# Seminars at the Landau Institute scientific council

Seminars are held on Fridays in the conference hall of Landau Institute for Theoretical Physics in Chernogolovka, beginning at 11:30.

## Effect of small dissipation on the NLS anomalous waves recurrence.

13 December in 11:30

P.G. Grinevich, P.M. Santini

We provide analytic formulas decribing the effect of small loss/gain on the recurrence of anomalous waves in the focusing Nonlinear Schrodinger equation. We show that very small loss or gain essentially affects the statistics and the character of the recurrence. In particular, our formulas explains the results of numerical simulations from the paper by O. Kimmoun, H.C. Hsu, H. Branger, M.S. Li, Y.Y. Chen, C. Kharif, M. Onorato, E.J.R. Kelleher, B. Kibler, N. Akhmediev, A. Chabchoub (2016).

## KP-2 solutions in the form of soliton sequences.

13 December in 11:30 (short)

P.G. Grinevich, S. Abenda

Some photos of the ocean surface demonstrate waves looking like lattices formed by solitons. They can be modelled by finite-gap Kadomtsev-Petviashvili 2 solutions corresponding to almost dgenerate spectral curves. We show how to construct such solutions in the first non-trivial case corresponding to GR(4,2).

## Efficient algorith for 2D Fourier transform. Implementation and comparison.

13 December in 11:30 (short)

A.O. Korotkevich

Efficient implementation of parallel algorithm for fast Fourier transformation for arrays of large dimensions, based on 1D transformation from FFTW library and block-transposition, was developed and implemented as a library. 50% Speed-up with respect to 2D Fourier transformation in standard de facto FFTW library was demonstrated on three different architectures, including multiprocessor (SMP) machines.

## Ordered fluctuations: about vestigial order in quantum materials

20 December in 11:30

Joerg Schmalian (Karlsruhe Institute of Technology)

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.

## Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape

20 December in 15:00

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 $\sim \sqrt{2^n / \Omega e^r}$ 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.

## Disorder and interaction in chiral chains: Majoranas versus complex fermions.

27 December in 11:30

Mirlin A.D.

We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. While in the noninteracting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the noninteracting fixed point. On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and explore correlations of wave functions that enter interaction matrix elements. Our numerical and analytical results exhibit a rich structure of critical eigenstate correlations. This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite-randomness fixed point. For the case of complex fermions, the interaction is irrelevant.

## Dual description of $\eta$-deformed OSP sigma-models

17 January 2020 in 11:30

Alexey Litvinov

My talk will be based on joint work with M. Alfimov, B. Fegin and B. Hoare. We propose a system of fermionic screening fields depending on a continuous parameter $b$, which defines $\eta$-deformed $OSP(n|2m)$ sigma-model in the limit $b\rightarrow\infty$ and a super-renormalizable QFT in $b\rightarrow0$. In the sigma-model regime we show that leading UV asymptotic of the RG group flow equations coincides with perturbation around Gaussian theory. In perturbative regime $b\rightarrow0$ we show that the tree level two-particle scattering matrix matches the expansion of the trigonometric $OSP(n|2m)$ $R$-matrix.