Andrey Gromov

Population genomics of Bronze Age Eurasia

The Bronze Age of Eurasia (around 3000–1000 BC) was a period of major cultural changes. However, there is debate about whether these changes resulted from the circulation of ideas or from human migrations, potentially also facilitating the spread of languages and certain phenotypic traits. We investigated this by using new, improved methods to sequence low-coverage genomes from 101 ancient humans from across Eurasia. We show that the Bronze Age was a highly dynamic period involving large-scale population migrations and replacements, responsible for shaping major parts of present-day demographic structure in both Europe and Asia. Our findings are consistent with the hypothesized spread of Indo-European languages during the Early Bronze Age. We also demonstrate that light skin pigmentation in Europeans was already present at high frequency in the Bronze Age, but not lactose tolerance, indicating a more recent onset of positive selection on lactose tolerance than previously thought.

Thermal Hall Effect and Geometry with Torsion.

We formulate a geometric framework that allows us to study momentum and energy transport in nonrelativistic systems. It amounts to a coupling of the nonrelativistic system to the Newton-Cartan (NC) geometry with torsion. The approach generalizes the classic Luttingers formulation of thermal transport. In particular, we clarify the geometric meaning of the fields conjugated to energy and energy current. These fields describe the geometric background with nonvanishing temporal torsion. We use the developed formalism to construct the equilibrium partition function of a nonrelativistic system coupled to the NC geometry in 2+1 dimensions and to derive various thermodynamic relations.

Density-curvature response and gravitational anomaly.

We study constraints imposed by the Galilean invariance on linear electromagnetic and elastic responses of two-dimensional gapped systems in a background magnetic field. Exact relations between response functions following from the Ward identities are derived. In addition to the viscosity-conductivity relations known in the literature, we find new relations between the density-curvature response and the thermal Hall response.

Synthetic Landau levels for photons

Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science. Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip. This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock–Darwin Hamiltonian for photons in a magnetic field and harmonic trap. Using spatial- and energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit, we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen–Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space. This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids and direct detection of anyons.

Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field

Recent interest to the Hall viscosity in the theory of Fractional Quantum Hall effect (FQHE) and the interest to the interplay of defects and mechanical stresses with electromagnetic properties of materials motivates studies of gravitational, electromagnetic and mixed responses in condensed matter physics. Gravitational field in condensed matter systems can be understood either as a way to represent deformational strains present in the material under consideration or as a technical tool allowing to extract correlation functions involving stress tensor components. It is always important to have a simple model system for which such responses can be calculated exactly. For the quantum Hall effect one can consider two-dimensional electron gas in a constant magnetic field (2DEGM) as such a model. When the density of fermions is commensurate with magnetic field the integer number of Landau levels is filled and one expects local and computable response to weak external fields. This model is as important starting point of analysis for quantum Hall systems as a free electron gas for the theory of metals. However, while some electromagnetic responses for 2DEGM can be found in literature we were not able to find the complete results for mixed and gravitational linear responses. The goal of this paper is to compute these responses providing the analogue of Lindhard 1 function, both e/m and gravitational, for 2DEGM. We compute the effective action encoding linear responses in the presence of external inhomogeneous, time-dependent, slowly changing electromagnetic and gravitational fields. We compare and find an agreement of the obtained responses with known e/m responses 2–5 and with known results for Hall viscosity at integer fillings 6,7 . In addition we find the stress, charge and current densities induced by spatial curvature. Another point of comparison is given by phenomenological hydrodynamic models for FQHE 8–13 and Ward identities following from the exact local Galilean symmetry (also known as non-relativistic diffeomorphism) of the model 14,15 . The paper is organized as follows. In Section II we describe the model as a non-relativistic quantum field theory and present our results in terms of the effective action. In Section III we extract the electromagnetic responses from the effective action. We demonstrate some peculiar physical effects such as charge accumulation/depletion in the presence of conic singularity in metric, non-dissipative current perpendicular to a gradient of curvature and report higher gradient corrections to Hall conductivity. Our main results are presented in the Section IV where we discuss the gravitational responses. We present higher gradient and dynamic corrections to Hall viscosity. We leave the in-depth discussion of dynamic responses and their relation to the local Galilean invariance for a separate publication.

Framing anomaly in the effective theory of the fractional quantum hall effect

We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.

Entanglement Entropy in 2D Non-abelian Pure Gauge Theory

Abstract We compute the Entanglement Entropy (EE) of a bipartition in 2D pure non-abelian U ( N ) gauge theory. We obtain a general expression for EE on an arbitrary Riemann surface. We find that due to area-preserving diffeomorphism symmetry EE does not depend on the size of the subsystem, but only on the number of disjoint intervals defining the bipartition. In the strong coupling limit on a torus we find that the scaling of the EE at small temperature is given by S ( T ) − S ( 0 ) = O ( m gap T e − m gap T ) , which is similar to the scaling for the matter fields recently derived in literature. In the large N limit we compute all of the Renyi entropies and identify the Douglas–Kazakov phase transition.

Boundary Effective Action for Quantum Hall States.

We consider quantum Hall states on a space with boundary, focusing on the aspects of the edge physics which are completely determined by the symmetries of the problem. There are four distinct terms of Chern-Simons type that appear in the low-energy effective action of the state. Two of these protect gapless edge modes. They describe Hall conductance and, with some provisions, thermal Hall conductance. The remaining two, including the Wen-Zee term, which contributes to the Hall viscosity, do not protect gapless edge modes but are instead related to the local boundary response fixed by symmetries. We highlight some basic features of this response. It follows that the coefficient of the Wen-Zee term can change across an interface without closing a gap or breaking a symmetry.

Bimetric Theory of Fractional Quantum Hall States

We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist of a topological Chern-Simons action, coupled to a symmetric rank two tensor, and an action a la bimetric gravity, describing the gapped dynamics of the spin-

Investigating Anisotropic Quantum Hall States with Bimetric Geometry

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