arXiv subjects

Igor Poboiko

Publications and source records attributed to Igor Poboiko.

13 recordsLinked to original sources

arXiv2026

Monitored free fermions under periodic driving

We investigate analytically and numerically a one-dimensional periodically driven free-fermionic system subjected to monitoring of the local particle density. Based on the analytical approach that describes the long-wavelength physics of the time-dependent Hamiltonian in the field-theoretical language using the nonlinear sigma-model (NLSM), we reveal that driving does not alter the universality class of the problem. As a consequence, the system retains the area-law behavior in the thermodynamic limit, with an intermediate diffusive regime giving rise to logarithmic growth of entanglement entropy for a small monitoring rate. At the same time, driving leads to a renormalization of the bare coupling constant of the NLSM, which controls the space-time ``conductivity'' in the diffusive regime. We derive the analytic form of this renormalization, which becomes particularly strong in the case of a ``maximally symmetric'' drive and sufficiently short driving period. In addition, we employ the Wiener-Hopf method to investigate the ballistic-diffusive crossover. These analytical predictions are corroborated by numerical simulations of the von-Neumann entanglement entropy and the density correlation function. Our numerical results clearly demonstrate that, with an increase in the system size, there are successive crossovers from ballistic to diffusive behavior and ultimately to localization. Furthermore, in the diffusive regime, we observe weak-localization corrections that are in agreement with the analytical predictions of the NLSM. Overall, our results provide a unified analytical and numerical framework for understanding the effects of monitoring in time-modulated fermionic systems, paving a way for broader investigations of driven quantum matter.

cond-mat.dis-nn↗

arXiv2025

Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition

We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case of finite evolution time $T$ and different classes of initial states, which lead to different NLSM boundary conditions. The analytical formalism is then used to study how quantum correlations gradually develop, with increasing $T$, from those determined by the initial state towards their steady-state form. The analytical results are confirmed by numerical simulations for several types of initial states. We further consider the long-time limit, when the system in $d+1$ space-time dimensions becomes quasi-one-dimensional, and analyze the scaling of the ``localization'' time (which is simultaneously the purification time and the charge-sharpening time for this class of problems). The analytical predictions for scaling properties are fully confirmed by numerical simulations in a $d=2$ model around the measurement-induced phase transition. We use this dynamical approach to determine numerically the measurement-induced transition point and the associated correlation-length critical exponent.

cond-mat.dis-nn↗

arXiv2025

Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition

We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are the particle-number covariance between spatially separated regions, $G_{AB}$, and the two-point density correlation function, $\mathcal{C}(r)$. Our results exhibit a remarkable analogy to Anderson localization, with $G_{AB}$ corresponding to two-terminal conductance and $\mathcal{C}(r)$ to two-point conductance, albeit with different replica limit and unconventional symmetry class, geometry, and boundary conditions. In the delocalized phase, $G_{AB}$ exhibits ``universal'', nearly Gaussian, fluctuations with variance of order unity. In the localized phase, we find a broad distribution of $G_{AB}$ with $\overline{-\ln G_{AB}} \sim L $ (where $L$ is the system size) and the variance $\mathrm{var}(\ln G_{AB}) \sim L^\mu$, and similarly for $\mathcal{C}(r)$, with $\mu \approx 0.5$. At the transition point, the distribution function of $G_{AB}$ becomes scale-invariant and $\mathcal{C}(r)$ exhibits multifractal statistics, $\overline{\mathcal{C}^{q}(r)}\sim r^{-q(d+1) - \Delta_{q}}$. We characterize the spectrum of multifractal dimensions $\Delta_q$. Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.

quant-ph↗

arXiv2025

Measurement-induced L\'evy flights of quantum information

We explore a model of free fermions in one dimension, subject to frustrated (non-commuting) local measurements across adjacent sites, which resolves the fermions into non-orthogonal orbitals, misaligned from the underlying lattice. For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate at one point in the Brillouin zone, which generates fractal-scaling entanglement entropy $S \propto \ell^{1/3}$ for a subsystem of length $\ell$. We derive an effective non-linear sigma model with long-range couplings responsible for L\'evy flights in entanglement propagation, which we confirm with large-scale numerical simulations. When the misalignment is reduced, the entanglement exhibits, with increasing $\ell$, consecutive regimes of superdiffusive, $S\propto \ell^{1/3}$, diffusive, $S\propto \ln \ell$, and localized, $S = \rm{const}$, behavior. Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians and measurements.

quant-ph↗

arXiv2024

Measurement-induced transitions for interacting fermions

Effect of measurements on interacting fermionic systems with particle-number conservation, whose dynamics is governed by a time-independent Hamiltonian, is studied. We develop Keldysh field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM), which incorporates boundary conditions specifically designed to produce generating functions for charge cumulants and entanglement entropies directly in the NLSM language. By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables. Crucially, the interaction-induced terms in the NLSM action reduce its symmetry, which affects the physics of the problem in a dramatic way. First, this leads to the "information-charge separation": charge cumulants get decoupled from entanglement entropies. Second, the interaction stabilizes the volume-law phase for the entanglement. Third, for spatial dimensionality $d=1$, the interaction stabilizes the phase with logarithmic growth of charge cumulants (in the thermodynamic limit). Thus, in the presence of interaction, there are measurement transitions in any $d$, at variance with free fermions, for which a $d=1$ system is always in the area-law phase. Analytical results are supported by numerical simulations using time-dependent variational principles for matrix product states, which, in particular, confirm the separation of information and charge as a hallmark of the delocalized phase.

quant-ph↗

arXiv2024

Mean-field theory of first-order quantum superconductor-insulator transition

Recent experimental studies on strongly disordered indium oxide films have revealed an unusual first-order quantum phase transition between the superconducting and insulating states (SIT). This transition is characterized by a discontinuous jump from non-zero to zero values of superfluid stiffness at the critical point, contradicting the conventional "scaling scenario" typically associated with SIT. In this paper, we present a theoretical framework for understanding this first-order transition. Our approach is based on the concept of competition between two fundamentally distinct ground states that arise from electron pairs initially localized by strong disorder: the superconducting state and the Coulomb glass insulator. These ground states are distinguished by two crucially different order parameters, suggesting a natural expectation of a discontinuous transition between them at $T=0$. This transition occurs when the magnitudes of the superconducting gap $\Delta$ and the Coulomb gap $E_C$ become comparable. Additionally, we extend our analysis to low non-zero temperatures and provide a mean-field "phase diagram" in the plane of $(T/\Delta,E_C/\Delta)$. Our results reveal the existence of a natural upper bound for the kinetic inductance of strongly disordered superconductors.

cond-mat.supr-con↗

arXiv2024

First-order quantum breakdown of superconductivity in amorphous superconductors

Continuous quantum phase transitions are widely assumed and frequently observed in various systems of quantum particles or spins. Their characteristic trait involves scaling laws governing a second-order, gradual suppression of the order parameter as the quantum critical point is approached. The localization of Cooper pairs in disordered superconductors and the resulting breakdown of superconductivity have long stood as a prototypical example. Here, we show a departure from this paradigm, showcasing that amorphous superconducting films of indium oxide undergo a distinctive, discontinuous first-order quantum phase transition tuned by disorder. Through systematic measurements of the plasmon spectrum in superconducting microwave resonators, we provide evidence for a marked jump of both the zero-temperature superfluid stiffness and the transition temperature at the critical disorder. This discontinuous transition sheds light on the previously overlooked role of repulsive interactions between Cooper pairs and the subsequent competition between superconductivity and insulating Cooper-pair glass. Furthermore, our investigation shows that the critical temperature of the films no longer relates to the pairing amplitude but aligns with the superfluid stiffness, consistent with the pseudogap regime of preformed Cooper pairs. Our findings raise fundamental new questions into the role of disorder in quantum phase transitions and carry implications for superinductances in quantum circuits.

cond-mat.mes-hall↗

arXiv2023

Measurement-induced phase transition for free fermions above one dimension

A theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. The critical point separates a gapless phase with $\ell^{d-1} \ln \ell$ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with $\ell^{d-1}$ scaling, where $\ell$ is a size of the subsystem. The problem is mapped onto an SU($R$) replica non-linear sigma model in $d+1$ dimensions, with $R\to 1$. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for $d = 1+ \epsilon$ with $\epsilon \ll 1$. Further, we carry out a numerical study of the transition for a $d=2$ model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, $\nu \approx 1.4$.

quant-ph↗

arXiv2023

Theory of free fermions under random projective measurements

We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, $\gamma / J \ll 1$ (where $\gamma$ is measurement rate per site and $J$ is hopping constant in the tight-binding model), we derive a non-linear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is described by a $U(2) / U(1) \times U(1) \simeq S_2$ sigma model with diffusive behavior, and the replica-asymmetric sector is a two-dimensional NLSM defined on $SU(R)$ manifold with the replica limit $R \to 1$. On the Gaussian level, valid in the limit $\gamma / J \to 0$, this model predicts a logarithmic behavior for the second cumulant of number of particles in a subsystem and for the entanglement entropy. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value $\sim (J / \gamma)^2$ even for rare measurements, which corresponds to the area-law phase. This implies the absence of a measurement-induced entanglement phase transition for free fermions. The crossover between logarithmic growth and saturation, however, happens at exponentially large scale, $\ln l_\text{corr} \sim J / \gamma$. This makes this crossover very sharp as a function of the measurement frequency $\gamma / J$, which can be easily confused with a transition from the logarithmic to area law in finite-size numerical calculations. We have performed a careful numerical analysis, which supports our analytical predictions.

quant-ph↗

arXiv2020

Two-dimensional Coulomb glass as a model for vortex pinning in superconducting films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields $B \ll H_{c2}$ at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase -- such as $\mathrm{In O}_x$, $\mathrm{Nb N}$, $\mathrm{Ti N}$, $\mathrm{Mo Ge}$, nano-granular aluminium, and others -- is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with large kinetic inductance per square $L_K$. Distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap, i.e. the probability to find a weakly pinned vortex is extremely low.

cond-mat.dis-nn↗

arXiv2017

Paraconductivity of pseudogapped superconductors

We calculate Aslamazov-Larkin paraconductity $σ_{AL}(T)$ for a model of strongly disordered superconductors (dimensions $d=2,3$) with a large pseudogap whose magnitude strongly exceeds transition temperature $T_c$. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same $ε= (T-T_c)/T_c$. Upon decreasing $ε$, Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at $ε\leq ε_1 \ll 1 $. Characteristic scale $ε_1 $ is much larger than the width $ε_2$ of the thermodynamical critical region, that is determined via the Ginzburg criterion, $ε_2 \approx ε_1^d$. We argue that in the intermediate region $ε_2 \leq ε\leq ε_1$ paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at $ε\leq ε_2$; in particular, conductivity occurs to be strongly inhomogeneous in real space.

cond-mat.supr-con↗

arXiv2016

Spin correlation functions and quasiparticle decay

We study one-dimensional anisotropic XXZ spin-$\frac12$ model with ferromagnetic sign of the coupling and $z-z$ exchange constant $J_z = ΔJ$, where $Δ< 1$, and $J$ is the coupling within XY spin plane. We calculate damping of low-energy excitations with $ω\ll T $ due to their scattering from thermal excitation bath with temperature $T \ll J$, taking into account nonzero curvature of the excitation spectrum, $ε(q) = u q + δε(q)$. We calculate also longitudinal spin-spin correlation function $\langle S^z(x,t)S^z(0,0) \rangle$ at $x \approx ut$ and find the shape of the spreading "wave packet".

cond-mat.str-el↗

arXiv2015

Thermal transport in disordered one-dimensional spin chains

We study one-dimensional anisotropic XY-Heisenberg spin-$\frac{1}{2}$ chain with weak random fields $h_i^z S^z_i$ by means of Jordan-Wigner transformation to spinless Luttinger liquid with disorder and bosonization technique. First we investigate phase diagram of the system in terms of dimensionless disorder $γ= \left /J^2 \ll 1$ and anisotropy parameter $Δ= J_z/J_{xy}$ and find the range of these parameters where disorder is irrelevant in the infrared limit and spin-spin correlations are described by power laws. Then we use the diagram technique in terms of plasmon excitations to study low-temperature behavior of heat conductivity $κ$ and spin conductivity $σ$ in this power-law phase. The obtained Lorentz number $L \equiv κ/σT$ differs from the value derived earlier by means of memory function method. We argue also that in the studied region inelastic scattering is strong enough to suppress quantum interference in the low-temperature limit.

cond-mat.mes-hall↗