arXiv subjects

Maksim Ulybyshev

Publications and source records attributed to Maksim Ulybyshev.

At least 19 recordsLinked to original sources

arXiv2026

Influence of interactions on the chiral effect in $1D$ Dirac semimetal

We consider the 1D Su-Schrieffer-Heeger (SSH) model. It was recently shown that, for the noninteracting model in its Dirac semimetal phase, the linear response of the axial charge density to an external electric field is proportional to the electrical conductivity in the presence of finite dissipation, with the proportionality factor determined by the coupling constants. This relation may be viewed as a manifestation of the chiral effect, which is a dimensional reduction of the 3D chiral magnetic effect. In the present work, we investigate the same model in the presence of two versions of local Hubbard-type interactions using numerical Quantum Monte Carlo simulations. We find, within the numerical resolution and for the parameters studied, that, even in the regime where sufficiently strong interactions drive the system into a Mott insulating phase, the proportionality between the induced axial charge density and the electrical conductivity remains unchanged. This result indicates that the chiral effect is not renormalized by local Hubbard interactions.

cond-mat.str-el↗

arXiv2026

Strain-Tuned Incommensurate Kekul\'e Spiral Order in Twisted Bilayer Graphene: a Quantum Many-Body Study

The physics of twisted bilayer graphene away from the exactly solvable chiral limit and the quantum Monte Carlo sign-problem-free charge neutrality point is elusive due to the exponential increase in the computational complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here we focus on the filling factor $\nu=\pm2$ and address the question of the strain dependence of the interacting ground state by approximate quantum Monte Carlo (AQMC), state-of-the-art exact diagonalization (ED) and Hartree-Fock (HF) mean field, in order to investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekul\'e spiral (IKS) state. While all three methods capture the KIVC order, only ED and HF detect the weaker IKS order that AQMC does not capture adequately. As the AQMC is still capable of capturing stronger orders like the KIVC, our combined protocol may open the door for further understanding of the rich phases of twisted bilayer graphene and other strongly-correlated systems.

cond-mat.str-el↗

arXiv2025

Plasmon excitations in half-filled graphene: A Comparative study between Quantum Monte Carlo and Random Phase Approximation

Transport properties of strongly correlated materials have contributions from quasiparticle excitations such as electrons and holes as well as emerging collective excitations such as plasmonic sound-like modes which are sustained by interactions. As was shown in Phys. Rev. B 106, 205127, the thermal excitation of the long-lived plasmons in graphene provides a substantial contribution to heat and momentum transport in the interaction-dominated regime. Detailed information on these excitations is therefore necessary for the quantitative understanding of hydrodynamic transport. On the other hand, dynamics of graphene plasmons is usually studied using Dirac perturbation theory, thus neglecting the effects of a finite Brillouin zone and higher-order perturbative corrections. Both these effects can be however significant for strong-interacting systems including free-standing graphene with the effective coupling constant of the order of alpha=2. In this paper, we studied the behavior of plasmons in half-filled free standing graphene using unbiased Quantum Monte Carlo calculations. We confirm the existence of well-defined resonance peaks for plasmons around the Gamma-point. Comparison with the Random-phase-approximation (RPA) calculation for the honeycomb lattice shows that RPA yields more stable plasmon modes, while QMC shows enhanced broadening due to non perturbative interaction effects. To account for this effect, we generalize the lattice RPA calculations by dressing the fermionic propagator by a constant lifetime. As a result, the plasmon frequencies are shifted towards higher energies and the spectrum is broadened, yielding a better agreement with QMC. Our findings highlight the need to account for both a finite Brillouin zone and strong interaction effects when developing theories of electronic transport in free-standing graphene.

cond-mat.mes-hall↗

arXiv2025

Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study

The fascinating quantum many-body states in twisted bilayber graphene (TBG) at magic angle, due to the interplay of Coulomb interactions and the quantum metrics of flat bands, have been well understood both experimentally and theoretically. However, the phase diagram and excitations as functions of twist angle and permittivity are still largely unknown. Here, via a newly developed momentum-space continuous-field quantum Monte Carlo method fully taking into account long-ranged Coulomb interactions and flat bands' quantum metrics with system sizes that were not accessible before, we show that charge-neutral TBG realizes an angle-tuned quantum phase transition from a gapped Kramers intervalley coherence (KIVC) state to a Dirac semimetal with critical angles around 1.2$°$. In single-particle spectra we demonstrate the evolution of a minimum gap at $Γ$ at the magic angle and towards touching points at Brillouin zone corners as the angle increases. The free energy and KIVC order parameter show that the transition belongs to fermionic Gross-Neveu criticality, and is robust upon varying the permittivity or the interlayer hopping.

cond-mat.str-el↗

arXiv2025

Hydrodynamics of particle-hole symmetric systems: a quantum Monte Carlo study

The emergence of hydrodynamic behavior in electronic flow within clean, particle-hole-symmetric systems at half-filling is a non-trivial problem. Navier-Stokes (NS) equations describe the momentum flow, while experimental measurements typically capture the current flow profiles. However, in particle-hole-symmetric systems, electric current and momentum flow are entirely decoupled because electrons and holes move in opposite directions with equal distribution functions. This makes it challenging to link NS equations to observed flow patterns. In this work, we demonstrate that the hydrodynamic behavior of the charge current at half filling can emerge despite the absence of momentum flow. By combining Boltzmann transport theory with numerically exact Quantum Monte Carlo simulations of clean graphene samples, we show that NS-type equations can be derived directly for the charge current, eliminating the need for any additional mechanism coupling the velocity field and charge current in explaining the experimentally observed hydrodynamic flow profiles in graphene at half-filling. We show that a new transport quantity - the current diffusion coefficient - replaces viscosity and expect this description to be valid for any particle-hole symmetric system. Our results provide new insights into the interpretation of experimental data and demonstrate how Quantum Monte Carlo calculations can serve as an alternative to experiments in transport measurements to verify the kinetic theory results.

cond-mat.mes-hall↗

arXiv2024

Beyond the instanton gas approach: dominant thimbles approximation for the Hubbard model

To each complex saddle point of an action, one can attach a Lefschetz thimble on which the imaginary part of the action is constant. Cauchy theorem states that summation over a set of thimbles produces the exact result. This reorganization of the path integral, is an appealing starting point for various approximations: In the realm of auxiliary quantum Monte Carlo methods it provides a framework to alleviate the negative sign problem. Here, we suggest to constrain the integration to the \textit{dominant} thimbles: the thimbles attached to the saddle points with the largest statistical weight. For the Hubbard model, in a formulation where the the Hubbard Stratonovitch field couples to the charge, this provides a \textit{symmetry} consistent approximation to the physics of the Hubbard model: constraining the integration domain does not explicitly break a symmetry. We can test this approach for the Hubbard model at half-filling on a bipartite lattice. The paper builds on the previously developed instanton gas approach, where an exhaustive saddle point approximation was constructed. We present results, showing that the dominant thimbles approximation provides results that are in remarkable agreement with the exact results for various fermionic observables including spin and charge order parameters and single electron spectral functions. We discuss implications of our results for simulations away of half filling.

cond-mat.str-el↗

arXiv2023

Flat band projections: Sign problem mapping for frustrated spin systems

Projection of the Coulomb potential onto flat bands paves the way to design various interactions in the particle-hole and particle-particle channels. Here we pose the question if we can use this mapping to overcome the negative sign problem for the simplest possible frustrated spin system consisting a trimer of spins-1/2 coupled with an antiferromagnetic exchange interaction. While the answer is negative, we show that we can map the sign problem for frustrated spin systems onto a problem where we need to simulate particle-hole symmetric systems but with long-ranged Coulomb interactions prevailing over short-ranged ones. While the latter systems are currently not accessible to auxiliary field determinant quantum Monte Carlo, this mapping motivates algorithmic development that may overcome this issue.

cond-mat.str-el↗

arXiv2023

Spectral functions of the honeycomb lattice with both the Hubbard and long-range Coulomb Interactions

The absence of screening of the non-local Coulomb interaction in Dirac systems at charge neutrality leads to the breakdown of the Fermi liquid and divergence of the Fermi velocity. On the other hand, Mott Hubbard physics and the concomitant formation of local moments is dominated by the local effective Hubbard interaction. Using quantum Monte Carlo methods combined with stochastic analytical continuation, we compute the single particle spectral function of fermions on the honeycomb lattice for a realistic interaction that includes both the Hubbard interaction and long-ranged Coulomb repulsion. To a first approximation, we find that the generic high-energy features such as the formation of the upper Hubbard band are independent of the long-ranged Coulomb repulsion and determined mostly by the local effective Hubbard interaction. The sub-leading effects of adding the long-range interaction include an enhancement of the bandwidth and a decrease of the spin-polaron quasi-particle weight and lifetime.

cond-mat.str-el↗

arXiv2023

Validity of SLAC fermions for the (1 + 1)-dimensional helical Luttinger liquid

The Nielson-Ninomiya theorem states that a chirally invariant free fermion lattice action, which is local, translation invariant, and real necessarily has fermion doubling. The SLAC approach gives up on locality and long range hopping leads to a linear dispersion with singularity at the zone boundary. We introduce a SLAC Hamiltonian formulation that is expected to realize a U(1) helical Luttinger liquid in a naive continuum limit. We argue that non-locality and concomitant singularity at the zone edge has important implications. Large momentum transfers yield spurious features already in the non-interacting case. Upon switching on interactions non-locality invalidates the Mermin-Wagner theorem and allows for long ranged magnetic ordering. In fact, in the strong coupling limit the model maps onto an XXZ-spin chain with $1/r^2$ exchange. Here, both spin-wave and DMRG calculations support long ranged order. While the long-ranged order opens a single particle gap the Dirac point, the singularity at the zone-boundary persists for any finite value of the interaction strength such that the ground state remains metallic. Hence, SLAC Hamiltonian does not flow to the $1$d helical Luttinger liquid fixed point. Aside from DMRG simulations, we have used auxiliary field quantum Monte Carlo simulations to arrive to the above conclusions.

cond-mat.str-el↗

arXiv2022

Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements

We propose a method to mitigate heavy-tailed distributions in fermion Quantum Monte Carlo simulations originating from zeros of the fermion determinant. In this case the second moment of the observables might be not well defined, and we show that by merely changing the synchronization between local updates and computation of observables, one can reduce the prefactor of the heavy-tailed distribution, thus substantially suppressing statistical fluctuations of observables. We also show that the average, or the first moment, is well defined and hence is independent on our measuring scheme. The method is especially suitable for local observables similar to e.g. double occupancy, where the resulting speedup can reach two orders of magnitude. For observables, containing spatial correlators, the speedup is more moderate, but still ranges between five and ten. Our results are independent on the nature of the auxiliary field, discrete or continuous, and pave the way to improve measurement strategies for Hybrid Monte Carlo simulations.

cond-mat.str-el↗

arXiv2022

Instanton gas approach to the Hubbard model

In this article we consider a path integral formulation of the Hubbard model based on a SU(2)-symmetrical Hubbard-Stratonovich transformation that couples auxiliary field to the local electronic density. This decoupling is known to have a regular saddle-point structure: each saddle point is a set of elementary field configurations localized in space and imaginary time which we coin instantons. We formulate a classical partition function for the instanton gas that has predictive power. Namely, we can predict the distribution of instantons and show that the instanton number is sharply defined in the thermodynamic limit, thus defining a unique dominant saddle point. Despite the fact that the instanton approach does not capture the magnetic transition inherent to the Hubbard model on the honeycomb lattice, we were able to describe the local moment formation accompanied by short-ranged anti-ferromagnetic correlations. This aspect is also seen in the single particle spectral function that shows clear signs of the upper and lower Hubbard bands. Our instanton approach bears remarkable similarities to local dynamical approaches, such as dynamical mean field theory, in the sense that it has the unique property of allowing for local moment formation without breaking the SU(2) spin symmetry. In contrast to local approaches, it captures short-ranged magnetic fluctuations. Furthermore, it also offers possibilities for systematic improvements by taking into account fluctuations around the dominant saddle point. Finally, we show that the saddle point structure depends upon the choice of lattice geometry. For the square lattice at half-filling, the saddle point structure reflects the itinerant to localized nature of the magnetism as a function of the coupling strength. The implications of our results for Lefschetz thimbles approaches to alleviate the sign problem are also discussed.

cond-mat.str-el↗

arXiv2021

Bridging the gap between numerics and experiment in free standing graphene

We report results of large-scale quantum Monte Carlo (QMC) simulations of graphene. Using cutting-edge algorithmic improvements, we are able to consider spatial volumes, corresponding to 20808 electrons, that allow us to access energy scales of direct relevance to experiments. Using constrained random phase approximation (cRPA) estimates of short-ranged interactions combined with a Coulomb tail, we are able to successfully confront numerical and experimental estimates of the Fermi velocity renormalization. These results and their comparison with perturbation theory not only show the non-Fermi liquid character of graphene, but also prove the importance of lattice-scale physics and higher-order perturbative corrections beyond RPA for the quantitative description of the experimental data for the Fermi velocity renormalization in suspended graphene.

cond-mat.str-el↗

arXiv2021

Quantum phase transitions on the hexagonal lattice

Hubbard-type models on the hexagonal lattice are of great interest, as they provide realistic descriptions of graphene and other related materials. Hybrid Monte Carlo simulations offer a first-principles approach to study their phase structure. Here, we review the present status of our work in this direction.

cond-mat.str-el↗

arXiv2020

Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice

We propose a framework to study the properties of the Lefschetz thimbles decomposition for lattice fermion models approaching the thermodynamic limit. The proposed set of algorithms includes the Schur complement solver and the exact computation of the derivatives of the fermion determinant. It allows us to solve the gradient flow (GF) equations taking into account the fermion determinant exactly, with high performance. We can find both real and complex saddle points and describe the structure of the Lefschetz thimbles decomposition for large enough lattices to extrapolate the results to the thermodynamic limit. The algorithms are described for a general lattice fermion model, with emphasis on two types of lattice discretizations for relativistic fermions (staggered and Wilson), as well as on interacting tight-binding models for condensed matter systems. We apply these algorithms to the Hubbard model on a hexagonal lattice, dealing with lattice volumes as large as 12x12 with 256 steps in Euclidean time, in order to capture the properties of the thimbles decomposition as the thermodynamic, low-temperature, and continuum limits are approached. The complexity of the thimbles decomposition appears to be dependent on the form of the Hubbard-Stratonovich (HS) transformation. In particular, the evidence is provided for the existence of an optimal regime for the hexagonal lattice Hubbard model, with a reduced number of thimbles being important in the overall sum. We have performed quantum Monte Carlo (QMC) simulations using GF to deform the integration contour into the complex plane and demonstrated the agreement with exact diagonalization on small volumes (8 sites in space) if optimal setup for HS transformation is used. The residual sign problem is compared with the state-of-the-art BSS-QMC. We show that the average sign can be kept substantially higher using the Lefschetz thimbles approach.

cond-mat.str-el↗

arXiv2019

Taming the sign problem of the finite density Hubbard model via Lefschetz thimbles

We study the sign problem in the Hubbard model on the hexagonal lattice away from half-filling using the Lefschetz thimbles method. We identify the saddle points, reduce their amount, and perform quantum Monte Carlo (QMC) simulations using the holomorphic gradient flow to deform the integration contour in complex space. Finally, the results are compared against exact diagonalization (ED). We show that the sign problem can be substantially weakened, even in the regime with low temperature and large chemical potential, where standard QMC techniques exhibit an exponential decay of the average sign.

cond-mat.str-el↗

arXiv2019

Numerical evidence of conformal phase transition in graphene with long-range interactions

Using state of the art Hybrid-Monte-Carlo (HMC) simulations we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement.

cond-mat.str-el↗

arXiv2018

Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice

Using first-principle Hybrid-Monte-Carlo (HMC) simulations, we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in the extended Hubbard model on the two dimensional hexagonal lattice at half filling. We determine the phase diagram in the space of on-site and nearest-neighbor couplings $U$ and $V$ in the region $V<U/3$, which can be simulated without a fermion sign problem, and find that a transition from semimetal to a SDW phase occurs at sufficiently large $U$ for basically all $V$. Tracing the corresponding phase boundary from $V=0$ to the $V=U/3$ line, we find evidence for critical scaling in the Gross-Neveu universality class for the entire boundary. With rather high confidence we rule out the existence of the CDW ordered phase anywhere in the range of parameters considered. We also discuss several improvements of the HMC algorithm which are crucial to reach these conclusions, in particular the improved fermion action with exact sublattice symmetry and the complexification of the Hubbard-Stratonovich field to ensure the ergodicity of the algorithm.

cond-mat.str-el↗

arXiv2018

Numerical analytic continuation of Euclidean data

In this work we present a direct comparison of three different numerical analytic continuation methods: the Maximum Entropy Method, the Backus-Gilbert method and the Schlessinger point or Resonances Via Padé method. First, we perform a benchmark test based on a model spectral function and study the regime of applicability of these methods depending on the number of input points and their statistical error. We then apply these methods to more realistic examples, namely to numerical data on Euclidean propagators obtained from a Functional Renormalization Group calculation, to data from a lattice Quantum Chromodynamics simulation and to data obtained from a tight-binding model for graphene in order to extract the electrical conductivity.

hep-ph↗