arXiv subjects

A. N. Rubtsov

Publications and source records attributed to A. N. Rubtsov.

At least 19 recordsLinked to original sources

arXiv2026

Pseudogap formation in the moderate correlated layered attractive Hubbard model

We consider the layered attractive Hubbard model with a moderate interaction strength at quarter filling. The Green's function, self-energy, and density of states are calculated for relatively large clusters using the fluctuating local field method within the approximation of vanishing effective interaction. The emergence of a pseudogap is demonstrated for the cluster system, and it is shown that integration over the fluctuating field is equivalent to the summation of zero-mode ladder diagrams above critical temperature. For the large layered system, a pseudogap in the density of states is obtained within a cluster scheme that treats the coupling between layers as a static $U(1)$ symmetry-breaking field.

cond-mat.str-el↗

arXiv2026

Localization pattern of a mobile impurity in the disordered Kitaev chain

We study a mobile impurity coupled to a Kitaev chain with chemical-potential disorder and ask whether the impurity behavior distinguishes different regimes of the host system. Exact diagonalization calculations for small periodic chains shows that in the deep topological regime the impurity localizes only partially, with a smooth increase of $\mathrm{IPR}_d$, whereas in the deep trivial regime it undergoes a much sharp transition to nearly single-site localization. For open chains at strong interaction, DMRG shows edge-localized impurity density near the Kitaev sweet spot. With increasing chemical potential, the impurity weight spreads into the bulk and eventually becomes almost uniform. We explain the edge preference analytically from the Majorana-dimer structure: a bulk impurity rearranges two neighboring dimers, while an edge impurity affects only one. Disorder competes with this clean edge bias and can pin the impurity in the bulk. Thus, the impurity is sensitive to the regime of the host system, although we do not find a strict one-to-one correspondence between the impurity localization pattern and the host topology. Instead, the disorder-averaged behavior suggests only an indirect correlation between impurity localization and the underlying phase of the chain.

cond-mat.str-el↗

arXiv2026

Quantized Collective Fluctuations in Correlated Fermion Systems

Collective excitations in fermionic systems play a crucial role in determining their physical properties. An important challenge is to develop efficient theoretical approaches for describing these excitations and their coupling to fermionic degrees of freedom. In this work, we revisit the problem of quantifying the contributions of individual bosonic modes of collective fluctuations to observable properties of correlated fermion systems within the framework of the Fluctuating Local Field (FLF) method. Whereas the auxiliary field in this method was previously considered only classically, we formulate its systematic extension termed Quantum FLF (Q-FLF) that incorporates selected bosonic Matsubara modes, thus tailoring it to description of quantum collective fluctuations. As a testbed, we apply the approach to a half-filled one-dimensional Hubbard chain and compute the Green's function, the total energy, and the antiferromagnetic susceptibility. Our results demonstrate that the proposed scheme enables an efficient and selective characterization of the contributions of individual bosonic modes. In particular, low Matsubara frequencies are found to have a quantitative impact on integrated observables such as total energy and antiferromagnetic susceptibility. At the same time, an accurate description of single-particle properties requires inclusion of higher-frequency bosonic modes.

cond-mat.str-el↗

arXiv2026

A Unified Approach to Strong Local Correlations and Collective Fluctuations: Eliminating Divergence in the Spin Channel

Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose a novel extended approach, which we term fluctuating dynamical mean-field theory (fDMFT). It incorporates collective fluctuations of auxiliary impurity models across different sites via functional integration. Technically, this method involves obtaining a family of DMFT solutions on a grid for a self-consistent auxiliary classical field applied to the lattice. While the result can, in principle, be improved diagrammatically, we find that the minimal version of the theory already yields accurate results, with lowest-order diagrammatic corrections offering only minor improvements. This consistent framework, based on our fluctuating local field concept, demonstrates superior performance for the nearly half-filled Hubbard model compared to other known diagrammatic extensions of DMFT.

cond-mat.str-el↗

arXiv2025

Time-dependent fluctuating local field approach for description of the correlated fermions dynamics

We formulate a time-dependent Fluctuating Local Field (TD-FLF) method for correlated fermion dynamics, extending the stationary FLF approach. The wavefunction is approximated as an ensemble of non-interacting states subject to a classical fluctuating field, with dynamics encoded in the field's time-dependent distribution. This reduces the time-dependent Schr\"odinger equation to a generalized eigenvalue problem in a significantly reduced basis. Applied to half-filled 2D Hubbard lattices, TD-FLF yields highly accurate results, outperforming mean-field theory and capturing oscillation frequencies and amplitudes in good agreement with exact diagonalization. Its low computational cost and flexibility make TD-FLF a promising tool for simulating driven correlated systems.

cond-mat.str-el↗

arXiv2025

A Mobile Impurity in the Kitaev Chain: Phase Diagram and Signatures of Topology

We study the physics of a mobile impurity immersed in a $1d$ topological superconductor. We discuss the system's phase diagram obtained with exact diagonalization. We argue that the character of the transition from a weak to strong coupling regime depends on the phase of the host superconductor. A smooth crossover between a weakly coupled polaron and a molecular state is observed in the topological phase. In contrast, the impurity undergoes a sharp phase transition in a topologically trivial background.

cond-mat.str-el↗

arXiv2024

Fluctuating field series: towards calculations of correlated systems with high accuracy

We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for medium-sized lattices. It can be also used as a solver for the cluster approximations for infinite-size lattices. We introduce classical fluctuating field coupled to fermionic collective mode(s). This way, fluctuations in selected modes are treated in a non-perturbative way. Other degrees of freedom are accounted for the diagram expansion performed at each value of the fluctuating field. The method is benchmarked for the $U/t=1$ and $U/t=2$ Hubbard lattices at half-filling. Results for susceptibility in the antiferromagnetic channel along with the single particle density of states are compared with the numerically exact quantum Monte Carlo data. Calculations up to the third order of the series expansion are performed and show a uniform convergence to the reference result for the susceptibility. This convergence is observed well below the DMFT Neél temperature and makes our practically simple method applicable in a much wider temperature range than DMFT-based diagrammatic schemes.

cond-mat.str-el↗

arXiv2024

Sample space filling analysis for boson sampling validation

Achieving a quantum computational advantage regime, and thus providing evidence against the extended Church-Turing thesis, remains one of the key challenges of modern science. Boson sampling seems to be a very promising platform in this regard, but to be confident of attaining the advantage regime, one must provide evidence of operating with a correct boson sampling distribution, rather than with a pathological classically simulatable one. This problem is often called the validation problem, and it poses a major challenge to demonstrating unambiguous quantum advantage. In this work, using the recently proposed wave function network approach, we study the sample space filling behavior with increasing the number of collected samples. We show that due to the intrinsic nature of the boson sampling wave function, its filling behavior can be computationally efficiently distinguished from classically simulated cases. Therefore, we propose a new validation protocol based on the sample space filling analysis and test it for problems of up to $20$ photons injected into a $400$-mode interferometer. Due to its simplicity and computational efficiency, it can be used among other protocols to validate future experiments to provide more convincing results.

quant-ph↗

arXiv2024

Classical modelling of a lossy Gaussian bosonic sampler

Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion, and increasing the number of terms of the expansion that are used in the calculation yields greater accuracy. The complexity of the algorithm is polynomial in the number of modes given the number of terms is fixed. We describe conditions for the input state squeezing parameter and loss level that provide the best efficiency for this algorithm (by efficient we mean that the Taylor series converges quickly). In recent experiments that claim to have demonstrated quantum advantage, these conditions are satisfied; thus, this algorithm can be used to classically simulate these experiments.

quant-ph↗

arXiv2023

Landau Free Energy of small clusters beyond mean field approach

The Landau Free Energy determines the landscape of order parameter fluctuations that occur in a physical system at thermal equilibrium and, in particular, characterizes the critical phenomena. We propose a semi-analytical approach based on the Fluctuating Local Field method, which allows to estimate Landau Free Energy for small clusters with discrete (Ising model) and continuous (Heisenberg model) order parameter.

cond-mat.stat-mech↗

arXiv2023

Locality of topological dynamics in Chern insulators

A system having macroscopic patches in different topological phases have no well-defined global topological invariant. To treat such a case, the quantities labeling different areas of the sample according to their topological state are used, dubbed local topological markers. Here we study their dynamics. We concentrate on two quantities, namely local Chern marker and on-site charge induced by an applied magnetic field. We demonstrate that the time-dependent local Chern marker is much more non-local object than equilibrium one. Surprisingly, in large samples driven out of equilibrium, it leads to a simple description of the local Chern marker's dynamics by a local continuity equation. Also, we argue that the connection between the local Chern marker and magnetic-field induced charge known in static holds out of equilibrium in some experimentally relevant systems as well. This gives a clear physical description of the marker's evolution and provides a simple recipe for experimental estimation of the topological marker's value.

cond-mat.mes-hall↗

arXiv2023

Dynamical Quantum Phase Transition Without An Order Parameter

Short-time dynamics of many-body systems may exhibit non-analytical behavior of the systems' properties at particular times, thus dubbed dynamical quantum phase transition. Simulations showed that in the presence of disorder new critical times appear in the quench evolution of the Ising model. We study the physics behind these new critical times. We discuss the spectral features of the Ising model responsible for the disorder-induced phase transitions. We found the critical value of the disorder sufficient to induce the dynamical phase transition as a function of the number of spins. Most importantly, we argue that this dynamical phase transition while non-topological lacks a local order parameter.

cond-mat.stat-mech↗

arXiv2022

Classical modelling of a bosonic sampler with photon collisions

When the problem of boson sampling was first proposed, it was assumed that little or no photon collisions occur. However, modern experimental realizations rely on setups where collisions are quite common, i.e. the number of photons $M$ injected into the circuit is close to the number of detectors $N$. Here we present a classical algorithm that simulates a bosonic sampler: it calculates the probability of a given photon distribution at the interferometer outputs for a given distribution at the inputs. This algorithm is most effective in cases with multiple photon collisions, and in those cases it outperforms known algorithms.

quant-ph↗

arXiv2022

Cracking the Quantum Advantage threshold for Gaussian Boson Sampling

Scientists in quantum technology aspire to quantum advantage: a computational result unattainable with classical computers. Gaussian boson sampling experiment has been already claimed to achieve this goal. In this setup squeezed light states interfere in a mid-sized linear optical network, where multi-photon collisions take place. The exact simulation of the counting statistics of $n$ threshold detectors is far beyond the possibilities of modern supercomputers once $n$ exceeds $100$. Here we challenge quantum advantage for a mid-sized Gaussian boson sampling setup and propose the approximate algorithm to obtain the probability of any specific measurement outcome. For an 70-mode device on a laptop, our approximation achieves accuracy competitive with the experimental one.

quant-ph↗

arXiv2021

Quantum Monte Carlo simulation of BEC-impurity tunneling

Polaron tunneling is a prominent example of a problem characterized by different energy scales, for which the standard quantum Monte Carlo methods face a slowdown problem. We propose a new quantum-tunneling Monte Carlo (QTMC) method which is free from this issue and can be used for a wide range of tunneling phenomena. We apply it to study an impurity interacting with a one-dimensional Bose-Einstein condensate and simultaneously trapped in an external double-well potential. Our scheme works for an arbitrary coupling between the particle and condensate and, at the same time, allows for an account of tunneling effects. We discover two distinct quasi-particle peaks associated, respectively, with the phonon-assisted tunneling and the self-trapping of the impurity, which are in a crossover regime for the system modeled. We observe and analyze changes in the weights and spectral positions of the peaks (or, equally, effective masses of the quasi-particles) when the coupling strength is increased. Possible experimental realizations using cold atoms are discussed.

cond-mat.quant-gas↗

arXiv2021

Effectively Trainable Semi-Quantum Restricted Boltzmann Machine

We propose a novel quantum model for the restricted Boltzmann machine (RBM), in which the visible units remain classical whereas the hidden units are quantized as noninteracting fermions. The free motion of the fermions is parametrically coupled to the classical signal of the visible units. This model possesses a quantum behaviour such as coherences between the hidden units. Numerical experiments show that this fact makes it more powerful than the classical RBM with the same number of hidden units. At the same time, a significant advantage of the proposed model over the other approaches to the Quantum Boltzmann Machine (QBM) is that it is exactly solvable and efficiently trainable on a classical computer: there is a closed expression for the log-likelihood gradient with respect to its parameters. This fact makes it interesting not only as a model of a hypothetical quantum simulator, but also as a quantum-inspired classical machine-learning algorithm.

cond-mat.dis-nn↗

arXiv2019

Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution

We present a new method to treat the two-dimensional (2D) Hubbard model for parameter regimes which are relevant for the physics of the high-$T_c$ superconducting cuprates. Unlike previous attempts to attack this problem, our new approach takes into account all fluctuations in different channels on equal footing and is able to treat reasonable large lattice sizes up to 32x32. This is achieved by the following three-step procedure: (i) We transform the original problem to a new representation (dual fermions) in which all purely local correlation effects from the dynamical mean field theory are already considered in the bare propagator and bare interaction of the new problem. (ii) The strong $1/(iν)^2$ decay of the bare propagator allows us to integrate out all higher Matsubara frequencies besides the lowest using low order diagrams. The new effective action depends only on the two lowest Matsubara frequencies which allows us to, (iii) apply the two-particle self-consistent parquet formalism, which takes into account the competition between different low-energy bosonic modes in an unbiased way, on much finer momentum grids than usual. In this way, we were able to map out the phase diagram of the 2D Hubbard model as a function of temperature and doping. Consistently with the experimental evidence for hole-doped cuprates and previous dynamical cluster approximation calculations, we find an antiferromagnetic region at low-doping and a superconducting dome at higher doping. Our results also support the role of the van Hove singularity as an important ingredient for the high value of $T_c$ at optimal doping. At small doping, the destruction of antiferromagnetism is accompanied by an increase of charge fluctuations supporting the scenario of a phase separated state driven by quantum critical fluctuations.

cond-mat.str-el↗

arXiv2019

Dual Boson approach with instantaneous interaction

The Dual Boson approach to strongly correlated systems generally involves a dynamic (frequency-dependent) interaction in the auxiliary impurity model. In this work, we explore the consequences of forcing this interaction to be instantaneous (frequency-independent) via the use of a self-consistency condition on the instantaneous susceptibility. The result is a substantial simplification of the impurity model, especially with an eye on realistic multiband implementations, while keeping desireable properties of the Dual Boson approach, such as the charge conservation law, intact. We show and illustrate numerically that this condition enforces the absence of phase transitions in finite systems, as should be expected from general physical considerations, and respects the Mermin-Wagner theorem. In particular, the theory does not allow the metal to insulator phase transition associated with the formation of the magnetic order in the two-dimensional system. At the same time, the metal to charge ordered phase transition is allowed, as it is not associated with the spontaneous breaking of a continuous symmetry, and is accurately captured by the introduced approach.

cond-mat.str-el↗