arXiv subjects

Lukas Weber

Publications and source records attributed to Lukas Weber.

14 recordsLinked to original sources

arXiv2026

AutoHF: a general Hartree-Fock solver utilizing direct energy minimization with automatic differentiation

We present autohf, a general, easy-to-use mean-field solver for quantum many-fermion Hamiltonians. It allows the user to bypass the process of deciphering the mean-field form for each many-body Hamiltonian $H$ and thus avoid setting up a tailored program for each $H$. Rather, autohf finds the optimal Slater determinant $|\Psi\rangle$, written in terms of orbital coefficients and subject to symmetry constraints, by directly minimizing the variational energy $\langle H \rangle$. By embracing this variational approach, autohf makes use of the growing power of automatic differentiation and optimization tools developed by the machine learning community.

cond-mat.str-el↗

arXiv2026

Engineering molecular potential energy surfaces using magnetic cavity quantum electrodynamics

We investigate the effects of coupling a quantum-magnetic cavity field to molecules. Our high-precision auxiliary-field quantum Monte Carlo calculations capture the effect of the cavity field in the presence of electron correlations, and their interplay and competition. In H$_2$, we find that a strong enough cavity coupling makes the original bound ground state metastable, along with inverting the singlet-triplet gap. In ring molecules (e.g., H$_n$), the magnetic cavity coupling stabilizes symmetric geometries. As a consequence, open-shell rings such as H$_4$, H$_8$, or C$_4$H$_4$, which would undergo Jahn-Teller distortions outside of the cavity, obtain exotic spin or ring-current polarized, antiaromatic ground states. These effects are enhanced by increasing the molecule concentration inside the cavity. Our results suggest cavity quantum electrodynamics beyond the long-wavelength approximation as a promising avenue for cavity-altered chemistry.

physics.chem-ph↗

arXiv2024

The light-matter correlation energy functional of the cavity-coupled two-dimensional electron gas via quantum Monte Carlo simulations

We perform extensive simulations of the two-dimensional cavity-coupled electron gas in a modulating potential as a minimal model for cavity quantum materials. These simulations are enabled by a newly developed quantum-electrodynamical (QED) auxiliary-field quantum Monte Carlo method. We present a procedure to greatly reduce finite-size effects in such calculations. Based on our results, we show that a modified version of weak-coupling perturbation theory is remarkably accurate for a large parameter region. We further provide a simple parameterization of the light-matter correlation energy as a functional of the cavity parameters and the electronic density. These results provide a numerical foundation for the development of the QED density functional theory, which was previously reliant on analytical approximations, to allow quantitative modeling of a wide range of systems with light-matter coupling.

cond-mat.str-el↗

arXiv2024

Phaseless auxiliary-field quantum Monte Carlo method for cavity-QED matter systems

We present a generalization of the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to cavity quantum-electrodynamical (QED) matter systems. The method can be formulated in both the Coulomb and the dipole gauge. We verify its accuracy by benchmarking calculations on a set of small molecules against full configuration interaction and state-of-the-art QED coupled cluster (QED-CCSD) calculations. Our results show that (i) gauge invariance can be achieved within correlation-consistent Gaussian basis sets, (ii) the accuracy of QED-CCSD can be enhanced significantly by adding the standard perturbative triples correction without light-matter coupling, and (iii) there is a straightforward way to evaluate the differential expression for the photon occupation number that works in any gauge. The high accuracy and favorable computational scaling of our AFQMC approach will enable a broad range of applications. Besides polaritonic chemistry, the method opens a way to simulate extended QED matter systems.

physics.chem-ph↗

arXiv2024

Carlo.jl: A general framework for Monte Carlo simulations in Julia

Carlo is a Monte Carlo simulation framework written in Julia. It provides MPI-parallel scheduling, organized storage of input, checkpoint, and output files, as well as statistical postprocessing. With a minimalist design, it aims to aid the development of high-quality Monte Carlo codes, especially for demanding applications in condensed matter and statistical physics. This hands-on user guide shows how to implement a simple code with Carlo and provides benchmarks to show its efficacy.

physics.comp-ph↗

arXiv2023

Cavity-renormalized quantum criticality in a honeycomb bilayer antiferromagnet

Strong light-matter interactions as realized in an optical cavity provide a tantalizing opportunity to control the properties of condensed matter systems. Inspired by experimental advances in cavity quantum electrodynamics and the fabrication and control of two-dimensional magnets, we investigate the fate of a quantum critical antiferromagnet coupled to an optical cavity field. Using unbiased quantum Monte Carlo simulations, we compute the scaling behavior of the magnetic structure factor and other observables. While the position and universality class are not changed by a single cavity mode, the critical fluctuations themselves obtain a sizable enhancement, scaling with a fractional exponent that defies expectations based on simple perturbation theory. The scaling exponent can be understood using a generic scaling argument, based on which we predict that the effect may be even stronger in other universality classes. Our microscopic model is based on realistic parameters for two-dimensional magnetic quantum materials and the effect may be within the range of experimental detection.

cond-mat.str-el↗

arXiv2022

Thermal critical points from competing singlet formations in fully frustrated bilayer antiferromagnets

We examine the ground-state phase diagram and thermal phase transitions in a plaquettized fully frustrated bilayer spin-1/2 Heisenberg model. Based on a combined analysis from sign-problem free quantum Monte Carlo simulations, perturbation theory and free-energy arguments, we identify a first-order quantum phase transition line that separates two competing quantum-disordered ground states with dominant singlet formations on inter-layer dimers and plaquettes, respectively. At finite temperatures, this line extends to form a wall of first-order thermal transitions, which terminates in a line of thermal critical points. From a perturbative approach in terms of an effective Ising model description, we identify a quadratic suppression of the critical temperature scale in the strongly plaquettized region. Based on free-energy arguments we furthermore obtain the full phase boundary of the low-temperature dimer-singlet regime, which agrees well with the quantum Monte Carlo data.

cond-mat.str-el↗

arXiv2022

Cluster quantum Monte Carlo study of two-dimensional weakly-coupled frustrated trimer antiferromagnets

We report results from spin trimer-based cluster quantum Monte Carlo simulations for the thermodynamic properties of two-dimensional frustrated quantum antiferromagnets that are composed of weakly-coupled three-spin (trimer) clusters. In particular, we consider the spin-1/2 kagome lattice with a strong breathing distortion, and the triangle-square lattice model proposed previously for the cuprate La${}_4$Cu${}_3$MoO${}_{12}$. For both cases, we demonstrate that an appropriately chosen trimer-based computational basis allows us to significantly reduce the quantum Monte Carlo sign problem down to the low-temperature regime. Besides exploring the thermodynamic behavior for the triangle-square lattice model we also assess a mean field theory-based prediction for the onset of chiral order. For the breathing distorted kagome lattice model, we observe a robust two-peak structure in the specific heat, both in the quantum spin liquid and the lattice-nematic regimes.

cond-mat.str-el↗

arXiv2022

Hierarchical single-ion anisotropies in spin-1 Heisenberg antiferromagnets on the honeycomb lattice

We examine the thermal properties of the spin-1 Heisenberg antiferromagnet on the honeycomb lattice in the presence of an easy-plane single-ion anisotropy as well as the effects of an additional weak in-plane easy-axis anisotropy. In particular, using large-scale quantum Monte Carlo simulations, we analyze the scaling of the correlation length near the thermal phase transition into the ordered phase. This allows us to quantify the temperature regime above the critical point in which -- in spite of the additional in-plane easy-axis anisotropy -- characteristic easy-plane physics, such as near a Berezinskii-Kosterlitz-Thouless transition, can still be accessed. Our theoretical analysis is motivated by recent neutron scattering studies of the spin-1 compound BaNi${}_2$V${}_2$O${}_8$ in particular, and it addresses basic quantum spin models for generic spin-1 systems with weak anisotropies, which we probe over the full range of experimentally relevant correlation length scales.

cond-mat.str-el↗

arXiv2021

Quantum Monte Carlo simulations of highly frustrated magnets in a cluster basis: The two-dimensional Shastry-Sutherland model

Quantum Monte Carlo (QMC) simulations constitute nowadays one of the most powerful methods to study strongly correlated quantum systems, provided that no "sign problem" arises. However, many systems of interest, including highly frustrated magnets, suffer from an average sign that is close to zero in standard QMC simulations. Nevertheless, a possible sign problem depends on the simulation basis, and here we demonstrate how a suitable choice of cluster basis can be used to eliminate or at least reduce the sign problem in highly frustrated magnets that were so far inaccessible to efficient QMC simulations. We focus in particular on the application of a two-spin (dimer)-based QMC method to the thermodynamics of the spin-1/2 Shastry-Sutherland model for SrCu$_2$(BO$_3$)$_2$.

cond-mat.str-el↗

arXiv2020

Spin vs. bond correlations along dangling edges of quantum critical magnets

Dangling edge spins of two-dimensional quantum critical antiferromagnets display strongly enhanced spin correlations with scaling dimensions that fall outside of the classical theory of surface critical phenomena. We provide large-scale quantum Monte Carlo results for both spin and bond correlation functions for the case of the columnar dimer model in particular. Unlike the spin correlations, we find the bond correlations to differ starkly between the spin-1/2 and spin-1 case. Furthermore, we compare the corresponding scaling dimensions to recent theoretical predictions. These predictions are, in part, supported by our numerical data, but cannot explain our findings completely. Our results thus put further constraints on completing the understanding of dangling edge correlations, as well as surface phenomena in strongly-correlated quantum systems in general.

cond-mat.str-el↗

arXiv2019

Emergent symmetries and coexisting orders in Dirac fermion systems

The quantum phase diagram and critical behavior of two-dimensional Dirac fermions coupled to two compatible order-parameter fields with $O(N_1)\oplus O(N_2)$ symmetry is investigated. Recent numerical studies of such systems have reported evidence for non-Landau-Ginzburg-Wilson transitions and emergent $O(N_1+N_2)$ symmetry between the two ordered states, which has been interpreted within a scenario of deconfined quantum criticality in (2+1)-dimensional Dirac materials. Here, we provide two theoretical approaches to refine the phase diagrams of such systems. In the immediate vicinity of the multicritical point between the ordered phases and the semimetallic phase, we employ a non-perturbative field-theoretical analysis based on the functional renormalization group. For the particular case of $N_1=3$, $N_2=1$, we perform a large-scale quantum Monte Carlo analysis of the strong-coupling region, where both orders meet. Our findings support the robust emergence of enhanced symmetry at the multicritical point and suggest the transition between the two ordered phases to take place via a sequence of continuous transitions. In particular, we find that intermediate regimes of coexistence are present in the phase diagram for all values of $N_1$ and $N_2$.

cond-mat.str-el↗

arXiv2019

Nonordinary criticality at the edges of planar spin-1 Heisenberg antiferromagnets

Dangling edge spins of dimerized two-dimensional spin-1 Heisenberg antiferromagnets are shown to exhibit nonordinary quantum critical correlations, akin to the scaling behavior observed in recently explored spin-1/2 systems. Based on large-scale quantum Monte Carlo simulations, we observe remarkable similarities between these two cases, and also examine the crossover to the fundamentally distinct behavior in the one-dimensional limit of strongly coupled edge spins. We complement our numerical analysis by a cluster mean-field theory that encompasses the qualitatively similar behavior for the spin-1 and the spin-1/2 case, and its dependence on the spatial edge spin configuration in a generic way.

cond-mat.str-el↗

arXiv2018

Nonordinary edge criticaliy of two-dimensional quantum critical magnets

Based on large-scale quantum Monte Carlo simulations, we examine the correlations along the edges of two-dimensional semi-infinite quantum critical Heisenberg spin-$1/2$ systems. In particular, we consider coupled quantum spin-dimer systems at their bulk quantum critical points, including the columnar-dimer model and the plaquette-square lattice. The alignment of the edge spins strongly affects these correlations and the corresponding scaling exponents, with remarkably similar values obtained for various quantum spin-dimer systems. We furthermore observe subtle effects on the scaling behavior from perturbing the edge spins that exhibit the genuine quantum nature of these edge states. Our observations furthermore challenge recent attempts that relate the edge spin criticality to the presence of symmetry-protected topological phases in such quantum spin systems.

cond-mat.str-el↗