arXiv subjects

E. Kozik

Publications and source records attributed to E. Kozik.

18 recordsLinked to original sources

arXiv2026

Emergent BEC mechanism in flat-band superconductors

The formation of bound bosonic pairs of fermions, followed by their Bose-Einstein (quasi) condensation (BEC), is a foundational mechanism of superconductivity. At low filling, flat-band superconductivity is well captured by this mechanism provided the flat band is separated from the occupied lower band by an energy gap. However, particularly high $T_c$ values are anticipated when the non-interacting flat and lower bands touch---as in the prototypical attractive Lieb-lattice model studied here---invalidating the conventional picture: while interactions might protect the bound state by opening a gap, no small parameter guarantees the separation of the bound-state energy from this gap or occupied-band excitations, leaving the pair's fate uncertain. Based on a controlled-precision numerical protocol---which we demonstrate to be essential in this fundamentally non-perturbative problem---we show that the BEC mechanism, underpinned by an interaction-induced gap, is generically robust and remarkably efficient: fermions doped into the flat band form bound pairs within this gap with an anomalously light effective mass, enabling an exceptionally high $T_c$.

cond-mat.supr-con↗

arXiv2026

Avoided Stoner instability at a single ordinary Van Hove point

When the Fermi surface and the Brillouin zone boundary touch at a Van Hove point, mean-field analysis predicts a ferromagnetic (Stoner) instability at finite $T_{MF}$ for any coupling strength due to the divergent density of states. However, the predicted effect has not been observed experimentally. Several qualitative theoretical proposals have been put forward to explain why the mean-field prediction fails. Based on numerically exact results for the two-dimensional Hubbard model with an ordinary Van Hove singularity, we uncover the mechanisms behind the suppression of the ferromagnetic instability. We employ two diagrammatic Monte Carlo approaches: (i) the four-channel self-consistent approximation and (ii) numerically exact method of combinatorial summation of diagrams with controlled resummation of the truncated expansion. We find that the system avoids the Stoner instability down to temperatures an order of magnitude below $T_{MF}$ due to the combination of the downward renormalization of the effective coupling and the suppression of the density of states by the loss of the quasiparticle residue.

cond-mat.str-el↗

arXiv2026

Numerically Exact Study of Flat-Band Superconductivity

Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, $T_c(U) = c|U|$. However, the value of $c$ and the full nonlinear $T_c(U)$ curve---with a maximum at large $|U|$---are known beyond mean-field and quantum geometry estimates only for systems with isolated flat bands. Using a controlled diagrammatic Monte Carlo technique, we trace the onset of superfluid response in the Lieb lattice with attractive Hubbard interaction. Focusing on the half-filled flat-band case, where the ordering mechanism differs fundamentally from both BCS and BEC (preformed Cooper pair) scenarios, we find that the pairing response diverges linearly with decreasing temperature over a broad range of $U$, leading to a sharp crossover to long-range correlations at a characteristic temperature $T_*$, which provides a controlled upper bound on $T_c$. The highest $T_*$ occurs when all three bands touch at a single momentum point, potentially corresponding to high $T_c$ values.

cond-mat.supr-con↗

arXiv2024

Physical and unphysical regimes of self-consistent many-body perturbation theory

In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $\mathcal{N}$ and plugged into the Dyson equation, which is then solved for the propagator $G_{\mathcal{N}}\,$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_{\mathcal{N}}\,$ converges when $\mathcal{N}\to\infty$ to a limit $G_\infty\,$, which coincides with the exact physical propagator $G_{\rm exact}\ $ at small enough coupling, while $G_\infty \neq G_{\rm exact}\ $ at strong coupling. This follows from the findings of [Kozik, Ferrero and Georges, PRL 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_\infty=G_{\rm exact}\ $ and $G_\infty\neq G_{\rm exact}\ $ regimes thanks to a criterion which does not require the knowledge of $G_{\rm exact}\ $, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)].

cond-mat.str-el↗

arXiv2020

Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model

In this work we introduce the Dual Boson Diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for non-perturbative description of local correlations with the systematic account of non-local corrections in the Dual Boson theory by the diagrammatic Monte Carlo approach. It allows us to get a numerically exact solution of the dual boson theory at the two-particle local vertex level for the extended Hubbard model. We show that it can be efficiently applied to description of single particle observables in a wide range of interaction strengths. We compare our exact results for the self-energy with the ladder Dual Boson approach and determine a physical regime, where description of collective electronic effects requires more accurate consideration beyond the ladder approximation. Additionally, we find that the order-by-order analysis of the perturbative diagrammatic series for the single-particle Green's function allows to estimate the transition point to the charge density wave phase.

cond-mat.str-el↗

arXiv2018

Contact and Momentum Distribution of the Unitary Fermi Gas

A key quantity in strongly-interacting resonant Fermi gases is the contact $\mathcal{C}$, which characterizes numerous properties such as the momentum distribution at large momenta or the pair correlation function at short distances. The temperature dependence of $\mathcal{C}$ was measured at unitarity, where existing theoretical predictions differ substantially even at the qualitative level. We report accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, obtained by Bold Diagrammatic Monte Carlo and Borel resummation. Our results agree with experimental data within error bars and provide crucial benchmarks for the development of advanced theoretical treatments and precision measurements.

cond-mat.quant-gas↗

arXiv2015

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

cond-mat.str-el↗

arXiv2013

Néel temperature and thermodynamics of the half-filled 3D Hubbard model by Diagrammatic Determinant Monte Carlo

We study thermodynamics of the 3D Hubbard model at half filling on approach to the Néel transition by means of large-scale unbiased Diagrammatic Determinant Monte Carlo simulations. We obtain the transition temperature in the strongly correlated regime, as well as temperature dependence of energy, entropy, double occupancy, and the nearest-neighbor spin correlation function. Our results improve the accuracy of previous unbiased studies and present accurate benchmarks in the ongoing effort to realize the antiferromagnetic state of matter with ultracold atoms in optical lattices.

cond-mat.quant-gas↗

arXiv2012

Feynman diagrams versus Fermi-gas Feynman emulator

Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by the intricate quantum statistics at play. Here we present a cross-validation between a new theoretical approach, Bold Diagrammatic Monte Carlo (BDMC), and precision experiments on ultra-cold atoms. Specifically, we compute and measure with unprecedented accuracy the normal-state equation of state of the unitary gas, a prototypical example of a strongly correlated fermionic system. Excellent agreement demonstrates that a series of Feynman diagrams can be controllably resummed in a non-perturbative regime using BDMC. This opens the door to the solution of some of the most challenging problems across many areas of physics.

cond-mat.quant-gas↗

arXiv2011

Sequential and simultaneous emission of fragments from p+Al collisions

The energy and angular dependencies of double differential cross sections d^2sigma/dOmegadE were measured for p,d,t,^{3,4,6}He,^{6,7,8}Li,{7,9,10}Be, and ^{10,11,12}B produced in collisions of 1.2, 1.9, and 2.5 GeV protons with an Al target. The spectra and angular distributions of Li, Be, and B isotopes indicate a presence of two contributions: an isotropic, low energy one which is attributed to the evaporation of particles from excited remnants of the intranuclear cascade, and an anisotropic part which is interpreted to be due to multifragmentation of the remnants. It was found that such a hypothesis leads to very good description of spectra and angular distributions of all intermediate mass fragments (^6He-^{12}B) using the critical value of the excitation energy per nucleon as a single parameter, varying slowly with the beam energy.

nucl-ex↗

arXiv2011

Diagrammatic Quantum Monte Carlo solution of the two-dimensional Cooperon-Fermion model

We investigate the two-dimensional cooperon-fermion model in the correlated regime with a new continuous-time diagrammatic determinant quantum Monte Carlo (DDQMC) algorithm. We estimate the transition temperature $T_{c}$, examine the effectively reduced band gap and cooperon mass, and find that delocalization of the cooperons enhances the diamagnetism. When applied to diamagnetism of the pseudogap phase in high-$T_{c}$ cuprates, we obtain results in a qualitative agreement with recent torque magnetization measurements.

cond-mat.supr-con↗

arXiv2010

Thermodynamics of the 3D Hubbard model on approach to the Neel transition

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Neel temperature using cluster dynamical mean-field theory. In particular we calculate the energy, entropy, density, double occupancy and nearest-neighbor spin correlations as a function of chemical potential, temperature and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle $S/N \approx 0.65(6)$ at $U/t=8$ is sufficient to achieve a Neel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.

cond-mat.quant-gas↗

arXiv2010

Diagrammatic Monte Carlo for Correlated Fermions

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.

cond-mat.str-el↗

arXiv2009

Evidence of Ni break-up from total production cross sections in p+Ni collisions

The total production cross sections of light charged particles (LCPs), intermediate mass fragments (IMFs) and heavy reaction products of p+Ni collisions available in the literature have been compared with predictions of a two-step model in the proton beam energy range from reaction threshold up to approximately 3 GeV. Model cross sections were calculated assuming, that the reaction proceeds via an intranuclear cascade of nucleon-nucleon collisions followed by evaporation of particles from an equilibrated, heavy target residuum. The shape of the excitation functions was well described by model calculations for all reaction products. The magnitude of the cross sections was reasonably well reproduced for heavy reaction products, i.e. for nuclei heavier than Al, but the cross sections for lighter products were systematically underestimated. This fact was used as an argument in favor of a significant break-up contribution to the reaction mechanism. The present conclusions are supported by recently published results of investigations of differential cross sections in p+Ni collisions, which showed that hypothesis of the break-up of target nucleus is indispensable for a good reproduction of d2 sigma/dOmega dE for LCPs and IMFs.

nucl-ex↗

arXiv2009

Variation of nonequilibrium processes in p+Ni system with beam energy

The energy and angular dependence of double differential cross sections dsigma/dOmega dE were measured for p, d, t, 3,4He, 6,7Li, 7,9Be, and 10,11B produced in collisions of 0.175 GeV protons with Ni target. The analysis of measured dfferential cross sections allowed to extract total production cross sections for ejectiles listed above. The shape of the spectra and angular distributions indicate the presence of other nonequilibrium processes besides the emission of nucleons from the intranuclear cascade, and besides the evaporation of various particles from remnants of intranuclear cascade. These nonequilibrium processes consist of coalescence of nucleons into light charged particles during the intranuclear cascade, of the fireball emission which contributes to the cross sections of protons and deuterons, and of the break-up of the target nucleus which leads to the emission of intermediate mass fragments. All such processes were found earlier at beam energies 1.2, 1.9, and 2.5 GeV for Ni as well as for Au targets, however, significant differences in properties of these processes at high and low beam energy are observed in the present study.

nucl-ex↗

arXiv2009

Comparison of nonequilibrium processes in p+Ni and p+Au collisions at GeV energies

The energy and angular dependence of double differential cross sections d2sigma/dOmega dE were measured for p, d, t, 3,4,6He, 6,7,8Li, 7,9,10Be, 10,11B, and C produced in collisions of 1.2, 1.9, and 2.5 GeV protons with a Ni target. The shape of the spectra and angular distributions does almost not change whereas the absolute value of the cross sections increases by a factor about 1.7 for all ejectiles in this beam energy range. It was found that energy and angular dependencies of the cross sections cannot be reproduced by the microscopic model of intranuclear cascade with coalescence of nucleons and the statistical model for evaporation of particles from excited, equilibrated residual nuclei. The inclusion of nonequilibrium processes, described by a phenomenological model of the emission from fast and hot moving sources, resulting from break-up of the target nucleus by impinging proton, leads to very good reproduction of data. Cross sections of these processes are quite large, exhausting approximately half of the total production cross sections. Due to good reproduction of energy and angular dependencies of d2sigma/dOmega dE by model calculation it was possible to determine total production cross sections for all studied ejectiles. Results obtained in this work point to the analogous reaction mechanism for proton induced reactions on Ni target as that observed previously for Au target in the same beam energy range.

nucl-ex↗

arXiv2008

Competition of coalescence and "fireball" processes in nonequilibrium emission of light charged particles from p+Au collisions

The energy and angular dependence of double differential cross sections was measured for p,d,t,He,Li,Be, and B isotopes produced in collisions of 1.2 and 1.9 GeV protons with Au target. The shape of the spectra and angular distributions almost does not change in the beam energy range from 1.2 to 2.5 GeV, however, the absolute value of the cross sections increases for all ejectiles. A phenomenological model of two emitting, moving sources reproduces very well spectra and angular distributions of intermediate mass fragments. Double differential cross sections for light charged particles (LCP) were analyzed in the frame of the microscopic model of intranuclear cascade (INC) with coalescence of nucleons and statistical model for evaporation of particles from excited residual nuclei. Energy and angular dependencies of data agree satisfactorily neither with predictions of microscopic intranuclear cascade calculations for protons, nor with coalescence calculations for other LCP. Phenomenological inclusion of another reaction mechanism - emission of LCP from a "fireball", i.e., fast and hot moving source - combined with the microscopic model calculations of INC, coalescence and evaporation of particles leads to very good description of the data. It was found that nonequilibrium processes are very important for production of LCP. They exhaust 40-80% of the total cross sections - depending on the emitted particles. Coalescence and "fireball" emission give comparable contributions to the cross sections with exception of 3He data where coalescence clearly dominates. The ratio of sum of all nonequilibrium processes to those proceeding through stage of statistical equilibrium does almost not change in the beam energy range from 1.2 GeV to 2.5 GeV for all light charged particles.

nucl-ex↗

arXiv2007

Non-equilibrium emission of complex fragments from p+Au collisions at 2.5 GeV proton beam energy

Energy and angular dependence of double differential cross sections d$^2σ$/d$Ω$dE was measured for reactions induced by 2.5 GeV protons on Au target with isotopic identification of light products (H, He, Li, Be, and B) and with elemental identification of heavier intermediate mass fragments (C, N, O, F, Ne, Na, Mg, and Al). It was found that two different reaction mechanisms give comparable contributions to the cross sections. The intranuclear cascade of nucleon-nucleon collisions followed by evaporation from an equilibrated residuum describes low energy part of the energy distributions whereas another reaction mechanism is responsible for high energy part of the spectra of composite particles. Phenomenological model description of the differential cross sections by isotropic emission from two moving sources led to a very good description of all measured data. Values of the extracted parameters of the emitting sources are compatible with the hypothesis claiming that the high energy particles emerge from pre-equilibrium processes consisting in a breakup of the target into three groups of nucleons; small, fast and hot fireball of $\sim$ 8 nucleons, and two larger, excited prefragments, which emits the light charged particles and intermediate mass fragments. The smaller of them contains $\sim$ 20 nucleons and moves with velocity larger than the CM velocity of the proton projectile and the target. The heavier prefragment behaves similarly as the heavy residuum of the intranuclear cascade of nucleon-nucleon collisions. %The mass and charge dependence of the total production cross %sections was extracted from the above analysis for all observed %reaction products. This dependence follows the power low behavior %(A$^{-τ}$ or Z$^{-τ}$).

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