arXiv subjects

Nikolay Prokof'ev

Publications and source records attributed to Nikolay Prokof'ev.

At least 19 recordsLinked to original sources

arXiv2026

Low-temperature Depletion of Superfluid Density in the Absence of Galilean Symmetry

Landau theory of superfluidity associates low-temperature flow of the normal component with the phonon wind. This picture does not apply to superfluids in which Galilean invariance is broken either by disorder, porous media, or lattice potential, and the phonon wind is no longer solely responsible for depletion of the superfluid component. Based on Popov's hydrodynamic action with anharmonic terms, we present a general theory for low-temperature ($T$) dependence of the superfluid stiffness, which reproduces Landau result as a special case when several parameters of the hydrodynamic action are fixed by Galilean invariance, and validate it with numerical simulations of interacting lattice bosons. In a broader context, our approach reveals universal low-temperature thermodynamics of superfluids with an intrinsic connection between finite-$T$ and finite-size ($L$) effects implying universal scaling, $T^{d+1}$ and $1/L^{d+1}$, respectively, for a large class of thermodynamic quantities. We discuss the experimental detection of this law, and compare our prediction to the existing literature.

cond-mat.quant-gas↗

arXiv2026

"Depletion" of Superfluid Density: Universal Low-temperature Thermodynamics of Superfluids

In a Galilean superfluid, the depletion of superfluid density with rising temperature can be attributed to thermally excited non-interacting phonons. For systems without Galilean symmetry, it has been shown [1] that ``phonon wind" is no longer responsible for the depletion of superfluid density. In this work, we develop the theory of superfluid density at low temperature ($T$) and provide detailed derivations of all results announced in [1]. Using Popov's hydrodynamic action, we show that the theory of low-temperature depletion in a $d$-dimensional quantum superfluid maps onto the problem of finite-size ($L$) corrections in a $(d+1)$-dimensional anisotropic (pseudo-)classical-field system with U(1)-symmetric complex-valued action. In addition to generalizing Landau's (canonical) formula, we develop the grand canonical theory, which in a broader context reveals a universal scaling, $T^{d+1}$ and $1/L^{d+1}$, for finite-$T$ and finite-$L$ effects of many thermodynamic quantities. We validate our theory with numeric simulations of interacting lattice bosons and the J-current model.

cond-mat.quant-gas↗

arXiv2026

Limits of validity for Migdal-Eliashberg theory: role of polarons/bi-polarons

It is widely believed that in an adiabatic limit a Fermi liquid state of an electron-phonon system described by Migdal-Eliashberg theory remains stable before a dressed phonon softens. Using Holstein model as a prototypical example and variational/analytic considerations we demonstrate that in a wide range of fillings both in 3D and 2D, a polaronic/bi-polaronic state emerges before phonon softening; at small filling in 3D this happens already at weak coupling. We show that a polaronic/bi-polaronic state emerges, upon increasing coupling, via an intermediate pseudogap-type mixed state, in which some fermions regain Fermi liquid behavior, yet Luttinger theorem is broken. At even larger couplings the density of states gradually approaches its form in the atomic limit.

cond-mat.str-el↗

arXiv2026

Breakdown of the Migdal-Eliashberg theory for electron-phonon systems. Role of polarons/bi-polarons

The Migdal-Eliashberg theory (MET) describes electrons interacting with phonons in the adiabatic limit when the phonon Debye frequency is much smaller than the Fermi energy. A conventional belief is that MET holds even at strong coupling, when electron self-energy is large, and breaks down only near the point where the dressed phonon spectrum softens to near zero. We analyze numerically and analytically a different option -- collapse to a polaronic/bipolaronic ground state. The last scenario has never been analyzed in precise quantitative terms for a generic electron density. Using variational considerations, we establish rigorous upper bounds on the coupling $λ$, at which a FL state transforms into the bipolaron/polaron state. We show that at small and near-maximum densities, this happens well before a dressed phonon softens. This is true both in 2D and 3D systems; in the latter the upper bound on $λ$ tends to zero in the limit of small or near-full density. We present analytical reasoning for this behavior based on hints extracted from exact diagrammatic treatment of the on-site Holstein model for the spin polarized case and argue that polarons are produced by fermions with energies comparable to the bandwidth; i.e., polaron formation is outside the realm of MET. Closer to half-filling, the leading instability upon increasing $λ$ is towards a charge-density-wave state (CDW), and there exists a strong coupling regime of MET near this instability, while the polaron/bipolaron state develops at larger $λ$ out of a CDW-ordered state and inherits a CDW order over some range of coupling.

cond-mat.str-el↗

arXiv2025

Polarons with arbitrary nonlinear electron-phonon interaction

We develop an exact computational method based on numerical X-propagators for solving polaron models with arbitrary nonlinear couplings of local vibration modes to the electron density and magnitude of the hopping amplitude. Our approach covers various polaron models, some of which were impossible to treat by any existing approximation-free techniques. Moreover, it remains efficient in the most relevant but computationally challenging regime of phonon frequencies much smaller than the electron bandwidth. As a case study, we consider the double-well type nonlinear model with quadratic ($g_2<0$) and quartic ($g_4>0$) interactions describing a broad class of technologically important materials, such as quantum paraelectric compounds and halide perovskites. We observe, depending on the model parameters, three qualitatively different regimes: (i) quantum interplay of quartic and quadratic interactions which suppresses effects of the quadratic coupling, (ii) intermediate-coupling regime with exponential $\propto \exp(αg_2 Ω^{-1/4})$ scaling of the quasiparticle weight and mass renormalization, and (iii) strong-coupling asymptotic behavior.

cond-mat.str-el↗

arXiv2025

Superconductivity of bipolarons from quadratic electron-phonon interaction

In systems with linear electron-phonon interaction (EPI), bound states of polarons, or bipolarons, form by gaining energy from the lattice deformation. The quadratic EPI case is fundamentally different: bipolarons form because electrons lose less energy when the total charge density is "compacted". As the coupling constant is increased, the bipolarons first appear as extended (but finite radius) soliton-type states. They subsequently decrease in radius until their size reaches the inter-atomic scale. We present the first numerically exact solution of the bipolaron problem from quadratic EPI in the presence of both on-site Hubbard and long-range Coulomb repulsion, and compute estimates of the largest superconducting transition temperature within the bipolaron mechanism. We find that $T_c/Ω$ ratios, where $Ω$ is the optical phonon frequency, can be several times larger than what one may expect from the linear EPI provided the phonon frequency is increased by orders of magnitude on occupied sites. Electron-electron repulsion can be tolerated at the expense of stronger EPI and the most detrimental effect comes from the Coulomb potential because it easily eliminates extended soliton states.

cond-mat.str-el↗

arXiv2024

Effects of phonon dispersion on the bond-bipolaron superconductivity

We employ the diagrammatic Monte Carlo method based on lattice path-integral representaion of the particle sector and real-space diagrammatics of the phonon sector to study effects of optical phonon dispersion on Bose-Einstein condensation of bipolarons in the bond model. For dispersionless phonons with frequency $ω$ this model was recently shown to give rise to small-size, light-mass bipolarons that undergo a superfluid transition at high values of the $T_c/ω$ ratio. We find that for dispersive phonons, $T_c$ remains relatively high over a broader range of the coupling strength and even keeps increasing in the deep adiabatic regime both in two and three dimensions. This result implies that phonon dispersion is not a limiting factor in the search for new materials with high superconducting temperatures.

cond-mat.str-el↗

arXiv2024

Autonomous dynamics of two-dimensional insulating domain with superclimbing edges

Superclimbing dynamics is the signature feature of transverse quantum fluids describing wide superfluid one-dimensional interfaces and/or edges with negligible Peierls barrier. Using Lagrangian formalism, we show how the essence of the superclimb phenomenon -- dynamic conjugation of the fields of the superfluid phase and geometric shape -- clearly manifests itself via characteristic modes of autonomous motion of the insulating domain (``droplet") with superclimbing edges. In the translation invariant case and in the absence of supercurrent along the edge, the droplet demonstrates ballistic motion with the velocity-dependent shape and zero bulk currents. In an isotropic trapping potential, the droplet features a doubly degenerate sloshing mode. The period of the ground-state evolution of the superfluid phase (dictating the frequency of the AC Josephson effect) is sensitive to the geometry of the droplet. The supercurrent along the edge dramatically changes the droplet dynamics: The motion acquires features resembling that of a 2D charged particle interacting with a perpendicular magnetic field. In a linear external potential (uniform force field), the state with a supercurrent demonstrates a spectacular gyroscopic effect -- uniform motion in the perpendicular to the force direction.

cond-mat.quant-gas↗

arXiv2024

Transverse Quantum Superfluids

Even when ideal solids are insulating, their states with crystallographic defects may have superfluid properties. It became clear recently that edge dislocations in $^4$He featuring a combination of microscopic quantum roughness and superfluidity of their cores may represent a new paradigmatic class of quasi-one-dimensional superfluids. The new state of matter, termed transverse quantum fluid (TQF), is found in a variety of physical setups. The key ingredient defining the class of TQF systems is infinite compressibility, which is responsible for all other unusual properties such as the quadratic spectrum (or even the absence) of normal modes, irrelevance of the Landau criterion, off-diagonal long-range order at $T = 0$, and the exponential dependence of the phase slip probability on the inverse flow velocity. From a conceptual point of view, the TQF state is a striking demonstration of the conditional character of many dogmas associated with superfluidity, including the necessity of elementary excitations, in general, and the ones obeying Landau criterion in particular.

cond-mat.quant-gas↗

arXiv2024

Superclimbing modes in transverse quantum fluids: signature statistical and dynamical features

Superclimbing modes are hallmark degrees of freedom of transverse quantum fluids describing wide superfluid one-dimensional interfaces and/or edges with negligible Peierls barrier. We report the first direct numeric evidence of quantum shape fluctuations -- caused by superclimbing modes -- in simple lattice models, as well as at the free edge of an incomplete solid monolayer of $^4$He adsorbed on graphite. Our data unambiguously reveals the defining feature of the superclimbing modes -- canonical conjugation of the edge displacement field to the field of superfluid phase -- and its unexpected implication, i.e., that superfluid stiffness can be inferred from density snapshots.

cond-mat.other↗

arXiv2024

Transverse Quantum Fluids

Motivated by remarkable properties of superfluid edge dislocations in solid Helium-4, we discuss a broad class of quantum systems -- boundaries in phase separated lattice states, magnetic domain walls, and ensembles of Luttinger liquids -- that can be classified as Transverse Quantum Fluids (TQF). After introducing the general idea of TQF, we focus on a coupled array of Luttinger liquids forming an incoherent TQF. This state is a long-range ordered quasi-one-dimensional superfluid, topologically protected against quantum phase slips by tight-binding of instanton dipoles, that has no coherent quasi-particle excitations at low energies. Incoherent TQF is a striking example of the irrelevance of the Landau quasiparticle criterion for superfluidity in systems that lack Galilean invariance. We detail its phenomenology, to motivate a number of experimental studies in condensed matter and cold atomic systems.

cond-mat.other↗

arXiv2023

Universal Correlations as Fingerprints of Transverse Quantum Fluids

We study universal off-diagonal correlations in transverse quantum fluids (TQF) -- a new class of quasi-one-dimensional superfluids featuring long-range-ordered ground states. These exhibit unique self-similar space-time relations scaling with $x^2/Dτ$ that serve as fingerprints of the specific states. The results obtained with the effective field theory are found to be in perfect agreement with {\it ab initio} simulations of hard-core bosons on a lattice -- a simple microscopic realization of TQF. This allows an accurate determination -- at nonzero temperature and finite system size -- of such key ground-state properties as the condensate and superfluid densities, and characteristic parameter $D$.

cond-mat.other↗

arXiv2023

Soliton States From Quadratic Electron-Phonon Interaction

We present the first numerically exact study of self-trapped, a.k.a. soliton, states of electrons that form in materials with strong quadratic coupling to the phonon coordinates. Previous studies failed to observe predictions based on the variational approach in continuum space because soliton states form only when system parameters are taken to the extreme limit. At the variational level, we establish that finite-radius solitons emerge through the weak first-order transition as the coupling strength is increased, and subsequently collapse to the single-site state through strong first-order transition. Both transitions transform into smooth crossovers between the light and heavy polaron states in the full quantum treatment. The most surprising effect not observed in any other polaron model is non-monotonic dependence of the soliton effective mass and the residue at strong coupling.

cond-mat.str-el↗

arXiv2023

Superfluid Edge Dislocation: Transverse Quantum Fluid

Recently, it has been argued by Kuklov et al., that unusual features associated with the superflow-through-solid effect observed in solid He4 can be explained by unique properties of dilute distribution of superfluid edge dislocations. We demonstrate that stability of supercurrents controlled by quantum phase slips (instantons), and other exotic infrared properties of the superfluid dislocations readily follow from a one-dimensional quantum liquid distinguished by an effectively infinite compressibility (in the absence of Peierls potential) associated with the edge dislocation's ability to climb. This establishes a new class of quasi-one-dimensional superfluid states that remain stable and long-range ordered despite their low dimensionality. We propose an experiment to test our mass-current--pressure characteristic prediction.

cond-mat.other↗

arXiv2022

Polaron with Quadratic Electron-phonon Interaction

We present the first numerically exact study of a polaron with quadratic coupling to the oscillator displacement, using two alternative methodological developments. Our results cover both anti-adiabatic and adiabatic regimes and the entire range of electron-phonon coupling $g_2$, from the system's stability threshold at attractive $g_2=-1$ to arbitrary strong repulsion at $g_2 \gg 1$. Key properties of quadratic polarons prove dramatically different from their linear counterparts. They (i) are insensitive even to large quadratic coupling except in the anti-adiabatic limit near the threshold of instability at attraction; (ii) depend only on the adiabatic ratio but are insensitive to the electron dispersion and dimension of space; (iii) feature weak lattice deformations even at the instability point. Our results are of direct relevance to properties of electrons at low densities in polar materials, including recent proposals for their superconducting states.

cond-mat.str-el↗

arXiv2021

Anomalously Small Excitation Gaps as a Precursor of Dislocation Core Superfluidity in Solid Helium-4

In the vicinity of the insulator-to-superfluid quantum phase transition in its core, a dislocation in a He-4 crystal supports particle-hole excitations with arbitrary small gaps. These exotic analogs of Frenkel interstitial-vacancy pairs should manifest themselves in various threshold and thermoactivation effects. In Worm Algorithm simulations, we reveal the presence of corresponding small gaps via anomalous thermoactivation behavior of particle number fluctuations, which we unambiguously associate with dislocations by "visualization" techniques. Experimentally, the related threshold and thermoactivation dependencies could be observed in the ultrasound absorption.

cond-mat.soft↗

arXiv2021

Thermal and structural properties of topological defects in solid Helium-4: Strain induced martensitic transformation from hcp to fc orthorhombic lattice

Several experimental studies have reported thermally activated behavior of the mechanical response of solid Helium-4 which does not fit into the model of thermally activated Frenkel pairs in an ideal crystal. The purpose of the present work is to investigate how structural topological defects modify the response. Using quantum Monte Carlo Worm Algorithm, we study temperature dependence of fluctuations of the total number of particles in samples of hcp solid Helium-4 containing several types of dislocations. Such fluctuations can be described by the thermal activation law with the activation energy dependent strongly on the type of the dislocation and the crystal density. The extracted values cover a range from about 1K to 20K. It is also found that annihilation of a jog-antijog pair can produce a local region of the solid characterized by the orthorhombic symmetry. This serendipitous observation suggests that hcp solid Helium-4 can undergo a displacive phase transition into the orthorhombic crystal under uniaxial stress of about 10-15%

cond-mat.other↗

arXiv2020

Fermi blockade of the electron-phonon interaction: why strong coupling effects may not be seen in optimally doped high temperature superconductors

We study how manifestations of strong electron-phonon interaction (EPI) depend on the carrier concentration by solving the two-dimensional Holstein model for the spin-polarized fermions using an approximation free bold-line diagrammatic Monte Carlo (BDMC) method. We show that the strong EPI, obviously present at very small Fermion concentration, is masked by the Fermi blockade effects and Migdal's theorem to the extent that it manifests itself as moderate one at large carriers densities. Suppression of strong EPI fingerprints is in agreement with experimental observations in doped high temperature superconductors

cond-mat.supr-con↗