arXiv subjects

Jakša Vučičević

Publications and source records attributed to Jakša Vučičević.

8 recordsLinked to original sources

arXiv2026

Hubbard vs. Emery model: spectra, transport and relevance for cuprates

Understanding the transport properties of cuprate superconductors is one of the central challenges in the physics of strongly correlated electrons. The most common approach is to define and solve a low-energy lattice model, but it is still unclear what the minimal model is to capture all relevant mechanisms and provide quantitative predictions. The main uncertainty concerns the choice of the orbital degrees of freedom to be included in the model, as well as the definition of the effective coupling. In this paper, we study the two most commonly considered models, namely the single-orbital Hubbard model and the three-orbital Emery model. We investigate and compare their spectral and transport properties, and find that the two models present a similar, but not the same, physical picture. We identify several strong quantitative differences which might allow one to discriminate between the two models by comparing theory with experiments. We compare our results for several physical quantities with 7 different experiments on 3 different La$_2$CuO$_4$-based cuprates, and in general find excellent agreement. The dc resistivity and the effective mass results suggest that the coupling constant in the effective Hubbard model is larger than expected. We find several more properties that are sensitive to the precise value of the coupling constant, including the critical doping for the Lifshitz transition, and the local spectral weight in the vicinity of the Fermi level; the latter provides a promising way to estimate the effective coupling constant in future photoemission experiments.

cond-mat.str-el↗

arXiv2026

Importance of effective Coulomb interactions for $T_c$ in cuprates

Cuprate superconductors exhibit the highest observed superconducting $T_c$ at atmospheric pressure. However, the magnitude of $T_c$ varies significantly between different cuprates. At present, it is unclear what properties of the crystal structure affect $T_c$ most strongly, yet such an understanding must underpin any efforts toward high-$T_c$ materials design. To address this issue, we perform a large scale systematic study, employing a combination of data collection, state-of-the-art numerical methods, and statistical analysis. We identify about 40 different cuprate compounds, and we compile detailed data about their $T_c$'s and crystal structures from literature and the available databases. Using a fully automated procedure, for each compound we compute the DFT bandstructure and downfold it to two of the most commonly studied low-energy lattice models, namely the single-band Hubbard and the three-band Emery models. The downfolding is based on the approach of MLWFs and cRPA. Finally, we apply a thorough and unbiased statistical analysis to investigate the correlations between the experimentally measured $T_c$'s and the computed parameters of our theoretical models. Our data indicates that more sophisticated models might be needed to describe all cuprates on the same footing. Nevertheless, we find that $T_c$ scales well with simple functions of model parameters. We confirm a previously observed trend that $t'$ in the single-band model correlates with the experimental $T_c$, and we find that $T_c$ appears to vanish below a finite value of $t'$, in agreement with recent ground-state calculations for the Hubbard model. However, we find that the coupling strength also plays a role: throughout our entire dataset, $T_c$ correlates the most with the Coulomb coupling on the $p$-orbitals in the 3-band model, highlighting the importance of the oxygen sites in the copper-oxide planes.

cond-mat.str-el↗

arXiv2026

H-NESSi: The Hierarchical Non-Equilibrium Systems Simulation package

We present H-NESSi (The Hierarchical Non-Equilibrium Systems Simulation package), an open-source software package for solving the Kadanoff-Baym equations (KBE) of nonequilibrium Green's function (NEGF) theory using hierarchical low-rank compression techniques. The simulation of strongly correlated quantum systems out of equilibrium is severely limited by the cubic scaling in propagation time and quadratic memory growth associated with conventional two-time formulations. H-NESSi overcomes these limitations by combining high-order time-stepping schemes with hierarchical off-diagonal low-rank (HODLR) representations of the retarded and lesser Green's functions, enabling controllable accuracy at substantially reduced computational cost and memory usage. Imaginary time quantities are efficiently represented using the discrete Lehmann representation (DLR), allowing compact and accurate treatment of thermal initial states. The implementation supports multiorbital systems, adaptive singular value truncation, and both shared-memory (OpenMP) and distributed-memory (MPI) parallelization strategies suitable for large-scale lattice calculations. The workflow closely mirrors established NEGF frameworks while introducing compression transparently into the propagation procedure. Benchmark applications to driven superconductors within dynamical mean-field theory and to the two-dimensional Hubbard model demonstrate favorable scaling compared to conventional implementations, with asymptotic time complexity significantly below the cubic scaling of uncompressed approaches. H-NESSi thus enables long-time and large-system nonequilibrium simulations of correlated quantum materials which were previously computationally prohibitive.

cond-mat.str-el↗

arXiv2026

Open Quantum Cluster Embedding Theory

The simulation of strongly correlated electron systems remains a formidable challenge. Certain experimentally relevant dynamical response functions are especially difficult to calculate, due to issues of finite-size effects and the ill posed analytic continuation. To address this we propose the quantum cluster embedding theory, an embedded cluster method aimed at computing the response of the system following an external perturbation; the frequency dependent dynamical susceptibility is obtained subsequently by means of inverse linear response theory. The embedded clusters, used within the method as representative of short range correlations, are open quantum systems governed by the Lindblad equation. The short-range correlations extracted from the clusters are used to close the equations of motion for the fermionic bilinear and the local double occupancy on the lattice. In turn, the clusters' Markovian baths are tuned to keep the bilinear and the double occupancy expectation values on the clusters and the lattice identical, throughout the concomitant evolution of the two sets of equations. The theory becomes numerically exact in the non-interacting, atomic and infinite cluster size limits, and it respects the total charge and energy conservation laws. We show that our approach can treat very large lattices while avoiding analytic continuation through the explicit time evolution. Finally we compute the charge-charge correlation function in the square lattice Hubbard model and compare with a recent cold atom experiment, finding good qualitative agreement.

cond-mat.str-el↗

arXiv2026

Exact downfolding and its perturbative approximation

Solving the many-electron problem, even approximately, is one of the most challenging and simultaneously most important problems in contemporary condensed matter physics with various connections to other fields. The standard approach is to follow a divide and conquer strategy that combines various numerical and analytical techniques. A crucial step in this strategy is the derivation of an effective model for a subset of degrees of freedom by a procedure called downfolding, which often corresponds to integrating out energy scales far away from the Fermi level. In this work we present a rigorous formulation of this downfolding procedure, which complements the renormalization group picture put forward by Honerkamp [PRB 85, 195129 (2012)}]. We derive an exact effective model in an arbitrarily chosen target space (e.g. low-energy degrees of freedom) by explicitly integrating out the the rest space (e.g. high-energy degrees of freedom). Within this formalism we state conditions that justify a perturbative truncation of the downfolded effective interactions to just a few low-order terms. Furthermore, we utilize the exact formalism to formally derive the widely used constrained random phase approximation (cRPA), uncovering underlying approximations and highlighting relevant corrections in the process. Lastly, we detail different contributions in the material examples of fcc Nickel and the infinite-layer cuprate SrCuO$_2$. Our results open up a new pathway to obtain effective models in a controlled fashion and to judge whether a chosen target space is suitable.

cond-mat.str-el↗

arXiv2025

Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models

Computing dynamical response functions in interacting lattice models is a long standing challenge in condensed matter physics. In view of recent results, the dc resistivity $ρ_\mathrm{dc}$ in the weak coupling regime of the Hubbard model is of great interest, yet it is not fully understood. The challenge lies in having to work with large lattices while avoiding analytical continuation. The weak-coupling $ρ_\mathrm{dc}$ results were so far computed at the level of the Boltzmann theory and at the level of the Kubo bubble approximation, which neglects vertex corrections. Neither theory was so far rigorously proven to give exact results even at infinitesimal coupling, and the respective dc resistivity results differ greatly. In this work we develop, cross-check and apply two state-of-the-art methods for obtaining dynamical response functions. We compute the optical conductivity at weak coupling in the Hubbard model in a fully controlled way, in the thermodynamic limit and without analytical continuation. We show that vertex corrections persist to infinitesimal coupling, with a constant ratio to the Kubo bubble. We connect our methods with the Boltzmann theory, and show that the latter applies additional approximations, which lead to quantitatively incorrect scaling of $ρ_\mathrm{dc}$ with respect to the coupling constant.

cond-mat.str-el↗

arXiv2024

Conductivity of lattice bosons at high temperatures

Quantum simulations are quickly becoming an indispensable tool for studying particle transport in correlated lattice models. One of the central topics in the study of transport is the bad-metal behavior, characterized by the direct current (dc) resistivity linear in temperature. In the fermionic Hubbard model, optical conductivity has been studied extensively, and a recent optical lattice experiment has demonstrated bad metal behavior in qualitative agreement with theory. Far less is known about transport in the bosonic Hubbard model. We investigate the conductivity in the Bose-Hubbard model, and focus on the regime of strong interactions and high-temperatures. We use numerically exact calculations for small lattice sizes. At weak tunneling, we find multiple peaks in the optical conductivity that stem from the Hubbard bands present in the many-body spectrum. This feature slowly washes out as the tunneling rate gets stronger. At high temperature, we identify a regime of $T$-linear resistivity, as expected. When the interactions are very strong, the leading inverse-temperature coefficient in conductivity is proportional to the tunneling amplitude. As the tunneling becomes stronger, this dependence takes quadratic form. At very strong coupling and half filling, we identify a separate linear resistivity regime at lower temperature, corresponding to the hard-core boson regime. Additionally, we unexpectedly observe that at half filling, in a big part of the phase diagram, conductivity is an increasing function of the coupling constant before it saturates at the hard-core-boson result. We explain this feature based on the analysis of the many-body energy spectrum and the contributions to conductivity of individual eigenstates of the system.

cond-mat.quant-gas↗

arXiv2023

Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space, and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states.

cond-mat.str-el↗