arXiv subjects

Oleksandr Gamayun

Publications and source records attributed to Oleksandr Gamayun.

At least 19 recordsLinked to original sources

arXiv2026

Cohomological beta function

We propose a cohomological approach to computing the conformal anomaly. Using the example of current-current deformations of two-dimensional conformal field theories, we reproduce the well-known Cardy formula for the leading contribution to the perturbative beta function as the coefficient of the cocycle that realizes the obstruction to deforming the conformal algebra module structure on the state space. In addition to offering a novel conceptual perspective on the conformal anomaly, the proposed approach is anticipated to provide an efficient tool for computing higher-order coefficients of perturbative beta functions.

math-ph↗

arXiv2026

Nonequilibrium full counting statistics of multicomponent strongly-interacting quantum gases with defects

We investigate the full counting statistics of a one-dimensional multicomponent impenetrable gas released from a bipartite state in the presence of a local defect. Spin--charge separation reduces the multivariate generating function to an exact Fredholm determinant whose kernel is built from time-evolved single-particle orbitals. Expressing these orbitals in terms of scattering data gives access to both transient dynamics and the nonequilibrium steady state. We derive the leading long-time asymptotics and identify persistent oscillations in densities and currents caused by multiple bound states at the junction. We argue that interactions between components lead to a linear low-temperature correction to the current, in contrast to the quadratic correction in the single-component case. At equilibrium, we obtain the M-Wright distribution of spin transfer with $t^{1/4}$ scaling.

cond-mat.quant-gas↗

arXiv2026

The exact dynamical structure factor of one-dimensional hard rods and its universal random matrix behavior

We obtain an exact analytic expression for the dynamical structure factor of one-dimensional quantum gas of hard rods. Our result is valid for an arbitrary many-body state of the system, with finite temperature states and the ground state being important special cases that we analyse in detail. We demonstrate that the expression obeys fundamental relations such like the f-sum rule and the detailed balance. We also reveal the hidden fermionic structure behind the correlator. In the static limit we show that it can be written in terms of universal functions which, at zero temperature, coincide with the level spacing distribution function of the Gaussian Unitary Ensemble. Our work provides a full and exact characterisation of a dynamic correlation function in a strongly correlated interacting quantum many-body system.

cond-mat.quant-gas↗

arXiv2026

Dynamical frustration in spacetime metamaterials enables cascading logic and synchronization

Spacetime metamaterials are engineered media whose constitutive parameters such as permittivity, permeability, stiffness, or mass density are modulated simultaneously in both space and time. These additional degrees of freedom, absent in conventional static metamaterials, unlock a cabinet of wave phenomena that cannot be achieved in time-invariant structures, e.g. compact nonreciprocal devices, topological insulators, and devices for efficient frequency conversion and mixing and pulse shaping. The vast majority of these studies, however, operate in the stable regime, where modulation parameters are chosen to yield linear wave propagation. Here, we push spacetime metamaterials into the regime of parametric instability, and discover a novel type of ``dynamically frustrated'' oscillating states, where nonlinear non-reciprocal, topologically protected phase dislocations emerge. We control these dislocations and make them stop, split, and recombine. We harness this control to create devices for cascading logic in branched networks, and synchronization in 2D metamaterials. Our findings are broadly applicable anywhere where spacetime modulation can be pushed beyond linear stability, from cold atoms and superconducting circuits to acoustics and RF circuits.

cond-mat.soft↗

arXiv2025

Non-reciprocal topological solitons in active metamaterials

From protein motifs to black holes, topological solitons are pervasive nonlinear excitations that are robust and can be driven by external fields. So far, existing driving mechanisms all accelerate solitons and antisolitons in opposite directions. Here we introduce a local driving mechanism for solitons that accelerates both solitons and antisolitons in the same direction instead: non-reciprocal driving. To realize this mechanism, we construct an active mechanical metamaterial consisting of non-reciprocally coupled oscillators subject to a bistable potential. We find that such nonlinearity coaxes non-reciprocal excitations - so-called non-Hermitian skin waves, which are typically unstable - into robust oneway (anti)solitons. We harness such non-reciprocal topological solitons by constructing an active waveguide capable of transmitting and filtering unidirectional information. Finally, we illustrate this mechanism in another class of metamaterials that displays the breaking of 'supersymmetry' causing only antisolitons to be driven. Our observations and models demonstrate a subtle interplay between non-reciprocity and topological solitons, whereby solitons create their own driving force by locally straining the material. Beyond the scope of our study, non-reciprocal solitons might provide an efficient driving mechanism for robotic locomotion and could emerge in other settings, e.g. quantum mechanics, optics and soft matter.

cond-mat.soft↗

arXiv2025

Non-reciprocal breathing solitons

Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They can propagate and carry information and energy in a variety of contexts such as plasmas, optical fibers and cold atoms, but propagating breathers have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative active metamaterials. Combining precision desktop experiments, numerical simulations and perturbation theory on generalizations of the sine-Gordon and nonlinear Schrödinger equations, we demonstrate that unidirectional breathers generically emerge in weakly nonlinear non-reciprocal materials, and that their dynamics are governed by an unstable fixed point. Crucially, breathing solitons can persist for arbitrarily long times provided: (i) this fixed point displays a bifurcation when a delicate balance between energy injection and dissipation is struck; (ii) the initial conditions allow the dynamics to reach this bifurcation point. Importantly, discrete effects tend to stabilize these non-reciprocal breathers over a wider range of initial conditions. Our work establishes non-reciprocity as a promising avenue to generate stable nonlinear unidirectional waves, and could be generalized beyond metamaterials to optics, soft matter and superconducting circuits.

cond-mat.soft↗

arXiv2025

Exactly solvable models for universal operator growth

Quantum observables of generic many-body systems exhibit a universal pattern of growth in the Krylov space of operators. This pattern becomes particularly manifest in the Lanczos basis, where the evolution superoperator assumes the tridiagonal form. According to the universal operator growth hypothesis, the nonzero elements of the superoperator, known as Lanczos coefficients, grow asymptotically linearly. We introduce and explore broad families of Lanczos coefficients that are consistent with the universal operator growth and lead to the exactly solvable dynamics. Within these families, the subleading terms of asymptotic expansion of the Lanczos sequence can be controlled and fine-tuned to produce diverse dynamical patterns. For one of the families, the Krylov complexity is computed exactly.

quant-ph↗

arXiv2024

Full-counting statistics for the alternating and domain-wall states

For a one-dimensional system of free fermions, we derive a connection between the full counting statistics of domain-wall and alternating occupancy (Néel) states. This allows us to demonstrate asymptotic linear growth with time of the even cumulants in the Néel state

cond-mat.stat-mech↗

arXiv2024

On finite-temperature Fredholm determinants

We consider finite-temperature deformation of the sine kernel Fredholm determinants acting on the closed contours. These types of expressions usually appear as static two-point correlation functions in the models of free fermions and can be equivalently presented in terms of Toeplitz determinants. The corresponding symbol, or the phase shift, is related to the temperature weight. We present an elementary way to obtain large-distance asymptotic behavior even when the phase shift has a non-zero winding number. It is done by deforming the original kernel to the so-called effective form factors kernel that has a completely solvable matrix Riemann-Hilbert problem. This allows us to find explicitly the resolvent and address the subleading corrections. We recover Szego, Hartwig and Fisher, and Borodin-Okounkov asymptotic formulas.

math-ph↗

arXiv2024

One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results

A mobile impurity particle immersed in a quantum fluid forms a polaron - a quasiparticle consisting of the impurity and a local disturbance of the fluid around it. We ask what happens to a one-dimensional polaron after a kick, i.e. an abrupt application of a force that instantly delivers a finite impulse to the impurity. In the framework of an integrable model describing an impurity in a one-dimensional gas of fermions or hard-core bosons, we calculate the distribution of the polaron momentum established when the post-kick relaxation is over. A remarkable feature of this distribution is a two-sided power-law singularity. It emerges due to one of two processes. In the first process, the whole impulse is transferred to the polaron, without creating phonon-like excitations of the fluid. In the second process, the impulse is shared between the polaron and the center-of-mass motion of the fluid, again without creating any fluid excitations. The latter process is, in fact, a Bragg reflection at the edge of the emergent Brillouin zone. We carefully analyze the conditions for each of the two processes. The asymptotic form of the distribution in the vicinity of the singularity is derived.

cond-mat.quant-gas↗

arXiv2023

First-order formalism for $β$ functions in bosonic sigma models from supersymmetry breaking

We consider the renormalization group flow equation for the two-dimensional sigma models with the Kähler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We demonstrate, however, that the conventional first-order formalism misses certain anomalies in the measure, and should be amended. We reconcile beta functions obtained within the conformal perturbation theory for the current-current deformations with traditional ``geometric" results obtained in the background field methods, in this way resolving the peculiarities pointed out in [JHEP10(2023)097]. The result is achieved by the supersymmetric completion of the first-order sigma model.

hep-th↗

arXiv2023

Peculiarities of beta functions in sigma models

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to $β$ functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. Moreover, in certain cases the first-order calculations produce results that are not symmetric under the classical diffeomorphisms of the target space. Although we could not present the full solution to this remarkable phenomenon, we found some indirect arguments indicating that an anomaly similar to that established in supersymmetric Yang-Mills theory might manifest itself starting from the second loop. We discuss why the difference between two answers might be an infrared effect, similar to that in $β$ functions in supersymmetric Yang-Mills theories. In addition to the generic Kähler target spaces we discuss in detail the so-called Lie-algebraic sigma models. In particular, this is the case when the perturbed field $G^{i\bar j}$ is a product of the holomorphic and antiholomorphic currents satisfying two-dimensional current algebra.

hep-th↗

arXiv2023

Kubo-Martin-Schwinger relation for an interacting mobile impurity

In this work we study the Kubo-Martin-Schwinger (KMS) relation in the Yang-Gaudin model of an interacting mobile impurity. We use the integrability of the model to compute the dynamic injection and ejection Green's functions at finite temperatures. We show that due to separability of the Hilbert space with an impurity, the ejection Green's in a canonical ensemble cannot be reduced to a single expectation value as per microcanonical picture. Instead, it involves a thermal average over contributions from different subspaces of the Hilbert space which, due to the integrability, are resolved using the so-called spin rapidity. It is then natural to consider the injection and ejection Green's functions within each subspace. By means of reformulating the original KMS condition as a Riemann-Hilbert problem, we analytically demonstrate that such Green's functions obey a refined analogous relation, which is finally corroborated by numerical evaluation.

cond-mat.quant-gas↗

arXiv2023

Finite temperature spin diffusion in the Hubbard model in the strong coupling limit

We investigate finite temperature spin transport in one spatial dimension by considering the spin-spin correlation function of the Hubbard model in the limiting case of infinitely strong repulsion. We find that in the absence of bias the transport is diffusive, and derive the spin diffusion constant. Our approach is based on asymptotic analysis of a Fredholm determinant representation. The obtained results are in agreement with Generalized Hydrodynamics approach.

cond-mat.str-el↗

arXiv2023

Emergence of anyonic correlations from spin and charge dynamics in one dimension

We propose a transformation for spin and charge degrees of freedom in one-dimensional lattice systems, constrained to have no doubly occupied sites, that allows direct access to the dynamical correlations of the system. The transformation delivers particle creation and annihilation operators in a form of a spinless particle and a non-local operator acting on the space of states of a spin-$1/2$ chain. This permits a decomposition of dynamical correlation functions as a convolution of those for impenetrable anyons together with those of a spin chain. Further analysis can be done by methods tailored for each part of the convolution, greatly increasing the impact and flexibility of the approach.

cond-mat.quant-gas↗

arXiv2022

Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe

The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational recipes in molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving non-autonomous time evolution in a large Hilbert space. We illustrate our general results by analyzing conditions for the transport quantization in a topological Thouless pump.

cond-mat.quant-gas↗

arXiv2022

Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations

The Kitaev model on the honeycomb lattice, while being integrable via the spin-fermion mapping, has generally resisted an analytical treatment of the far-from-equilibrium dynamics due to the extensive number of relevant configurations of conserved charges. Here we study a close proxy of this model, the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. Instead of relying on the spin-fermion mapping, we take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. The simplest operator in this subset corresponds to the energy contribution of a single bond direction. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant (or staggered-translation-invariant) initial state with arbitrary initial (staggered) polarization.

cond-mat.stat-mech↗

arXiv2022

Mobile impurity in a one-dimensional gas at finite temperatures

We consider the McGuire model of a one-dimensional gas of free fermions interacting with a single impurity. We compute the static one-body function and momentum distribution of the impurity at finite temperatures. The results involve averages over Fredholm determinants that we further analyse using the effective form factors approach. With this approach, we derive the large-distance behaviour of the one-body function, which takes the form of an averaged exponential decay. This method allows us to study an experimentally important regime of small momenta of the impurity's momentum distribution. We also consider the one-body function at short distances and compute finite temperature Tan's contact.

cond-mat.quant-gas↗