arXiv subjects

Shadan Ghassemi Tabrizi

Publications and source records attributed to Shadan Ghassemi Tabrizi.

16 recordsLinked to original sources

arXiv2026

Kramers pseudospin and the quantum number proposed for the many-electron Dirac?Coulomb Hamiltonian

The square of a sum of single-electron time reversals has been proposed as a conserved quantity with an integer eigenvalue spectrum for the many-electron Dirac-Coulomb Hamiltonian [Phys. Rev. A 94, 052104 (2016)], and its expectation value is in use as a diagnostic of Kramers contamination. This work identifies the operator behind the construction, a component of a pseudospin attached to the chosen Kramers pairs, whose angular-momentum algebra reproduces the reported spectrum and yields the eigenvectors in closed form. The label $k$ entering the proposed quantum number $-k^2$ is twice the magnitude of a pseudospin projection onto an axis fixed by the basis and changes when the Kramers pairs are rephased. The commutation with the Hamiltonian is unfounded, and the proposed quantum number does not stand.

quant-ph↗

arXiv2026

Systematic extinctions in inelastic neutron scattering from molecular spin clusters

Inelastic neutron scattering on a single crystal resolves how the intensity of a magnetic transition of a molecular spin cluster varies with the momentum-transfer vector $\mathbf{Q}$. The point group fixes that dependence completely when a single symmetry species mediates the transition and the local spin operators contain only one occurrence of that species. Functions for such universal $\mathbf{Q}$ dependences have been tabulated. As we show here, even when these conditions are not fulfilled, the point group still fixes, at a given geometry, momentum transfers at which the intensity vanishes for every Hamiltonian that has the symmetry of the cluster. We call such momentum transfers extinctions and derive an equation whose every zero is an extinction, built from the symmetry species of the two levels and from the positions and scattering amplitudes of the magnetic sites. The extinctions follow in closed form in two cases: when each orbit of symmetry-equivalent sites contributes a single occurrence of the mediating species, and when the site phases recur under a subgroup up to one common factor.

cond-mat.str-el↗

arXiv2026

Hidden symmetry at the diabolical points of a biaxial spin

In a rotated frame the biaxial spin Hamiltonian $k_1S_x^2+k_2S_y^2-\mathbf{h}\cdot\mathbf{S}$ is a finite tight-binding chain whose hopping amplitudes are tuned by the applied field. A chain with no vanishing hopping has a nondegenerate spectrum, so a degeneracy can occur only where the field severs the chain. We show that at every point of the exact diabolical-point lattice found by Kececioglu and Garg the chain is severed twice over, in two different rotated frames and at two bonds that are fixed independently. The two severings are carried by projectors that commute with the Hamiltonian but not with each other. In that form they realize the hidden symmetry anticipated by Garg. A single operator built from them pairs the degenerate levels; its rank gives the multiplicity of every lattice point, replacing an earlier continuity and topological argument. Because the two partners of a doublet occupy disjoint stretches of the chain, an exact and manifestly negative determinant fixes the orientation of every cone. At every degeneracy of the model the lower level therefore carries Chern charge -1 in the convention used here.

cond-mat.str-el↗

arXiv2026

GPU-accelerated finite-temperature Lanczos method for Heisenberg spin systems with non-Abelian permutation symmetries

We extend a recent GPU implementation of the finite-temperature Lanczos method (FTLM) for Heisenberg spin Hamiltonians, which uses only total-magnetization symmetry, to the full permutation symmetry, including non-Abelian point and space groups. For highly symmetric clusters such as icosahedral polyhedra, the multidimensional irreducible representations (irreps) of the permutation group reduce the block dimensions substantially further than any Abelian subgroup. Here, we provide a matrix-free formalism (avoiding explicit storage of the projected Hamiltonian) for using such symmetries. The implementation applies equally to Abelian groups, retaining the advantages of GPU acceleration. Several cluster topologies are built in; beyond these, symmetry groups can be supplied as site-permutation generators, with irrep matrices computed automatically, so that user-defined clusters run without any code changes. We demonstrate the approach in production runs on a single NVIDIA B200 accelerator for the s=3/2 Heisenberg antiferromagnet on the dodecahedron (Hilbert-space dimension 4^20 ~ 1.1x10^12) and for the s=1/2 square lattice of 5x8 sites (M=0 dimension 1.4x10^11). With R=24 random vectors per symmetry block and 60 Lanczos steps, the dodecahedron campaign (with the largest iterated symmetry block having a dimension of 3.6x10^9) requires about 50 GPU-hours. The code is openly available under the Apache-2.0 license at https://github.com/ghasdeke/ftlm-pg-gpu, archived at DOI: 10.5281/zenodo.21445872.

cond-mat.str-el↗

arXiv2026

GPU-accelerated finite-temperature Lanczos method for spin Hamiltonians

We present a GPU implementation of the finite-temperature Lanczos method (FTLM) for Heisenberg spin Hamiltonians that targets workstation hardware rather than distributed-memory clusters. The Hamiltonian action is evaluated matrix-free in a row-wise gather formulation. We introduce and compare two state-to-index strategies: a compressed lookup table (CLT), which reduces lookup memory by a factor of 16 relative to a full table while retaining a fixed, branch-light access pattern, and a GPU-adapted combinatorial-ranking scheme that removes the lookup table altogether. Numerical tests against FP64 CPU references show that FP32 GPU arithmetic changes heat capacities and magnetic susceptibilities by amounts several orders of magnitude below the stochastic uncertainty of the FTLM trace estimator at typical sample sizes. Benchmarks show speedups of up to about one order of magnitude over optimized multicore CPU calculations and enable Hilbert-space sectors of dimension ~10^8 on a single workstation GPU. The MATLAB/CUDA implementation, including example input files and benchmark scripts, is openly available at https://github.com/ghasdeke/ftlm-gpu (archived at DOI: 10.5281/zenodo.20378647) under the Apache-2.0 license.

cond-mat.str-el↗

arXiv2026

SCF framework, HF stability and RPA correlation for Jordan-Wigner-transformed spin Hamiltonians on arbitrary coupling topologies

Mapping spins to fermions via the Jordan-Wigner (JW) transformation can render mean-field (Hartree-Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering, because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-Algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytic orbital Hessian to diagnose HF stability and compute ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J1-J2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

cond-mat.str-el↗

arXiv2025

Scalable implementations of mean-field and correlation methods based on Lie-algebraic similarity transformation of spin Hamiltonians in the Jordan-Wigner representation

Recent work has highlighted that the strong correlation inherent in spin Hamiltonians can be effectively reduced by mapping spins to fermions via the Jordan-Wigner transformation (JW). The Hartree-Fock method is straightforward in the fermionic domain and may provide a reasonable approximation to the ground state. Correlation with respect to the fermionic mean-field can be recovered based on Lie-algebraic similarity transformation (LAST) with two-body correlators. Specifically, a unitary LAST variant eliminates the dependence on site ordering, while a non-unitary LAST yields size-extensive correlation energies. Whereas the first recent demonstration of such methods was restricted to small spin systems, we present efficient implementations using analytical gradients for the optimization with respect to the mean-field reference and the LAST parameters, thereby enabling the treatment of larger clusters, including systems with local spins s > 1/2.

cond-mat.str-el↗

arXiv2025

Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters

While either spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin S and the irreducible representation of the point-group is limited by the complexity of transformations between different coupling-schemes that are related by site-permutations. To overcome these challenges, we apply projection-operators directly to uncoupled basis-states, enabling the simultaneous treatment of spin and point-group symmetry without the need for recoupling-transformations. This provides a simple and efficient approach for the exact diagonalization of isotropic spin-models that we illustrate with applications to Heisenberg spin-rings and polyhedra, including systems that are computationally inaccessible with conventional coupling-techniques.

cond-mat.str-el↗

arXiv2024

Projective spin adaptation for the exact diagonalization of isotropic spin clusters

Spin Hamiltonians, like the Heisenberg model, are used to describe magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spinrotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin's projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin's theorem for s = 1/2 to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon spin projection. We illustrate the procedure with a few examples.

cond-mat.str-el↗

arXiv2024

Analytical solutions of symmetric isotropic spin clusters

Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically solve isotropic spin clusters, based on adapting the basis to both total-spin and point-group symmetry to factor the Hamiltonian matrix into sufficiently small blocks. We demonstrate applications to small rings and polyhedra, some of which are straightforward to solve by successive spin-coupling for Heisenberg terms only; additional interactions, such as biquadratic exchange or multi-center terms necessitate symmetry adaptation.

cond-mat.str-el↗

arXiv2024

Hartree-Fock-Bogoliubov theory for number-parity--violating fermionic Hamiltonians

It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan-Wigner transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms which contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry, and requires wave functions which do not have this symmetry either. In this work, we discuss the extension of standard Hartree-Fock-Bogoliubov (HFB) theory to the number-parity--nonconserving case. These ideas had appeared in the literature before, but, perhaps for lack of practical applications, had to the best of our knowledge never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2$M$ + 1) Lie group, where $M$ is the number of orbitals. We also show how using these unusual mean-field states can provide significant improvements when studying the Jordan-Wigner transformation of chemically relevant spin Hamiltonians.

cond-mat.str-el↗

arXiv2023

Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory (DFT). The energies of these configurations are interpreted in terms of the Heisenberg model to determine coupling constants for spin pairs. However, this energy-based procedure has inherent limitations, primarily in its inability to provide information on isotropic spin interactions beyond those included in the Heisenberg model. Biquadratic exchange or multi-center terms, for example, are usually inaccessible and hence assumed to be negligible. The present work introduces a novel approach employing BS mean-field solutions, specifically Hartree-Fock wave functions, for the construction of effective spin Hamiltonians. This expanded method facilitates the extraction of a broader range of coupling parameters by considering not only the energies, but also Hamiltonian and overlap elements between different BS states. We demonstrate how comprehensive s = 1/2 Hamiltonians, including multi-center terms, can be straightforwardly constructed from a complete set of BS solutions. The approach is exemplified for small clusters within the context of the half-filled single-band Hubbard model. This allows to contrast the current strategy against exact results, thereby offering an enriched understanding of the spin-Hamiltonian construction from BS solutions.

cond-mat.str-el↗

arXiv2022

Calculation of molecular g-tensors by sampling spin orientations of generalised Hartree-Fock states

The variational inclusion of spin-orbit coupling in self-consistent field (SCF) calculations requires a generalised two-component framework, which permits the single-determinant wave function to completely break spin symmetry. The individual components of the molecular g-tensor are commonly obtained from separate SCF solutions that align the magnetic moment along one of the three principal tensor axes. However, this strategy raises the question if energy differences between solutions are relevant, or how convergence is achieved if the principal axis system is not determined by molecular symmetry. The present work resolves these issues by a simple two-step procedure akin to the generator coordinate method (GCM). First, a few generalised Hartree Fock (GHF) solutions are converged, applying, where needed, a constraint to the orientation of the magnetic-moment or spin vector. Then, superpositions of GHF determinants are formed through non-orthogonal configuration interaction. This procedure yields a Kramers doublet for the calculation of the complete g-tensor. Alternatively, for systems with weak spin-orbit effects, diagonalisation in a basis spanned by spin rotations of a single GHF determinant affords qualitatively correct g-tensors by eliminating errors related to spin contamination. For small first-row molecules, these approaches are evaluated against experimental data and full configuration interaction results. It is further demonstrated for two systems (a fictitious tetrahedral CH4+ species, and a CuF4(2-) complex) that a GCM strategy, in contrast to alternative mean-field methods, can correctly describe the spin-orbit splitting of orbitally-degenerate ground states, which causes large g-shifts and may lead to negative g-values.

physics.chem-ph↗

arXiv2022

Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach

Recent work on approximating ground states of Heisenberg spin clusters by projected Hartree-Fock theory (PHF) is extended to a cluster-based ansatz (cPHF). Whereas PHF variationally optimizes a site-spin product state for the restoration of spin- and point-group symmetry, cPHF groups sites into discrete clusters and uses a cluster-product state as the broken-symmetry reference. Intracluster correlation is thus already included at the mean-field level and intercluster correlation is introduced through symmetry projection. Variants of cPHF differing in the broken and restored symmetries are evaluated for ground states and singlet-triplet gaps of antiferromagnetic spin rings for various cluster sizes, where cPHF in general affords a significant improvement over ordinary PHF, although the division into clusters lowers the cyclical symmetry. On the other hand, certain two- or three-dimensional spin arrangements permit cluster groupings compatible with the full spatial symmetry. We accordingly demonstrate that cPHF yields approximate ground states with correct spin and point-group quantum numbers for honeycomb lattice fragments and symmetric polyhedra.

cond-mat.str-el↗

arXiv2021

Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory

We apply Projected Hartree-Fock theory (PHF) for approximating ground states of Heisenberg spin clusters. Spin-rotational, point-group and complex-conjugation symmetry are variationally restored from a broken-symmetry mean-field reference, where the latter corresponds to a product of local spin states. A fermionic formulation of the Heisenberg model furnishes a conceptual connection to PHF applications in quantum chemistry and detailed equations for a self-consistent field optimization of the reference state are provided. Different PHF variants are benchmarked for ground-state energies and spin-pair correlation functions of antiferromagnetic spin rings and three different polyhedra, with various values of the local spin-quantum number s. The low computational cost and the compact wave-function representation make PHF a promising complement to existing approaches for ground states of molecular spin clusters, particularly for large s and moderately large N. The present work may also motivate future explorations of more accurate post-PHF methods for Heisenberg spin clusters.

cond-mat.str-el↗

arXiv2021

Symmetry-Induced Universal Momentum-Transfer Dependencies for Inelastic Neutron Scattering on Anisotropic Spin Clusters

Inelastic neutron scattering (INS) is a key method for studying magnetic excitations in spin systems, including molecular spin clusters. The method has significantly advanced in recent years and now permits to probe the scattering intensity as a function of the energy transfer and the momentum-transfer vector Q. It was recently shown that high molecular symmetry facilitates the analysis of spectra. Point-group symmetry imposes selection rules in isotropic as well as anisotropic spin models. Furthermore, the Q-dependence of the INS intensity may be completely determined by the point-group symmetry of the states involved in a transition, thereby affording a clear separation of dynamics (energies, transition strengths) and geometrical features (Q-dependencies). The present work addresses this issue for anisotropic spin models. We identify a number of cases where the Q-dependence is completely fixed by the point-group symmetry. For six- and eight-membered planar spin rings and two polyhedra (the cube and the icosahedron) we tabulate and plot the corresponding powder-averaged universal intensity functions. The outlined formalism straightforwardly applies to other highly-symmetric systems and should be useful for future analyses of INS spectra by focusing on those features that contain information on either spin dynamics or the point-group symmetry of states.

cond-mat.str-el↗