arXiv subjects

I. V. Gornyi

Publications and source records attributed to I. V. Gornyi.

At least 19 recordsLinked to original sources

arXiv2025

Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field

Krylov complexity measures the spread of an evolved state in a natural basis, induced by the generator of the dynamics and the initial state. Here, we study the spread in Hilbert space of the state of an Ising chain subject to a complex-valued transverse magnetic field, initialized in a trivial product state with all spins pointing down. We demonstrate that Krylov spread reveals structural features of many-body systems that remain hidden in correlation functions that are traditionally employed to determine the phase diagram. When the imaginary part of the spectrum of the non-Hermitian Hamiltonian is gapped, the system state asymptotically approaches the non-Hermitian Bogoliubov vacuum for this Hamiltonian. We find that the spread of this evolution unravels three different dynamical phases based on how the spread reaches its infinite-time value. Furthermore, we establish a connection between the Krylov spread and the static correlation function for the z-components of spins in the underlying non-Hermitian Bogoliubov vacuum, providing a full analytical characterization of correlations across the phase diagram. Specifically, for a gapped imaginary spectrum in a finite magnetic field, we find that the correlation function exhibits an oscillatory behavior that decays exponentially in space. Conversely, for a gapless imaginary spectrum, the correlation function displays an oscillatory behavior with an amplitude that decays algebraically in space; the underlying power law depends on the manifestation of two exceptional points within this phase.

quant-ph↗

arXiv2025

Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity

We investigate phase transitions in a non-Hermitian Su-Schrieffer-Heeger (SSH) model with an imaginary chemical potential via Krylov spread complexity and Krylov fidelity. The spread witnesses the $\mathcal{PT}$-transition for the non-Hermitian Bogoliubov vacuum of the SSH Hamiltonian, where the spectrum goes from purely real to complex (oscillatory dynamics to damped oscillations). In addition, it also witnesses the transition occurring in the $\mathcal{PT}$-broken phase, where the spectrum goes from complex to purely imaginary (damped oscillations to sheer decay). For a purely imaginary spectrum, the Krylov spread fidelity, which measures how the time-dependent spread reaches its stationary state value, serves as a probe of previously undetected dynamical phase transitions.

cond-mat.str-el↗

arXiv2024

Quantum state engineering by steering in the presence of errors

Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed in the past for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against various errors. We study a set of errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of erroneous choice of system-detector coupling, re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the system-detector interaction. We show that the protocol remains fully robust against the erroneous choice of system-detector coupling parameters and presents reasonable robustness against other errors. We employ various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes.

quant-ph↗

arXiv2023

Two-dimensional electron hydrodynamics in a random array of impenetrable obstacles: Magnetoresistivity, Hall viscosity, and the Landauer dipole

We formulate a general framework to study the flow of the electron liquid in two dimensions past a random array of impenetrable obstacles in the presence of a magnetic field. We derive a linear-response formula for the resistivity tensor $\hatρ$ in hydrodynamics with obstacles, which expresses $\hatρ$ in terms of the vorticity and its harmonic conjugate, both on the boundary of obstacles. In the limit of rare obstacles, in which we calculate $\hatρ$, the contributions of the flow-induced electric field to the dissipative resistivity from the area covered by the liquid and the area inside obstacles are shown to be equal to each other. We demonstrate that the averaged electric fields outside and inside obstacles are rotated by Hall viscosity from the direction of flow. For the diffusive boundary condition on the obstacles, this effect exactly cancels in $\hatρ$. By contrast, for the specular boundary condition, the total electric field is rotated by Hall viscosity, which means the emergence of a Hall-viscosity-induced effective -- proportional to the obstacle density -- magnetic field. Its effect on the Hall resistivity is particularly notable in that it leads to a deviation of the Hall constant from its universal value. We show that the applied magnetic field enhances hydrodynamic lubrication, giving rise to a strong negative magnetoresistance. We combine the hydrodynamic and electrostatic perspectives by discussing the distribution of charges that create the flow-induced electric field around obstacles. We provide a connection between the tensor $\hatρ$ and the disorder-averaged electric dipole induced by viscosity at the obstacle. This establishes a conceptual link between the resistivity in hydrodynamics with obstacles and the notion of the Landauer dipole. We show that the viscosity-induced dipole is rotated from the direction of flow by Hall viscosity.

cond-mat.mes-hall↗

arXiv2021

Anti-Poiseuille flow in neutral graphene

Hydrodynamic flow of charge carriers in graphene is an energy flow unlike the usual mass flow in conventional fluids. In neutral graphene, the energy flow is decoupled from the electric current, making it difficult to observe the hydrodynamic effects and measure the viscosity of the electronic fluid by means of electric current measurements. In particular, we show that the hallmark Poiseuille flow in a narrow channel cannot be driven by the electric field irrespective of boundary conditions at the channel edges. Nevertheless one can observe nonuniform current densities similarly to the case of the well-known ballistic-diffusive crossover. The standard diffusive behavior with the uniform current density across the channel is achieved under the assumptions of specular scattering on the channel boundaries. This flow can also be made nonuniform by applying weak magnetic fields. In this case, the curvature of the current density profile is determined by the quasiparticle recombination processes dominated by the disorder-assisted electron-phonon scattering -- the so-called supercollisions.

cond-mat.mes-hall↗

arXiv2021

Resistance of 2D superconducting films

We consider the problem of finite resistance $R$ in superconducting films with geometry of a strip of width $W$ near zero temperature. The resistance is generated by vortex configurations of the phase field. In the first type of process, quantum phase slip, the vortex worldline in 2+1 dimensional space-time is space-like (i.e., the superconducting phase winds in time and space). In the second type, vortex tunneling, the worldline is time-like (i.e., the phase winds in the two spatial directions) and connects opposite edges of the film. For moderately disordered samples, processes of second type favor a train of vortices, each of which tunnels only across a fraction of the sample. Optimization with respect to the number of vortices yields a tunneling distance of the order of the coherence length $ξ$, and the train of vortices becomes equivalent to a quantum phase slip. Based on this theory, we find the resistance $\ln R \sim -g W/ξ$, where $g$ is the dimensionless normal-state conductance. Incorporation of quantum fluctuations indicates a quantum phase transition to an insulating state for $g \lesssim 1$.

cond-mat.supr-con↗

arXiv2021

Contacts, equilibration, and interactions in fractional quantum Hall edge transport

We study electron transport through a multichannel fractional quantum Hall edge in the presence of both interchannel interaction and random tunneling between channels, with emphasis on the role of contacts. The prime example in our discussion is the edge at filling factor 2/3 with two counterpropagating channels. Having established a general framework to describe contacts to a multichannel edge as thermal reservoirs, we particularly focus on the line-junction model for the contacts and investigate incoherent charge transport for an arbitrary strength of interchannel interaction beneath the contacts and, possibly different, outside them. We show that the conductance does not explicitly depend on the interaction strength either in or outside the contact regions (implicitly, it only depends through renormalization of the tunneling rates). Rather, a long line-junction contact is characterized by a single parameter which defines the modes that are at thermal equilibrium with the contact and is determined by the interplay of various types of scattering beneath the contact. This parameter -- playing the role of an effective interaction strength within an idealized model of thermal reservoirs -- is generically nonzero and affects the conductance. We formulate a framework of fractionalization-renormalized tunneling to describe the effect of disorder on transport in the presence of interchannel interaction. Within this framework, we give a detailed discussion of charge equilibration for arbitrarily strong interaction in the bulk of the edge and arbitrary effective interaction characterizing the line-junction contacts.

cond-mat.mes-hall↗

arXiv2021

Multifractally-enhanced superconductivity in thin films

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.

cond-mat.mes-hall↗

arXiv2021

Hydrodynamic approach to electronic transport in graphene: energy relaxation

In nearly compensated graphene, disorder-assisted electron-phonon scattering or "supercollisions" are responsible for both quasiparticle recombination and energy relaxation. Within the hydrodynamic approach, these processes contribute weak decay terms to the continuity equations at local equilibrium, i.e., at the level of "ideal" hydrodynamics. Here we report the derivation of the decay term due to weak violation of energy conservation. Such terms have to be considered on equal footing with the well-known recombination terms due to nonconservation of the number of particles in each band. At high enough temperatures in the "hydrodynamic regime" supercollisions dominate both types of the interaction). We also discuss the contribution of supercollisions to the heat transfer equation (generalizing the continuity equation for the energy density in viscous hydrodynamics).

cond-mat.mes-hall↗

arXiv2021

Hydrodynamic collective modes in graphene

Collective behavior is one of the most intriguing aspects of the hydrodynamic approach to electronic transport. Here we provide a consistent, unified calculation of the dispersion relations of the hydrodynamic collective modes in graphene. Taking into account viscous effects, we show that the hydrodynamic sound mode in graphene becomes overdamped at sufficiently large momentum scales. Extending the linearized theory beyond the hydrodynamic regime, we connect the diffusive hydrodynamic charge density fluctuations with plasmons.

cond-mat.mes-hall↗

arXiv2021

Entanglement entropy and particle number cumulants of disordered fermions

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in $d$ dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

cond-mat.mes-hall↗

arXiv2020

Measurement-induced steering of quantum systems

We set out a general protocol for steering the state of a quantum system from an arbitrary initial state towards a chosen target state by coupling it to auxiliary quantum degrees of freedom. The protocol requires multiple repetitions of an elementary step: during each step the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term 'detector qubits') that have been prepared in a specified initial state. The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes. The steering harnesses back-action of the detector qubits on the system, arising from entanglement generated during the coupled evolution. We establish principles for the design of the system-detector coupling that ensure steering of a desired form. We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state). We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering. Our protocols are amenable to implementations using present-day technology. Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.

cond-mat.stat-mech↗

arXiv2020

Transparency enhancement in a double-barrier structure by the Fano antiresonance

We show that the presence of a side-attached state strongly modifies the transmission through a one-dimensional double-barrier system in the window of wavevectors around the Fano antiresonance. Specifically, the interplay between the Fano interference and the size quantization inside the structure gives rise to narrow resonant peaks in the transmission coefficient. The height of the peaks may become close to unity (perfect transmission) even for an asymmetric setup with strong barriers, where the transmission coefficient in the absence of the Fano state is strongly suppressed at all other wavevectors. Thus, the two types of the interference phenomena, each by itself leading to the suppression of the transmission, conspire in a peculiar way to produce the transparency enhancement.

cond-mat.mes-hall↗

arXiv2020

Absolute Poisson's ratio and the bending rigidity exponent of a crystalline two-dimensional membrane

We compute the absolute Poisson's ratio $ν$ and the bending rigidity exponent $η$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d = 2 + d_c$, $d_c \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the absolute Poisson's ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $ν= -1 +2/d_c-a/d_c^2+\dots$ where $a\approx 1.76\pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $η= 2/d_c+(73-68ζ(3))/(27 d_c^2)+\dots$. These results cannot be captured by self-consistent screening approximation.

cond-mat.mes-hall↗

arXiv2019

Emergent chirality in multi-lead Luttinger-liquid junctions out of equilibrium

We study charge transport through $N$-lead junctions ($N\geq 3$) of spinless Luttinger liquid wires with bias voltages applied to Fermi-liquid reservoirs. In particular, we consider a Y junction, which is a setup characteristic of the tunneling experiment. In this setup, the strength of electron-electron interactions in one of the arms ("tunneling tip") is different from that in the other two arms (which form together the "main wire"). For a generic single-particle $S$ matrix of the junction, we find that the bias voltage $V$ applied---even symmetrically---to the main wire generates a current proportional to $|V|$ in the tip wire. We identify two mechanisms of this nonequilibrium-induced "emergent chirality" in a setup characterized by the time-reversal and parity symmetric Hamiltonian of the junction. These are: (i) the emergence of an effective magnetic flux, which breaks time-reversal symmetry, and (ii) the emergence of parity-breaking asymmetry of the setup, both proportional to the interaction strength and the sign of the voltage. The current in the tip wire generated by mechanism (i) is reminiscent of the Hall current in the linear response of a system the Hamiltonian of which breaks time-reversal symmetry; however, in the absence of any magnetic field or a local magnetic moment. Similarly, mechanism (ii) can be thought of as an emergent "photogalvanic effect"; however, in the presence of inversion symmetry within the main wire. The nonequilibrium chirality implies a rectification of the current in the tip when the main wire is biased by $\it ac$ voltage.

cond-mat.str-el↗

arXiv2019

Asymmetry of non-local dissipation: From drift-diffusion to hydrodynamics

We study dissipation in inhomogeneous two-dimensional electron systems. We predict a relatively strong current-induced spatial asymmetry in the heating of the electron and phonon systems -- even if the inhomogeneity responsible for the electrical resistance is symmetric with respect to the current direction. We also show that the heat distributions in the hydrodynamic and impurity-dominated limits are essentially different. In particular, within a wide, experimentally relevant interval of driving fields, the dissipation profile in the hydrodynamic limit turns out to be asymmetric, and the characteristic spatial scale of the temperature distribution can be controlled by the driving field. By contrast, in the same range of parameters, impurity-dominated heating is almost symmetric, with the size of the dissipation region being independent of the field. This allows one to distinguish experimentally the hydrodynamic and impurity-dominated limits. Our results are consistent with recent experimental findings on transport and dissipation in narrow constrictions and quantum point contacts.

cond-mat.mes-hall↗

arXiv2019

From weak to strong disorder in Weyl semimetals: Self-consistent Born approximation

We analyze theoretically the conductivity of Weyl semimetals within the self-consistent Born approximation (SCBA) in the full range of disorder strength, from weak to strong disorder. In the range of intermediate disorder, we find a critical regime which separates the semimetal and diffusion regimes. While the numerical values of the critical exponents are not expected to be exact within the SCBA, the approach allows us to calculate functional dependences of various observables (density of states, quasiparticle broadening, conductivity) in a closed form. This sheds more light on the qualitative behavior of the conductivity and its universal features in disordered Weyl semimetals. In particular, we have found that the vertex corrections in the Kubo formula are of crucial importance in the regime of strong disorder and lead to saturation of the dc conductivity with increasing disorder strength. We have also analyzed the evolution of the optical conductivity with increasing disorder strength, including its scaling properties in the critical regime.

cond-mat.dis-nn↗

arXiv2018

Valley subband splitting in bilayer graphene quantum point contact

We report a study of one-dimensional subband splitting in a bilayer graphene quantum point contact in which quantized conductance in steps of $4\,e^2/h$ is clearly defined down to the lowest subband. While our source-drain bias spectroscopy measurements reveal an unconventional confinement, we observe a full lifting of the valley degeneracy at high magnetic fields perpendicular to the bilayer graphene plane for the first two lowest subbands where confinement and Coulomb interactions are the strongest and a peculiar merging/mixing of $K$ and $K'$ valleys from two non-adjacent subbands with indices $(N,N+2)$ which are well described by our semi-phenomenological model.

cond-mat.mes-hall↗