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Evgeny Kozik

Publications and source records attributed to Evgeny Kozik.

At least 37 records · Page 2Linked to original sources
arXiv2019

Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime

We develop a numerically exact method for the summation of irreducible Feynman diagrams for fermionic self-energy in the thermodynamic limit. The technique, based on the Diagrammatic Determinant Monte Carlo and its recent extension to connected diagrams, allows us to reach high ($\sim 10$) orders of the weak-coupling expansion for the self-energy of the two-dimensional Hubbard model. Access to high orders reveals a non-trivial analytic structure of the self-energy and enables its controlled reconstruction with arbitrary momentum resolution in the nonperturbative regime of essentially strong correlations, which has recently been reached with ultracold atoms in optical lattices.

cond-mat.str-el↗
arXiv2017

Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model

The repulsive Fermi Hubbard model on the square lattice has a rich phase diagram near half-filling (corresponding to the particle density per lattice site $n=1$): for $n=1$ the ground state is an antiferromagnetic insulator, at $0.6 < n \lesssim 0.8$, it is a $d_{x^2-y^2}$-wave superfluid (at least for moderately strong interactions $U \lesssim 4t$ in terms of the hopping $t$), and the region $1-n \ll 1$ is most likely subject to phase separation. Much of this physics is preempted at finite temperatures and to an extent driven by strong magnetic fluctuations, their quantitative characteristics and how they change with the doping level being much less understood. Experiments on ultra-cold atoms have recently gained access to this interesting fluctuation regime, which is now under extensive investigation. In this work we employ a self-consistent skeleton diagrammatic approach to quantify the characteristic temperature scale $T_{M}(n)$ for the onset of magnetic fluctuations with a large correlation length and identify their nature. Our results suggest that the strongest fluctuations---and hence highest $T_{M}$ and easiest experimental access to this regime---are observed at $U/t \approx 4-6$.

cond-mat.str-el↗
arXiv2017

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique

The dual-fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work we compute the dual-fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact Diagrammatic Determinant Monte Carlo simulations to systematically assess convergence of the dual-fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual-fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered ($4 \leq U/t \leq 12$), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find however that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

cond-mat.str-el↗
arXiv2016

Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model

We introduce a method for summing Feynman's perturbation series based on diagrammatic Monte Carlo that significantly improves its convergence properties. This allows us to investigate in a controllable manner the pseudogap regime of the Hubbard model and to study the nodal/antinodal dichotomy at low doping and intermediate coupling. Marked differences from the weak coupling scenario are manifest, such as a higher degree of incoherence at the antinodes than at the `hot spots'. Our results show that the pseudogap and reduction of quasiparticle coherence at the antinode is due to antiferromagnetic spin correlations centered around the commensurate $(π,π)$ wavevector. In contrast, the dominant source of scattering at the node is associated with incommensurate momentum transfer. Umklapp scattering is found to play a key role in the nodal/antinodal dichotomy.

cond-mat.str-el↗
arXiv2016

Fulde-Ferrell-Larkin-Ovchinnikov pairing as leading instability on the square lattice

We study attractively interacting spin-1/2 fermions on the square lattice subject to a spin population imbalance. Using unbiased diagrammatic Monte Carlo simulations we find an extended region in the parameter space where the Fermi liquid is unstable towards formation of Cooper pairs with non-zero center-of-mass momentum, known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In contrast to earlier mean-field and quasi-classical studies we provide quantitative and well-controlled predictions on the existence and location of the relevant Fermi-liquid instabilities. The highest temperature where the FFLO instability can be observed is about half of the superfluid transition temperature in the unpolarized system.

cond-mat.supr-con↗
arXiv2015

Ground state phase diagram of the repulsive fermionic $t-t^{\prime}$ Hubbard model on the square lattice from weak-coupling

We obtain a complete and exact in the weak-coupling limit ($U \rightarrow 0$) ground state phase diagram of the repulsive fermionic Hubbard model on the square lattice for filling factors $0 < n < 2$ and next-nearest-neighbour hopping amplitudes $0 \le t^{\prime} \le 0.5$. Phases are distinguished by the symmetry and the number of nodes of the superfluid order parameter. The phase diagram is richer than may be expected and typically features states with a high --- higher than that of the fundamental mode of the corresponding irreducible representation --- number of nodes. The effective coupling strength in the Cooper channel $λ$, which determines the critical temperature $T_c$ of the superfluid transition, is calculated in the whole parameter space and regions with high values of $λ$ are identified. It is shown that besides the expected increase of $λ$ near the Van Hove singularity line, joining the ferromagnetic and antiferromagnetic points, another region with high values of $λ$ can be found at quarter filling and $t^{\prime}=0.5$ due to the presence of a line of nesting at $t^{\prime} \ge 0.5$. The results can serve as benchmarks for controlled non-perturbative methods and guide the ongoing search for high-$T_c$ superconductivity in the Hubbard model.

cond-mat.str-el↗
arXiv2015

Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram

A significant part of the phase diagram of the two-dimensional fermionic Hubbard model for moderate interactions and filling factors ($U < 4, \, n<0.7$) is governed by effective Fermi liquid physics with weak BCS-type instabilities. We access this regime in a controlled way by a combination of the bold-line diagrammatic Monte Carlo method with an additional ladder-diagram summation trick and semi-analytic treatment of the weak instability in the Cooper channel. We obtain the corresponding ground-state phase diagram in the $(n,U)$ plane describing the competition between the $p-$ and $d-$wave superfluid states. We also claim the values of the dimensionless BCS coupling constants controlling the superfluid $T_c$ at the phase boundaries, which prove to be very small up to $U=4, n = 0.6$.

cond-mat.str-el↗
arXiv2015

Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models

The Luttinger-Ward functional $Φ[\mathbf{G}]$, which expresses the thermodynamic grand potential in terms of the interacting single-particle Green's function $\mathbf{G}$, is found to be ill-defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy $\mathbfΣ[\mathbf{G}] \propto δΦ[\mathbf{G}]/δ\mathbf{G}$ is not a single-valued functional of $\mathbf{G}$: in addition to the physical solution for $\mathbfΣ[\mathbf{G}]$, there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubbard atom, the Anderson impurity model, and the full two-dimensional Hubbard model. Despite this pathology, the skeleton Feynman diagrammatic series for $\mathbfΣ$ in terms of $\mathbf{G}$ is found to converge at least for moderately low temperatures. However, at strong interactions, its convergence is to the unphysical branch. This reveals a new scenario of breaking down of diagrammatic expansions. In contrast, the bare series in terms of the non-interacting Green's function $\mathbf{G}_0$ converges to the correct physical branch of $\mathbfΣ$ in all cases currently accessible by diagrammatic Monte Carlo. Besides their conceptual importance, these observations have important implications for techniques based on the explicit summation of diagrammatic series.

cond-mat.str-el↗
arXiv2015

p-wave Superfluidity by Spin-Nematic Fermi Surface Deformation

We study attractively interacting fermions on a square lattice with dispersion relations exhibiting strong spin-dependent anisotropy. The resulting Fermi surface mismatch suppresses the s-wave BCS-type instability, clearing the way for unconventional types of order. Unbiased sampling of the Feynman diagrammatic series using Diagrammatic Monte Carlo methods reveals a rich phase diagram in the regime of intermediate coupling strength. Instead of a proposed Cooper-pair Bose metal phase [A. E. Feiguin and M. P. A. Fisher, Phys. Rev. Lett. 103, 025303 (2009)] we find an incommensurate density wave at strong anisotropy and two different p-wave superfluid states with unconventional symmetry at intermediate anisotropy.

cond-mat.quant-gas↗
arXiv2010

Vortex-Phonon Interaction in the Kosterlitz-Thouless Theory

The "canonical" variables of the Kosterlitz-Thouless theory--fields $Φ_0({\bf r})$ and $ϕ({\bf r})$, generally believed to stand for vortices and phonons (or their XY equivalents, like spin waves, etc.) turn out to be neither vortices and phonons, nor, strictly speaking, {\it canonical} variables. The latter fact explains paradoxes of (i) absence of interaction between $Φ_0$ and $ϕ$, and (ii) non-physical contribution of small vortex pairs to long-range phase correlations. We resolve the paradoxes by explicitly relating $Φ_0$ and $ϕ$ to canonical vortex-pair and phonon variables.

cond-mat.stat-mech↗
arXiv2010

Comment on "Symmetries and Interaction Coefficients of Kelvin waves" [arXiv:1005.4575] by Lebedev and L'vov

We comment on the claim by Lebedev and L'vov [arXiv:1005.4575] that the symmetry with respect to a tilt of a quantized vortex line does not yet prohibit coupling between Kelvin waves and the large-scale slope of the line. Ironically, the counterexample of an effective scattering vertex in the local induction approximation (LIA) attempted by Lebedev and L'vov invalidates their logic all by itself being a notoriously known example of how symmetries impose stringent constraints on kelvon kinetics---not only the coupling in question but the kinetics in general are absent within LIA. We further explain that the mistake arises from confusing symmetry properties of a specific mathematical representation in terms of the canonical vortex position field w(z) = x(z) + iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of the z-axis, with those of the real physical system recovered in final expressions.

cond-mat.other↗
arXiv2010

Geometric Symmetries in Superfluid Vortex Dynamics

Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, $w(z)=x(z)+iy(z)$, describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which---apart from their rather specific expressions in terms of $w(z)$---are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines---the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wavenumber space. Similar considerations apply to other systems with purely geometric degrees of freedom.

cond-mat.other↗
arXiv2010

The 17/5 spectrum of the Kelvin-wave cascade

Direct numeric simulation of the Biot-Savart equation readily resolves the 17/5 spectrum of the Kelvin-wave cascade from the 11/3 spectrum of the non-local (in the wavenumber space) cascade scenario by L'vov and Nazarenko. This result is a clear-cut visualisation of the unphysical nature of the 11/3 solution, which was established earlier on the grounds of symmetry.

cond-mat.other↗
arXiv2010

Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77kB which is about twice as large as the entropy at the Neel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy.

cond-mat.quant-gas↗
arXiv2008

Critical Temperature Curve in the BEC-BCS Crossover

The strongly-correlated regime of the BCS-BEC crossover can be realized by diluting a system of two-component fermions with a short-range attractive interaction. We investigate this system via a novel continuous-space-time diagrammatic determinant Monte Carlo method and determine the universal curve $T_c/ε_F$ for the transition temperature between the normal and the superfluid states as a function of the scattering length with the maximum on the BEC side. At unitarity, we confirm that $T_c/ε_F = 0.152(7)$.

cond-mat.str-el↗
arXiv2008

Scanning Superfluid-Turbulence Cascade by Its Low-Temperature Cutoff

On the basis of recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, $L$, controlled by the frictional coefficient, $α(T) \ll 1$, responsible for the cutoff. The curve $\ln L(\ln α)$ is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wavenumber regions. Excellent agreement with recent experiment by Walmsley {\it et al.} [arXiv:0710.1033]--in which $L(T)$ has been measured down to $T \sim 0.08 $K--implies that the scenario of low-temperature superfluid turbulence is now experimentally validated, and allows to quantify the Kelvin-wave cascade spectrum.

cond-mat.other↗
arXiv2008

Diagrammatic Monte Carlo

Diagrammatic Monte Carlo (DiagMC) is a numeric technique that allows one to calculate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is typically fatal to Monte Carlo approaches, appears to be manageable with DiagMC. Starting with a general introduction to the principles of DiagMC, we present a detailed description of the DiagMC scheme for interacting fermions (Hubbard model), as well as the first illustrative results for the equations of state.

cond-mat.stat-mech↗