[Landau ITP Seminars] Friday 20.12.2019

[Serge Krashakov]

Уважаемые сотрудники ИТФ,

В пятницу 20 декабря состоится 2 коллоквиума.

На Ученом совете в 11:30 будет заслушан доклад :

Joerg Schmalian (Karlsruhe Institute of Technology)
*Ordered fluctuations: about vestigial order in quantum materials*

A hallmark of the phase diagrams of quantum materials is the existence 
of multiple electronic ordered states. In many cases those are not 
independent, competing phases, but instead display a complex 
intertwinement. In this talk, we focus on a realization of intertwined 
orders with a fluctuation-driven vestigial phase characterized by a 
composite order parameter. In other words, we are investigating the 
condensation of fluctuations.
We demonstrate that this concept naturally explains the nematic state in 
iron-based superconductors and nematic superconductivity in doped 
topological insulators. In addition we propose a natural mechanism for 
charge 4e superconductivity with half flux quanta. We present a 
formalism that provides a framework to understand the complexity of 
quantum materials based on symmetry, largely without resorting to 
microscopic models.


В 15:00 будет заслушан доклад :

Vadim Smelyanskiy (Google, Los Angeles)
*Non-ergodic delocalized states for efficient population transfer within 
a narrow band of the energy landscape*

We will review the advances and challenges in the field of quantum 
combinatorial optimization and closely related problem of low-energy 
eigenstates and coherent dynamics in transverse field quantum spin glass 
models. We will discuss the role of collective spin tunneling that gives 
rise to bands of delocalized non-ergodic quantum states providing the 
coherent pathway for the population transfer (PT) algorithm: the quantum 
evolution under a constant transverse field that starts at a low-energy 
spin configuration and ends up in a superposition of spin configurations 
inside a narrow energy window. We study the transverse field induced 
quantum dynamics of the following spin model: zero energy of all spin 
configurations except for a small fraction of spin configuration that 
form a narrow band at large negative energy. We use the cavity method 
for heavy-tailed random matrices to obtain the statistical properties of 
the low-energy eigenstates in an explicit analytical form. In a broad 
interval of transverse fields, they are non-ergodic, albeit extended 
giving rise to a qualitatively new type of quantum dynamics. For large 
transverse fields »1 the typical runtime of PT algorithm ∼2n/Ωer‾‾‾‾‾‾‾√
scales with n and Ω as that of the Grover’s quantum search, except for 
the small correction to the exponent θ ≈ 1/(2). The model we consider is 
non-integrable. As a result, our PT protocol does not require any 
fine-tuning of and may be initialized in a computational basis state. We 
argue that our approach can be applied to study PT protocol in other 
optimization problems with the potential quantum advantage over 
classical algorithms.
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