arXiv subjects

Martin Ulaga

Publications and source records attributed to Martin Ulaga.

10 recordsLinked to original sources

arXiv2026

Electronic Green's function across the pseudogap to stripe transition in the $t$-$t'$-$J$ model

Superconducting domes in strongly correlated electronic systems are often accompanied by charge density waves and peculiar features in the electronic structure. The appearance of a pseudogap, in particular, and its relation to charge density waves remains insufficiently understood. Here, we investigate the electronic Green's function of the underdoped $t$-$t'$-$J$ model of the cuprate superconductors using tensor network algorithms for finite temperature dynamics on cylinders of width $4$. We find the prominent momentum differentiation, the hallmark of the pseudogap, to be strongly dependent on $t'$, which develops into a momentum-dependent opening of a gap upon decreasing temperature, consistent with the formation of a Fermi arc at intermediate temperatures. The nodal gap around ${\bf k}=(\pi/2,\pi/2)$ closes and fills with increasing temperature as coherent stripe order melts into a regime of fluctuating charge clusters.

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arXiv2026

Evolution of superconductivity from charge clusters to stripes in the $t$-$t'$-$J$ model

Competition and coexistence of charge orders and superconductivity are hallmarks in many strongly correlated electron systems. Here, we unravel the precise role of charge fluctuations on the superconducting state in the $t$-$t'$-$J$ model of the high-temperature cuprate superconductors. Using finite-temperature tensor network simulations, we investigate thermal snapshots in the underdoped regime where the ground state features a superconducting stripe phase. At intermediate temperatures, where stripes have melted and hole clustering is observed, we find that pairing correlations are tightly localized on the hole clusters. Upon entering the stripe regime at lower temperatures, pairing increasingly delocalizes across different hole clusters to ultimately become coherent across the full system in the ground state. This pair-charge locking gives rise to an intuitive picture of the parent state of the superconducting stripe phase: pairing is localized on hole clusters formed via hole attraction due to the onset of magnetic correlations at intermediate temperature. We discuss how this microscopic picture is consistent with a broad range of experimental observations in cuprate superconductors, including scanning tunneling microscopy (STM) evidence for local pairing above $T_c$ and nuclear magnetic resonance (NMR) signatures of charge clustering in the underdoped regime.

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arXiv2025

The anisotropic Heisenberg model close to the Ising limit: triangular lattice vs. effective models

Stimulated by recent experiments on materials representing the realization of the anisotropic Heisenberg spin-$1/2$ model on the triangular lattice, we explore further properties of such a model in the easy-axis regime $\alpha = J_\perp/J_z < 1$ and the plausibility of finding effective models that capture similar physics. We show that, at finite fields, the magnetization curve as well as the transverse magnetization (superfluid) order parameter $m_\perp$ of the triangular lattice model are indeed qualitatively reproduced by anisotropic Heisenberg models on the honeycomb or the square lattice. At the point of correspondence to the zero-field triangular lattice model, however, the bipartite models are qualitatively different as they remain gapless even at $\alpha \ll 1$ with a small but finite $m_\perp >0 $. Conversely, we present several additional numerical studies of the full model on the triangular lattice which support the appearance of a gap at zero field and $\alpha \ll 1$. In particular, the magnetization curve $m(h)$ as well as the spin stiffness $\rho_s$ indicate a transition/crossover from gappless to gapped regimes at $\alpha \sim \alpha^*$ with $\alpha^* \lesssim 0.5$. We also show that deviations from the linear spin-wave theory and the emergence of the gap can be traced back to the strong effective repulsion between magnon excitations, showcasing similarity to strongly correlated systems.

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arXiv2025

XDiag: Exact Diagonalization for Quantum Many-Body Systems

Exact diagonalization (ED) is a cornerstone technique in quantum many-body physics, enabling precise solutions to the Schr\"odinger equation for interacting quantum systems. Despite its utility in studying ground states, excited states, and dynamical behaviors, the exponential growth of the Hilbert space with system size presents significant computational challenges. We introduce XDiag, an open-source software package designed to combine advanced and efficient algorithms for ED with and without symmetry-adapted bases with user-friendly interfaces. Implemented in C++ for computational efficiency and wrapped in Julia for ease of use, XDiag provides a comprehensive toolkit for ED calculations. Key features of XDiag include the first publicly accessible implementation of sublattice coding algorithms for large-scale spin system diagonalizations, efficient Lin table algorithms for symmetry lookups, and random-hashing techniques for distributed memory parallelization. The library supports various Hilbert space types (e.g., spin-1/2, electron, and t-J models), facilitates symmetry-adapted block calculations, and automates symmetry considerations. The package is complemented by extensive documentation, a user guide, reproducible benchmarks demonstrating near-linear scaling on thousands of CPU cores, and over 20 examples covering ground-state calculations, spectral functions, time evolution, and thermal states. By integrating high-performance computing with accessible scripting capabilities, XDiag allows researchers to perform state-of-the-art ED simulations and explore quantum many-body phenomena with unprecedented flexibility and efficiency.

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arXiv2024

Easy-axis Heisenberg model on the triangular lattice: from supersolid to gapped solid

We investigate the easy-axis Heisenberg model on the triangular lattice by numerically studying excitations and the dynamical spin structure factor $S^{\mu\mu}({\bf q},\omega)$. Results are analyzed within the supersolid scenario, characterized by the translation-symmetry-breaking parameter $m_z$ and the supersolid offdiagonal order parameter $m_\perp$. We find very robust $m_z > 0$ in the whole easy-axis anisotropy regime $\alpha = J_\perp/J_z > 0$, even enhanced by the magnetic field $h>0$, as well as $m_\perp >0$ for intermediate $\alpha <1$ and $h>0$. Still, at small $\alpha \lesssim 0.2$, relevant for recent experiments on the magnetic material K$_2$Co(SeO$_3$)$_2$, we find at $h=0$ rather vanishing $m_\perp \sim 0$, which appears compatible with the numerically established finite magnon excitation gap $\Delta_1 \sim 0.25 \alpha J$.

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arXiv2023

Thermoelectric effect on diffusion in the two-dimensional Hubbard model

We study charge and heat transport in the square lattice Hubbard model at strong coupling using the finite-temperature Lanczos method. We construct the diffusion matrix and estimate the effect of thermoelectric terms on diffusive and hydrodynamic time evolution. The thermoelectric terms prevent the interpretation of the diffusion in terms of a single time scale. We discuss our results in relation to cold-atom experiments and measurements of heat conductivity based on the measurements of heat diffusion.

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arXiv2023

Finite-temperature properties of the easy-axis Heisenberg model on frustrated lattices

Motivated by recent experiments on a compound {displaying Ising-like short-range correlations on the triangular lattice, we study the anisotropic easy-axis spin-$1/2$ Heisenberg model on the triangular and kagome lattice} by performing numerical calculations of finite-temperature properties, in particular of static spin structure factor and of thermodynamic quantities, on systems with up to 36 sites. On the triangular lattice, the low-temperature spin structure factor {exhibits long-range} spin correlations in the whole range of anisotropies, whereas thermodynamic quantities reveal a crossover upon increasing the anisotropy, most pronounced in the vanishing generalized Wilson ratio in the easy-axis regime. In contrast, on the kagome lattice, the spin structure factor is short-range, and thermodynamic quantities evolve steadily between the easy-axis and the isotropic case, consistent with the interpretation in terms of {a} spin liquid.

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arXiv2022

Thermal conductivity and heat diffusion in the two-dimensional Hubbard model

We study the electronic thermal conductivity $\kappa_\textrm{el}$ and the thermal diffusion constant $D_\textrm{Q,el}$ in the square lattice Hubbard model using the finite-temperature Lanczos method. We exploit the Nernst-Einstein relation for thermal transport and interpret the strong non-monotonous temperature dependence of $\kappa_\textrm{el}$ in terms of that of $D_\textrm{Q,el}$ and the electronic specific heat $c_\textrm{el}$. We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dynamical mean-field theory. We show that $\kappa_\textrm{el}$ is below the corresponding Mott-Ioffe-Regel value in almost all calculated regimes, while the mean free path is typically above or close to lattice spacing. We discuss the opposite effect of quasi-particle renormalization on charge and heat diffusion constants. We calculate the Lorenz ratio and show that it differs from the Sommerfeld value. We discuss our results in relation to experiments on cuprates. Additionally, we calculate the thermal conductivity of overdoped cuprates within the anisotropic marginal Fermi liquid phenomenological approach.

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arXiv2021

Spin Seebeck coefficient and spin-thermal diffusion in the two-dimensional Hubbard model

We investigate the spin Seebeck coefficient $S_s$ in the square lattice Hubbard model at high temperatures of relevance to cold-atom measurements. We solve the model with the finite-temperature Lanczos and with the dynamical mean-field theory methods and find they give similar results in the considered regime. $S_s$ exceeds the atomic 'Heikes' estimates and the Kelvin entropic estimates drastically. We analyze the behavior in terms of a mapping onto the problem of a doped attractive model and derive an approximate expression that allows relating the enhancement of $S_s$ to distinct scattering of the spin-majority and the spin-minority excitations. Our analysis reveals the limitations of entropic interpretations of Seebeck coefficient even in the high-temperature regime. Large values of $S_s$ could be observed on optical lattices. We also calculate the full diffusion matrix. We quantify the spin-thermal diffusion, that is, the extent of the mixing between the spin and the thermal diffusion and discuss the results in the context of recent measurements of the spin-diffusion constant in cold atoms.

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arXiv2020

Spin diffusion and spin conductivity in the 2d Hubbard model

We study the spin diffusion and spin conductivity in the square lattice Hubbard model by using the finite-temperature Lanczos method. We show that the spin diffusion behaves differently from the charge diffusion and has a nonmonotonic $T$ dependence. This is due to a progressive liberation of charges that contribute to spin transport and enhance it beyond that active at low temperature due to the Heisenberg exchange. We further show that going away from half-filling and zero magnetization increases the spin diffusion, but that the increase is insufficient to reconcile the difference between the model calculations and the recent measurements on cold-atoms.

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