arXiv subjects

Steven R. White

Publications and source records attributed to Steven R. White.

At least 19 recordsLinked to original sources

arXiv2026

Reference-Density Hartree Screening for Gausslet Hamiltonians

Gausslets are among the few electronic-structure bases that permit the four-index electron--electron interaction to be replaced by an accurate two-index integral diagonal approximation (IDA). Near a many-electron nucleus, however, the nuclear attraction and core-electron Hartree field are individually large and substantially cancel. Treating the first as a full finite-basis matrix while treating the second with IDA leaves an avoidable imbalance. We introduce reference-density Hartree screening: the Hartree field of a chosen reference density is represented accurately, and IDA is applied only to density fluctuations about it. Tests on He, Ne, atomic F, F$_2$, and Cr$_2$ show large reductions in direct Hartree errors, including transfer of fitted neutral-atom fields to molecules. For Cr$_2$, atomic-core screening prevents the spurious HF collapse found with the unscreened $q=5$ and $q=7$ Hamiltonians, whereas finite-reference matching without screening does not. Screening leaves exchange and residual correlation unchanged. We therefore also introduce a low-rank one-particle correction that uses an accurate conventional Gaussian-basis Hartree--Fock calculation to match either occupied-space exchange information or the complete occupied Fock vectors. In F$_2$ and Cr$_2$, $X_{\rm HF}$ reproduces the finite-reference energy and occupied Fock vectors to numerical precision and the selected states return after orbital perturbations. For Cr$_2$, the corrected $q=5$ basis uses one quarter as many functions as the $q=7$ control while retaining sub-mHa mean-field accuracy. Screening provides the physical improvement to the direct field; the state-specific correction then restores the remaining accuracy of the Gaussian-basis mean-field reference.

physics.chem-ph↗

arXiv2026

Projected q-Shells for Nested Gausslet Bases

Electronic-structure calculations require a finite representation of both the electronic wave functions and their Coulomb interaction. Conventional compact basis sets lead to a four-index interaction. Gausslet basis sets are one of a very small number of approaches that allow a much smaller two-index interaction, similar to a real-space grid, but with far fewer points. The continuing challenge in their development is reducing further the number of functions needed while maintaining high accuracy. Here we introduce projected q-shells (PQS), an improvement to the nested Cartesian gausslets of White and Lindsey. Their standard nesting construction divides a joining shell into disjoint faces, edges, and corners, reducing its polynomial completeness from order q to order q-2. PQS approximately restores the two lost orders. In terms of completeness, we prove that for an ideal, undistorted parent, the span of the PQS basis is equivalent to an overcomplete basis of overlapping patches. Coordinate distortions, which are always used in practice, harm this equivalence only slightly. The moment properties that allow two-index interactions also become inexact, even without distortion, but we show that the improvement in order more than makes up for this loss. For similar basis sizes, PQS gives smaller one-electron and interaction errors on small molecules, such as H2+, H2, and C2, than standard nesting. The improvement is largest for more compact bases with smaller q.

physics.chem-ph↗

arXiv2026

Spinless charged excitation at the interface between a conventional topological insulator and a topological Mott insulator

We investigate the interface separating two topologically distinct insulating phases of matter using extensive density-matrix renormalization group calculations to study the triangular-lattice Hofstadter-Hubbard model with a spatially varying interaction strength, chosen to realize both integer quantum Hall and chiral spin liquid states in different spatial regions. We find that the integer quantum Hall-chiral spin liquid interface hosts a spinless charged excitation that is bound to the interface. This mode at the interface is identified through charge and spin pumping, and by direct calculations of low-lying excited states. We also characterize bulk excitations in both phases, finding evidence for fractionalization in the chiral spin liquid and for spin-triplet exciton formation in the integer quantum Hall phase.

cond-mat.str-el↗

arXiv2026

Fast Tensor Network Imaginary Time Evolution by Implicit Stepping on Logarithmic Grids

We present a new method for the efficient imaginary time evolution of quantum many-body wavefunctions represented by matrix product states (MPS). We first show that logarithmic time grids are sufficient to resolve long imaginary time dynamics, yielding an exponential reduction in the number of time steps compared with standard approaches. We then show that A-stable implicit time-stepping methods for ordinary differential equations allow stable propagation for any time step size. The resulting scheme requires only matrix-vector products and linear solves, standard operations in the MPS toolbox. We validate our approach with two examples: a Heisenberg spin chain, which we use to demonstrate a speedup of several orders of magnitude over the standard time-dependent variational principle method with uniform time steps, and a single-site Anderson impurity model with a metallic bath, for which propagation to large imaginary times allows one to observe the exponential dependence of the Kondo temperature on the interaction strength.

cond-mat.str-el↗

arXiv2026

Angular Gausslets

Gausslets are one of the few basis constructions for electronic structure that combine locality, orthonormality, variable resolution, and an accurate diagonal approximation for the electron-electron interaction, but the original construction is tied to one dimension. Radial gausslets extended this idea to atoms while leaving the angular degrees of freedom in spherical harmonics, so the atomic interaction remained only partially diagonal in the combined basis. Here we introduce generalized gausslets on the sphere and combine them shell by shell with radial gausslets to form an atom-centered basis in which the electron-electron interaction takes a two-index integral-diagonal form. The angular basis starts from localized spherical Gaussians and uses injection to make a low-$\ell$ spherical-harmonic subspace exact. Tests of the kinetic spectrum, low-$\ell$ Coulomb matrix elements, spherium, first-row Hartree--Fock calculations, and He exact diagonalization show systematic convergence with increasing angular resolution. We also develop DMRG methods for this basis, including compact MPOs, correlated small-space starting states, Givens-rotation transfers between nearby angular sizes, and embedded sampled variance extrapolation (ESVE). We show that this combination of ingredients can be used to solve the Be atom, with extrapolations in the number of angular functions but with fixed radial resolution, to within about 0.1 mH of the complete basis set limit exact energy. This shows that DMRG calculations of first row atoms which include both static and accurate dynamic correlation on the same footing are feasible.

physics.chem-ph↗

arXiv2026

Radial Gausslets

Gausslets are one of the few examples of basis sets for electronic structure which allow for two-index/diagonal electron-electron interaction terms. A weakness of gausslets is that, because of their 1D origin, they have been tied to Cartesian coordinates. Here we generalize the gausslet construction for the radial coordinate in three dimensions for atomic basis sets. These radial gausslets make a very compact radial basis with a relatively modest number of functions, with diagonal interaction terms. We illustrate the accuracy of this construction with Hartree--Fock and exact diagonalization on atomic systems.

physics.chem-ph↗

arXiv2026

Competing states in the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model: a dynamical density-matrix renormalization group study

Previous studies of the $S=1/2$ triangular-lattice $J_1$--$J_2$ Heisenberg antiferromagnet have inferred the existence of a non-magnetic ground-state phase for an intermediate range of $J_2$, but disagree concerning whether it is a gapped $\mathbb{Z}_2$ quantum spin liquid (QSL), a gapless (Dirac) QSL, or a weakly symmetry-broken phase. Using an improved dynamical density-matrix renormalization group method, we investigate the relevant intermediate $J_2$ regime for cylinders with circumferences from 6 to 9. Depending on the initial state and boundary conditions, we find two {\it distinct} variational states. The higher energy state is consistent with a Dirac QSL. In the lower-energy state, both the static and dynamical properties are qualitatively similar to the magnetically ordered state at $J_2=0$, suggestive of either a weakly magnetically ordered non-QSL or a gapped QSL proximate to a continuous transition to such an ordered state.

cond-mat.str-el↗

arXiv2025

Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model

We investigate the weak interaction integer quantum Hall (IQH) phase, the intermediate interaction phase identified as a chiral spin liquid (CSL) and the transition between them in the triangular lattice Hofstadter-Hubbard model at a density of one electron per site in an orbital magnetic field corresponding to one-quarter flux per plaquette. Our primary tool is the finite system density matrix renormalization group (DMRG) method with both interaction-strength scan and fixed interaction techniques for cylinders of circumference 3, 5, and 7 and lengths up to 240. For the IQH phase, we use single particle exact diagonalization to clarify finite size effects, including an excess charge on the edges of our cylinders, and the limitations of entanglement spectra degeneracies on small circumference cylinders. For both phases, we use DMRG to study the entanglement spectra, the entanglement entropy, and the effect of flux insertion on charge and spin pumping, all of which show key differences between the two phases. To study the transition, we use interaction-strength scans extending between the two phases, and apply a scaling data collapse of a bond-dimerization order parameter to extract critical exponents. We also extract critical behavior from the divergence of correlation lengths on the IQH side, measuring decay away from edges of both the dimerization order parameter and transverse edge currents. The critical behavior and exponents are consistent with an Ising transition in 1+1 dimensions. Finally, we obtain excited states in various quantum number sectors finding that the gap to a charge neutral momentum $\pi$ excitation corresponding to fluctuations of the dimerization order parameter closes in the vicinity of the critical point but gaps to other excitations remain large.

cond-mat.str-el↗

arXiv2025

Site Basis Excitation Ansatz for Matrix Product States

We introduce a simple and efficient variation of the tangent-space excitation ansatz used to compute elementary excitation spectra of one-dimensional quantum lattice systems using matrix product states (MPS). A small basis for the excitation tensors is formed based on a single diagonalization analogous to a single site DMRG step but for multiple states. Once overlap and Hamiltonian matrix elements are found, obtaining the excitation for any momentum only requires diagonalization of a tiny matrix, akin to a non-orthogonal band-theory diagonalization. The approach is based on an infinite MPS description of the ground state, and we introduce an extremely simple alternative to variational uniform matrix product states (VUMPS) based on finite system DMRG. For the $S=1$ Heisenberg chain, our method -- site basis excitation ansatz (SBEA) -- efficiently produces the one-magnon dispersion with high accuracy. We also examine the role of MPS gauge choices, finding that not imposing a gauge condition -- leaving the basis nonorthogonal -- is crucial for the approach, whereas imposing a left-orthonormal gauge (as in prior work) severely hampers convergence. We also show how one can construct Wannier excitations, analogous to the Wannier functions of band theory, where one Wannier excitation, translated to all sites, can reconstruct the single magnon modes exactly for all momenta.

cond-mat.str-el↗

arXiv2025

The Saga of $α$-RuCl$_3$: Parameters, Models, and Phase Diagrams

RuCl$_3$ was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the $_{44}$Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form $α$-RuCl$_3$ rose to exceptional prominence. This "re-discovery" of $α$-RuCl$_3$ has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of $α$-RuCl$_3$, and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the non-trivial physical properties of this material. These constraints allow one to focus on the relevant region of the multi-dimensional phase diagram of the $α$-RuCl$_3$ model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the $α$-RuCl$_3$ parameter space using quasi-classical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization group methods, demonstrating a remarkably c... (arxiv cutoff; for the rest, see the paper)

cond-mat.str-el↗

arXiv2025

Ground-State-Based Model Reduction with Unitary Circuits

We present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wavefunction with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling, and obtain more accurate effective spin models than the standard perturbative approach.

cond-mat.str-el↗

arXiv2025

Phase Diagram of the Easy-Axis Triangular-Lattice $J_1\!-\!J_2$ Model

The phase diagram of the $S\!=\!1/2$ easy-axis triangular-lattice $J_1\!-\!J_2$ model is investigated using the density-matrix renormalization group and analytical insights. We find a significant spin-liquid region extending from the Heisenberg limit and residing between the Y phase-known as the magnetic analogue of the "supersolid"-and collinear stripe phase. The order parameters of the supersolid are analyzed and an understanding of its lack of ferromagnetic moment is suggested.

cond-mat.str-el↗

arXiv2025

Quantum Phases in the Honeycomb-Lattice $J_1$--$J_3$ Ferro-Antiferromagnetic Model

Using large-scale density-matrix renormalization group calculations and minimally augmented spin-wave theory, we demonstrate that the phase diagram of the quantum $S\!=\!\frac12$ $J_1$--$J_3$ ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-z phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases replace the classical spiral state.

cond-mat.str-el↗

arXiv2025

Unusual energy spectra of matrix product states

In approximate ground states obtained from imaginary-time evolution, the spectrum of the state -- its decomposition into exact energy eigenstates -- falls off exponentially with the energy. Here we consider the energy spectra of approximate matrix product ground states, such as those obtained with the density matrix renormalization group. Despite the high accuracy of these states, contributions to the spectra are roughly constant out to surprisingly high energy, with an increase in the bond dimension reducing the amplitude but not the extent of these high-energy tails. The unusual spectra appear to be a general feature of compressed wavefunctions, independent of boundary or dimensionality, and are also observed in neural network wavefunctions. The unusual spectra can have a strong effect on sampling-based methods, yielding large fluctuations. The energy variance, which can be used to extrapolate observables to eliminate truncation error, is subject to these large fluctuations when sampled. Nevertheless, we devise a sampling-based variance approach which gives excellent and efficient extrapolations.

cond-mat.str-el↗

arXiv2024

Variational Benchmarks for Quantum Many-Body Problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

quant-ph↗

arXiv2023

Quantum Fourier Transform Has Small Entanglement

The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would think it can introduce large entanglement to qubit systems and would be difficult to simulate classically. While early results showed QFT indeed has maximal operator entanglement, we show that this is entirely due to the bit reversal in the QFT. The core part of the QFT has Schmidt coefficients decaying exponentially quickly, and thus it can only generate a constant amount of entanglement regardless of the number of qubits. In addition, we show the entangling power of the QFT is the same as the time evolution of a Hamiltonian with exponentially decaying interactions, and thus a variant of the area law for dynamics can be used to understand the low entanglement intuitively. Using the low entanglement property of the QFT, we show that classical simulations of the QFT on a matrix product state with low bond dimension only take time linear in the number of qubits, providing a potential speedup over the classical fast Fourier transform (FFT) on many classes of functions. We demonstrate this speedup in test calculations on some simple functions. For data vectors of length $10^6$ to $10^8$, the speedup can be a few orders of magnitude.

quant-ph↗

arXiv2023

Nested Gausslet Basis Sets

We introduce nested gausslet (NG) bases, an improvement on previous gausslet bases which can treat systems containing atoms with much larger atomic number. We also introduce pure Gaussian distorted gausslet bases, which allow the Hamiltonian integrals to be performed analytically, as well as hybrid bases in which the gausslets are combined with standard Gaussian-type bases. All these bases feature the diagonal approximation for the electron-electron interactions, so that the Hamiltonian is completely defined by two $N_b\times N_b$ matrices, where $N_b \approx 10^4$ is small enough to permit fast calculations at the Hartree-Fock level. In constructing these bases we have gained new mathematical insight into the construction of one-dimensional diagonal bases. In particular we have proved an important theorem relating four key basis set properties: completeness, orthogonality, zero-moment conditions, and diagonalization of the coordinate operator matrix. We test our basis sets on small systems with a focus on high accuracy, obtaining, for example, an accuracy of $2\times10^{-5}$ Ha for the total Hartree-Fock energy of the neon atom in the complete basis set limit.

physics.chem-ph↗

arXiv2023

Density-matrix-renormalization-group-based downfolding of the three-band Hubbard model: the importance of density-assisted hopping

Typical Wannier-function downfolding starts with a mean-field or density functional set of bands to construct the Wannier functions. Here we carry out a controlled approach, using DMRG-computed natural orbital bands, to downfold the three-band Hubbard model to an effective single band model. A sharp drop-off in the natural orbital occupancy at the edge of the first band provides a clear justification for a single-band model. Constructing Wannier functions from the first band, we compute all possible two-particle terms and retain those with significant magnitude. The resulting single-band model includes two-site density-assisted hopping terms with $t_n \sim 0.6 t$. These terms lead to a reduction of the ratio $U/t_{\rm eff}$, and are important in capturing the doping-asymmetric carrier mobility, as well as in enhancing the pairing in a single-band model for the hole-doped cuprates.

cond-mat.str-el↗