantly, improved monofunctionalization selectivity is achieved in the Pd-catalyzed C(sp3)–H oxygenation compared to conventional approaches using PhI(OAc)2 as the chemical oxidant. Physical separators are sometimes used to prevent the electrochemical deposition of Pd black on the cathode resulting from reduction of high valent Pd species. We skirted this issue through the development a Cu-catalyzed electrochemical C(sp2)–H amination using n-Bu4NI as a redox cocatalyst in an undivided cell. In addition, we developed Ir-catalyzed electrochemical vinylic C–H functionalization of acrylic acids with alkynes in an undivided cell, affording various substituted α-pyrones in good to excellent yield. More importantly, chemical oxidants, including Ag2CO3, Cu(OAc)2, and PhI(OAc)2, resulted in much lower yields in the absence of electrical current under otherwise identical conditions. As elaborated below, progress in the area of electrochemical transition metal-catalyzed synthesis provides an effective platform for environmentally friendly and sustainable selective chemical transformations.
A
bstract
Inspired by the Hayden-Preskill protocol for black hole evaporation, we consider the dynamics of a quantum many-body qudit system coupled to an external environment, where the time ...evolution is driven by the continuous limit of certain 2-local random unitary circuits. We study both cases where the unitaries are chosen with and without a conserved U(1) charge and focus on two aspects of the dynamics. First, we study analytically and numerically the growth of the entanglement entropy of the system, showing that two different time scales appear: one is intrinsic to the internal dynamics (the scrambling time), while the other depends on the system-environment coupling. In the presence of a U(1) conserved charge, we show that the entanglement follows a Page-like behavior in time: it begins to decrease in the middle stage of the “evaporation”, and decreases monotonically afterwards. Second, we study the time needed to retrieve information initially injected in the system from measurements on the environment qudits. Based on explicit numerical computations, we characterize such time both when the retriever has control over the initial configuration or not, showing that different scales appear in the two cases.
We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit ...model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume-law and area-law scaling entanglement entropy in steady states. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.
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