arXiv subjects

Steven Johnston

Publications and source records attributed to Steven Johnston.

At least 37 records · Page 2Linked to original sources

arXiv2024

SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl. It also provides detailed benchmarks of the package's output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

cond-mat.stat-mech↗

arXiv2024

Classical dynamics of the antiferromagnetic Heisenberg $S=1/2$ spin ladder

We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the $S = 1/2$ ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical approximation with density matrix renormalization group and exact diagonalization calculations in finite size ladders, we demonstrate that the classical dynamics offers an accurate approximation across the entire temperature range when the interdimer coupling is weak and a good approximation in the high temperature regime even when the interdimer coupling is strong. This agreement is achieved after appropriately rescaling the temperature axis and renormalizing expectation values to satisfy a quantum sum rule, following D. Dahlbom et al. [Phys. Rev. B 109, 014427 (2024)]. We anticipate the method will be particularly effective when applied to 2D and 3D lattices composed of weakly-coupled dimers, situations that remain challenging for alternative numerical methods.

cond-mat.str-el↗

arXiv2024

Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger Model and its relevance to Graphene

We perform sign-problem-free determinant quantum Monte Carlo simulations of the optical Su-Schrieffer-Heeger (SSH) model on a half-filled honeycomb lattice. In particular, we investigate the model's semi-metal (SM) to Kekul{é} Valence Bond Solid (KVBS) phase transition at zero and finite temperatures as a function of phonon energy and interaction strength. Using hybrid Monte Carlo sampling methods we can simulate the model near the adiabatic regime, allowing us to access regions of parameter space relevant to graphene. Our simulations suggest that the SM-KVBS transition is weakly first-order at all temperatures, with graphene situated close to the phase boundary in the SM region of the phase diagram. Our results highlight the important role bond-stretching phonon modes play in the formation of KVBS order in strained graphene-derived systems.

cond-mat.str-el↗

arXiv2024

Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model

Most nonperturbative numerical studies of electron-phonon interactions focus on model Hamiltonians where the electrons interact with a phonon branch via a single type of microscopic mechanism. Two commonly explored couplings in this context are the Holstein and Su-Schrieffer-Heeger (SSH) interactions, which describe phonons modulating the on-site energy and intersite electron hopping, respectively. Many materials, however, have multiple phonon branches that can each interact with electronic degrees of freedom in different ways. We present here a determinant quantum Monte Carlo study of the half-filled two-dimensional (bond) SSH-Holstein Hamiltonian, where electrons couple to different phonon branches via either the Holstein or SSH mechanism. We map the model's phase diagram and determine the nature of the transitions between charge-density wave, bond order wave, and antiferromagnetic order.

cond-mat.str-el↗

arXiv2023

A comparative study of the superconductivity in the Holstein and optical Su-Schrieffer-Heeger models

Theoretical studies suggest that Su-Schrieffer-Heeger-like electron-phonon ($e$-ph) interactions can mediate high-temperature bipolaronic superconductivity that is robust against repulsive electron-electron interactions. Here we present a comparative analysis of the pairing and competing charge/bond correlations in the two-dimensional Holstein and optical Su-Schrieffer-Heeger (SSH) models using numerically exact determinant quantum Monte Carlo. We find that the SSH interactions support light bipolarons and strong superconducting correlations out to relatively large values of the $e$-ph coupling $λ$ and densities near half-filling, while the Holstein interaction does not due to the formation of heavy bipolarons and competing charge-density-wave order. We further find that the Holstein and SSH models have comparable pairing correlations in the weak coupling limit for carrier concentrations $\langle n \rangle \ll 1$, where competing orders and polaronic effects are absent. These results support the proposal that SSH (bi)polarons can support superconductivity to larger values of $λ$ in comparison to the Holstein polaron, but that the resulting $T_\mathrm{c}$ gains are small in the weak coupling limit. We also find that the SSH model's pairing correlations are suppressed after including a weak on-site Hubbard repulsion. These results have important implications for identifying and engineering bipolaronic superconductivity.

cond-mat.supr-con↗

arXiv2023

A comparative determinant quantum Monte Carlo study of the acoustic and optical variants of the Su-Schrieffer-Heeger model

We compare the acoustic Su-Schrieffer-Heeger (SSH) model with two of its optical variants where the phonons are defined on either on the sites or bonds of the system. First, we discuss how to make fair comparisons between these models in any dimension by ensuring their dimensionless coupling $λ$ and relevant phonon energies are the same. We then use determinant quantum Monte Carlo to perform non-perturbative and sign-problem-free simulations of all three models on one-dimensional chains at and away from half-filling. By comparing the results obtained from each model, we demonstrate that the optical and acoustic models produce near identical results within error bars for suitably chosen phonon energies and $λ$ at half-filling. In contrast, the bond model has quantitatively different behavior due to its coupling to the $q = 0$ phonon mode. These differences also manifest in the total length of the chain, which shrinks for the bond model but not for the acoustic and optical models when $λ\neq 0$. Our results have important implications for quantum Monte Carlo modeling of SSH-like interactions, where these models are sometimes regarded as being interchangeable

cond-mat.str-el↗

arXiv2023

Charge order in the kagome lattice Holstein model: A hybrid Monte Carlo study

The Holstein model is a paradigmatic description of the electron-phonon interaction, in which electrons couple to local dispersionless phonon modes, independent of momentum. The model has been shown to host a variety of ordered ground states such as charge density wave (CDW) order and superconductivity on several geometries, including the square, honeycomb, and Lieb lattices. In this work, we study CDW formation in the Holstein model on the kagome lattice, using a recently developed hybrid Monte Carlo simulation method. We present evidence for $\sqrt{3} \times \sqrt{3}$ CDW order at an average electron filling of $\langle n \rangle =2/3$ per site, with an ordering wavevector at the $K$-points of the Brillouin zone. We estimate a phase transition occurring at $T_{c}\approx t/18$, where $t$ is the nearest-neighbor hopping parameter. Our simulations find no signature of CDW order at other electron fillings or ordering momenta for temperatures $T \geq t/20$.

cond-mat.str-el↗

arXiv2023

A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in BaBiO$_3$

The relationship between electron-phonon ($e$-ph) interactions and charge-density-wave (CDW) order in the bismuthate family of high-temperature superconductors remains unresolved. We address this question using nonperturbative hybrid Monte Carlo calculations for the parent compound BaBiO$_3$. Our model includes the Bi $6s$ and O $2p_σ$ orbitals and coupling to the Bi-O bond-stretching branch of optical phonons via modulations of the Bi-O hopping integral. We simulate three-dimensional clusters of up to 4000 orbitals, with input model parameters taken from {\it ab initio} electronic structure calculations and a phonon energy $\hbarΩ_0 = 60$~meV. Our results demonstrate that the coupling to the bond-stretching modes is sufficient to reproduce the CDW transition in this system, despite a relatively small dimensionless coupling. We also find that the transition deviates from the weak-coupling Peierls' picture. This work demonstrates that off-diagonal $e$-ph interactions in orbital space are vital in establishing the bismuthate phase diagram.

cond-mat.str-el↗

arXiv2023

A flexible class of exact Hubbard-Stratonovich transformations

We consider a class of Hubbard-Stratonovich transformations suitable for treating Hubbard interactions in the context of quantum Monte Carlo simulations. A tunable parameter $p$ allows us to continuously vary from a discrete Ising auxiliary field ($p=\infty$) to a compact auxiliary field that couples to electrons sinusoidally ($p=0$). In tests on the single-band Hubbard model, we find that the severity of the sign problem decreases systematically with increasing $p$. Selecting $p$ finite, however, enables continuous sampling methods like the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

cond-mat.str-el↗

arXiv2023

Ground state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model

We present a density matrix renormalization group (DMRG) study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Hegger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground and excited state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon ($e$-ph) coupling strengths below a parameter-dependent critical value $g_\mathrm{c}$. For larger $e$-ph coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e$-ph coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.

cond-mat.str-el↗

arXiv2023

Charge correlations suppress unconventional pairing in the Holstein model

In a recent work by Schrodi $\textit{et al}$. [Phys. Rev. B. $\textbf{104}$, L140506 (2021)], the authors find an unconventional superconducting state with a sign-changing order parameter using the Migdal-Eliashberg theory, including the first vertex correction. This unconventional solution arises despite using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting band structure and identical parameters to Schrodi $\textit{et al}$.. Our Monte Carlo results for these parameters suggest that unconventional pairing correlations do not exceed their noninteracting values at any carrier concentration we have checked. Instead, strong charge-density-wave correlations persist at the lowest accessible temperatures for dilute and nearly half-filled bands. Lastly, we present arguments for how vertex-corrected Migdal-Eliashberg calculation schemes can lead to uncontrolled results in the presence of Fermi surface nesting.

cond-mat.supr-con↗

arXiv2023

A Group-Equivariant Autoencoder for Identifying Spontaneously Broken Symmetries

We introduce the group-equivariant autoencoder (GE-autoencoder) -- a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use group theory to deduce which symmetries of the system remain intact in all phases, and then use this information to constrain the parameters of the GE-autoencoder such that the encoder learns an order parameter invariant to these ``never-broken'' symmetries. This procedure produces a dramatic reduction in the number of free parameters such that the GE-autoencoder size is independent of the system size. We include symmetry regularization terms in the loss function of the GE-autoencoder so that the learned order parameter is also equivariant to the remaining symmetries of the system. By examining the group representation by which the learned order parameter transforms, we are then able to extract information about the associated spontaneous symmetry breaking. We test the GE-autoencoder on the 2D classical ferromagnetic and antiferromagnetic Ising models, finding that the GE-autoencoder (1) accurately determines which symmetries have spontaneously broken at each temperature; (2) estimates the critical temperature in the thermodynamic limit with greater accuracy, robustness, and time-efficiency than a symmetry-agnostic baseline autoencoder; and (3) detects the presence of an external symmetry-breaking magnetic field with greater sensitivity than the baseline method. Finally, we describe various key implementation details, including a new method for extracting the critical temperature estimate from trained autoencoders and calculations of the DNN initialization and learning rate settings required for fair model comparisons.

cond-mat.stat-mech↗

arXiv2023

Stripe Symmetry of Short-range Charge Density Waves in Cuprate Superconductors

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios has been challenging for the short-range CDW in bismuth-based cuprates. Here, we employed high-resolution resonant inelastic x-ray scattering to uncover the spatial symmetry of the CDW in Bi$_2$Sr$_{2-x}$La$_{x}$CuO$_{6+δ}$. Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes were found in reciprocal space. Based on Fourier transform analysis of real-space models, we interpret the results as evidence of unidirectional charge stripes, hosted by mutually 90$^\circ$-rotated anisotropic domains. Our work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

cond-mat.str-el↗

arXiv2022

Robust charge-density wave correlations in the electron-doped single-band Hubbard model

There is growing evidence that the hole-doped single-band Hubbard and $t$-$J$ models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

cond-mat.str-el↗

arXiv2022

A Symbolic Representation of Human Posture for Interpretable Learning and Reasoning

Robots that interact with humans in a physical space or application need to think about the person's posture, which typically comes from visual sensors like cameras and infra-red. Artificial intelligence and machine learning algorithms use information from these sensors either directly or after some level of symbolic abstraction, and the latter usually partitions the range of observed values to discretize the continuous signal data. Although these representations have been effective in a variety of algorithms with respect to accuracy and task completion, the underlying models are rarely interpretable, which also makes their outputs more difficult to explain to people who request them. Instead of focusing on the possible sensor values that are familiar to a machine, we introduce a qualitative spatial reasoning approach that describes the human posture in terms that are more familiar to people. This paper explores the derivation of our symbolic representation at two levels of detail and its preliminary use as features for interpretable activity recognition.

cs.AI↗

arXiv2022

Stripe correlations in the two-dimensional Hubbard-Holstein model

Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon ($e$-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped singleband Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping $t^\prime$ or phonon energy $Ω$. Our results help elucidate how the $e$-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-$T_\mathrm{c}$ cuprates.

cond-mat.str-el↗

arXiv2022

Suppressed superexchange interactions in the cuprates by bond-stretching oxygen phonons

We study a multi-orbital Hubbard--Su-Schrieffer-Heeger model for the one-dimensional (1D) corner-shared cuprates in the adiabatic and nonadiabatic limits using the exact diagonalization and determinant quantum Monte Carlo methods. Our results demonstrate that lattice dimerization can be achieved only over a narrow range of couplings slightly below a critical coupling $g_c$ at half-filling. Beyond this critical coupling, the sign of the effective hopping changes, and the lattice becomes unstable. We also examine the model's temperature-dependent uniform magnetic susceptibility and the dynamical magnetic susceptibility and compare them to the results of an effective spin-$1/2$ Heisenberg model. In doing so, we numerically demonstrate that the lattice fluctuation induced by the $e$-ph interaction suppresses the effective superexchange interaction. Our results elucidate the effect of bond-stretching phonons in the parent cuprate compounds in general and are particularly relevant to 1D cuprates, where strong $e$-ph interactions have recently been inferred.

cond-mat.str-el↗

arXiv2022

Embedding Causal Sets into Minkowski Spacetime

We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to construct matrices of inner products which are then factored using the singular value decomposition to give coordinates in Minkowski spacetime. Results are presented showing good quality embeddings into Minkowski spacetime for dimensions d=2,3,4. The method applies in any dimension and does not require spacelike distances to be used as an input. It offers a new way to define spatial orientation and spacelike distances in a causal set.

gr-qc↗