arXiv subjects

Anders W. Sandvik

Publications and source records attributed to Anders W. Sandvik.

At least 19 recordsLinked to original sources

arXiv2026

Imaginary-time correlations in time-sliced stochastic series expansion

Combined with numerical analytic continuation techniques, quantum Monte Carlo (QMC) methods enable the extraction of real-frequency dynamical properties from imaginary-time correlation functions. However, the efficient computation of imaginary-time correlation functions by QMC simulations can (depending on the particular model used) be challenging, particularly for operators that are off-diagonal in the computational basis. In this work, we present an efficient and general algorithm within the stochastic series expansion (SSE) framework for evaluating imaginary-time correlation functions of both diagonal and off-diagonal operators. The algorithm builds on a discrete imaginary-time slicing of the SSE operator string, which provides correlation functions on a grid of well-defined imaginary-time points with no discretization error. For off-diagonal operators, we derive estimators that integrate directly into the existing SSE directed-loop or cluster updating schemes, introducing only minimal computational overhead. We benchmark the method on the one-dimensional transverse-field Ising model (sampling with cluster updates) and XXZ spin chain (using directed-loop sampling), demonstrating excellent agreement (with only statistical errors) with exact diagonalization of small systems. We also study larger systems to demonstrate efficiency.

cond-mat.str-el↗

arXiv2026

Single-hole spectral functions in one-dimensional quantum magnets with different ground states

Recent advances in numerical analytic continuation with physics-motivated constraints allow sharp spectral features to be extracted from imaginary-time quantum Monte Carlo (QMC) data. We apply these methods to one-dimensional $S=1/2$ spin systems with a single ejected fermion, computing the momentum- and energy-dependent single-hole spectral function $A(k,ω)$. The real-space Green's function $G(r,τ)$ is evaluated using Angelucci's canonical transformation [Phys. Rev. B 51, 11580 (1995)] implemented within stochastic series expansion QMC, and $A(k,ω)$ is obtained by constrained stochastic analytic continuation. We contrast systems exhibiting spin-charge separation with those forming a spin polaron through effective spin-charge attraction. For the conventional $t$-$J$ chain, we recover the established signatures of spin-charge separation. Adding a multispin interaction $Q$ drives the system into a spontaneously dimerized valence-bond-solid (VBS) state; spin-charge-separation features persist up to the transition. Although the spectra generally agree with the conventional analytical ansatz, we find a gap between two holon bands that the ansatz predicts to be degenerate at $k=0$ and $k=π$. Deep in the VBS phase, the spectra provide evidence for spinon-holon binding at large $Q/J$. In a statically dimerized $t$-$J$ chain, we observe equally spaced spin-polaron bands associated with increasingly large bound states and two internal modes, even and odd under parton permutation. These results demonstrate the power of constrained analytic continuation combined with large-scale QMC for resolving sharp spectral features and distinguishing fractionalized from bound excitations.

cond-mat.str-el↗

arXiv2026

Using operator covariance to disentangle scaling dimensions in lattice models

In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2Δ}$ governed by scaling dimensions $Δ$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions can be extracted by data fitting, which is difficult when two or more powers contribute significantly. Here a method utilizing covariance between multiple lattice operators is developed where the r dependent eigenvalues of the covariance matrix reflect scaling dimensions of individual field operators. This disentangling is demonstrated explicitly for conformal field theories. The scheme is first tested on the critical point of the 2D Ising model, where the two primary scaling dimensions and their respective two lowest descendant dimensions are extracted. The 3D Ising model is studied next, revealing the two relevant primaries and their lowest descendants to high precision. The 2D tricritical Ising point is studied with the Blume-Capel model. Here the scaling dimensions of all three symmetric primary operators are successfully isolated along with the leading descendants. The eigenvectors are also studied and give useful information on the boundary between the ordered and disordered phases in the neighborhood of the tricritical point. Finally, the crossover from regular to tricritical Ising scaling is investigated on several points on the phase boundary of the Blume-Capel model away from its tricritical point. The scaling of the eigenvalues corresponding to tricritical descendant operators are found to be remarkably stable even far from the tricritical point. The covariance method represents a simple extension of standard analysis of correlation functions and can significantly enhance the utility of Monte Carlo simulations and other computational methods in studies of criticality, in particular conformal critical points.

cond-mat.stat-mech↗

arXiv2026

Moiré magnetism in a bilayer Ising model

Moiré patterns in magnetic bilayers generate spatially modulated interlayer exchange interactions that can give rise to nonuniform magnetic textures. We study a minimal classical bilayer Ising model with a moiré-modulated interlayer coupling, generated either by relative twist or differential strain between the layers. Using large-scale classical Monte Carlo simulations, we show that the ordering transition remains in the conventional two-dimensional Ising universality class, even when the low-temperature state is domain-textured. At low temperatures, we find a smooth crossover between a uniform ferromagnet and domain-textured state, in which the spins locally follow the sign of the interlayer exchange. We demonstrate that there is no breaking of layer symmetry for twisted bilayers. The location of the crossover is determined by a simple geometric energy balance between bulk interlayer exchange and intralayer domain-wall costs. Our results provide a minimal framework for understanding how moiré-modulated magnetic textures can emerge from geometric energetics without requiring a thermodynamic phase transition.

cond-mat.stat-mech↗

arXiv2026

SU($N$) Quantum Spin Model with Weak and Strong First-Order Néel to Valence-Bond Solid Transitions

We introduce an SU($N$) symmetric two-dimensional quantum spin model, the X-Q model, which hosts a ground state transition between Néel antiferromagnetic and spontaneously dimerized states. The Q terms are products of two adjacent singlet projectors on first-neighbor sites, as in the often studied J-Q model (where J is the Heisenberg exchange), while the X terms are products of two permutation operators on second-neighbor sites. Quantum Monte Carlo simulations reveal close proximity to a deconfined quantum critical point for $N=2$, as in the J-Q model. However, for $N>2$ the transformation becomes strongly first order, contrary to conventional expectations that increasing $N$ should weaken discontinuities. We attribute this behavior to the inability of the X term, which dominates at the transition for large $N$, to induce significant U(1) fluctuations of the dimer pattern. These results provide insights into the microscopic interactions that support deconfined criticality.

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arXiv2026

High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice

Several ground state properties of the square-lattice $S=1/2$ Heisenberg antiferromagnet are computed (the energy, order parameter, spin stiffness, spinwave velocity, long-wavelength susceptibility, and staggered susceptibility) using extensive quantum Monte Carlo simulations with the stochastic series expansion method. Moderately sized lattices are studied at temperatures $T$ sufficiently low to realize the $T \to 0$ limit. Results for periodic $L\times L$ lattices with $L \in [6,96]$ are tabulated versus $L$ and extrapolations to infinite system size are carried out. The extrapolated ground state energy density is $e_0=-0.669441857(7)$, which represents an improvement in precision of three orders of magnitude over the previously best result. The leading and subleading finite-size corrections to $e_0$ are in full quantitative agreement with predictions from chiral perturbation theory, thus further supporting the soundness of both the extrapolations and the theory. The extrapolated sublattice magnetization is $m_s=0.307447(2)$, which agrees well with previous estimates but with a much smaller statistical error. The coefficient of the linear in $L^{-1}$ correction to $m^2_s$ agrees with the value from chiral perturbation theory and the presence of a factor $\ln^γ(L)$ in the second-order correction is also confirmed, with the previously not known value of the exponent being $γ= 0.82(4)$. The finite-size corrections to the staggered susceptibility point to logarithmic corrections also in this quantity. To facilitate benchmarking of methods for which periodic boundary conditions are challenging, results for systems with open and cylindrical boundaries are also listed and their spatially inhomogeneous order parameters are analyzed.

cond-mat.str-el↗

arXiv2025

Spinons and Spin-Charge Separation at the Deconfined Quantum Critical Point

Using quantum Monte Carlo and numerical analytic continuation methods, we study the dynamic spin structure factor and the single-hole spectral function of a two-dimensional quantum magnet ($J$-$Q$ model) at its quantum phase transition separating Néel antiferromagnetic and spontaneously dimerized ground states. At this putative deconfined quantum-critical point, we find a broad continuum of spinon excitations that can be accounted for by the fermionic $π$-flux state; a known mean-field model for deconfined quantum criticality. We find that the best description of the two-spinon continuum is with a version of the model with a $2\times 2$ unit cell, reflecting non-trivial mutual statistics of spinons and anti-spinons. The single-hole spectral function can be described by the same spinon dispersion relation and an independently propagating holon. Thus, the system exhibits spin-charge separation and will likely evolve into an extended holon metal phase at finite doping.

cond-mat.str-el↗

arXiv2025

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

quant-ph↗

arXiv2025

Single-Particle Dispersion and Density of States of the Half-Filled 2D Hubbard Model

Implementing an improved method for analytic continuation and working with imaginary-time correlation functions computed using quantum Monte Carlo simulations, we resolve the single-particle dispersion relation and the density of states (DOS) of the two-dimensional Hubbard model at half-filling. At intermediate interactions of $U/t = 4,6$, we find quadratic dispersion around the gap minimum at wave-vectors $\mathbf{k} = (\pm π/2, \pm π/2)$ (the $Σ$ points). We find saddle points at $\mathbf{k} = (\pm π,0),(0,\pm π)$ (the X points) where the dispersion is approximately quartic, leading to a sharp DOS maximum above the almost flat ledge arising from the states close to $Σ$. The fraction of quasiparticle states within the ledge is $n_{\rm ledge} \approx 0.15$. Upon doping away from half-filling, within the rigid-band approximation, these results support Fermi pockets around the $Σ$ points, with states around the X points becoming filled only at doping fractions $x \ge n_{\rm ledge}$. The high density of states away from the $Σ$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.

cond-mat.str-el↗

arXiv2025

Defects and their Time Scales in Quantum and Classical Annealing of the Two-Dimensional Ising Model

We investigate defects in the two-dimensional transverse-field Ising ferromagnet on periodic $L\times L$ lattices after quantum annealing from high to vanishing field. With exact numerical solutions for $L \le 6$, we observe the expected critical Kibble-Zurek (KZ) time scale $\propto L^{z+1/ν}$ (with $z=1$ and $1/ν\approx 1.59$) at the quantum phase transition. We also observe KZ scaling of the ground-state fidelity at the end of the process. The excitations evolve by coarsening dynamics of confined defects, with a time scale $\propto L^2$, and interface fluctuations of system-spanning defects, with life time $\propto L^3$. We build on analogies with classical simulated annealing, where we characterize system-spanning defects in detail and find differences in the dynamic scales of domain walls with winding numbers $W=(1,0)/(0,1)$ (horizontal/vertical) and $W=(1,1)$ (diagonal). They decay on time scales $\propto L^3$ (which applies also to system-spanning domains in systems with open boundaries) and $\propto L^{3.4}$, respectively, when imposed in the ordered phase. As a consequence of $L^{3.4}$ exceeding the classical KZ scale $L^{z+1/ν}=L^{3.17}$ the probability of $W=(1,1)$ domains in SA scales with the KZ exponent even in the final $T=0$ state. In QA, also the $W=(1,0)/(0,1)$ domains are controlled by the KZ time scale $L^{2.59}$. The $L^3$ scale can nevertheless be detected in the excited states, using a method that we develop that should also be applicable in QA experiments.

quant-ph↗

arXiv2025

Dynamic structure factor of a spin-1/2 Heisenberg chain with long-range interactions

We study the dynamic structure factor $S(k,ω)$ of the spin-1/2 chain with long-range, power-law decaying unfrustrated (sign alternating) Heisenberg interactions $J_r \sim (-1)^{r-1} r^{-α}$ by means of stochastic analytic continuation (SAC) of imaginary-time correlations computed by quantum Monte Carlo calculations. We do so in both the long-range antiferromagnetic (AFM, for $α\lesssim 2.23$) and quasi-long-range-ordered (QLRO, for $α\gtrsim 2.23$) ground-state phases, employing different SAC parametrizations of $S(k,ω)$ to resolve sharp edges characteristic of fractional quasi-particles and sharp peaks expected with conventional quasi-particles. In order to identify the most statistically accurate parametrization, we apply a newly developed cross-validation method as a ``model selection'' tool. We confirm that the spectral function contains a power-law divergent edge in the QLRO phase and a very sharp (likely $δ$-function) magnon peak in the AFM phase. From our SAC results, we extract the dispersion relation in the different regimes of the model, and in the AFM phase we extract the weight of the magnon pole. In the limit where the model reduces to the conventional Heisenberg chain with nearest-neighbor interactions, our $S(k,ω)$ agrees well with known Bethe ansatz results. In the AFM phase the low-energy dispersion relation is known to be nonlinear, $ω_k \sim k^z$, and we extract the corresponding dynamic exponent $z(α)$, which in general is somewhat above the form obtained in linear spin-wave theory. We also find a significant continuum above the magnon peak. This study serves as a benchmark for SAC/QMC studies of systems with a transition from conventional to fractionalized quasi-particles.

cond-mat.str-el↗

arXiv2025

Multiscale Excitations in the Diluted Two-dimensional S = 1/2 Heisenberg Antiferromagnet

We study the excitation spectrum of the $S=1/2$ Heisenberg model on the randomly diluted square lattice by analytic continuation of QMC data. At dilution fractions $p=1/16$ and $p=1/8$, the dynamic structure factor $S({\bf q},ω)$ exhibits a damped magnon peak with anomalous dispersion near ${\bf q}=(0,0)$ and $(π,π)$, a non-dispersive low-energy localization peak, and a second peak between these two features. A magnon with anomalous dispersion, close to our result, was predicted in spin wave and $T$-matrix theory [A. Chernyshev et al., PRB {\bf 65}, 104407 (2002)], above the localization energy. However, no intermediate mode was predicted. Analyzing spectral functions in real space for individual vacancy realizations by energy tomography, we find that these excitations are concentrated on a small subset of the spins adjacent to vacancies. We argue that the low-energy excitations are those of a sparse random network of effective moments at a fraction of the vacancies. There is a shift in magnon spectral weight distribution, from the spins away from vacancies at high energy to those adjacent to vacancies at lower energy. We also analyze the Anderson quantum rotor excitation at $ω\propto N^{-1}$ (with $N=L^2$ the system size), which in the clean system is visible in $S({\bf q},ω)$ only at ${\bf q}=(π,π)$ but spreads through the Brillouin zone when $p>0$. Weight close to ${\bf q}=(0,0)$ and $(π,π)$ is explained by local sublattice imbalance within a dimer-monomer model but there is also structure arising from correlated singlet fluctuations, which we demonstrate by enhancing said fluctuations with four-spin couplings. All spectral features found here should be observable by elastic neutron scattering experiments on layered quantum antiferromagnets doped with nonmagnetic impurities.

cond-mat.str-el↗

arXiv2025

Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point

Deconfined quantum criticality (DQC) arises from fractionalization of quasi-particles and leads to fascinating behaviors beyond the Landau-Ginzburg-Wilson description of phase transitions. Here, we study the critical dynamics when driving a two-dimensional quantum magnet through a weakly first-order transition point near a putative deconfined multicritical point separating antiferromagnetic and spontaneously dimerized ground states. Numerical simulations show that the conventional Kibble-Zurek scaling (KZS) mechanism is inadequate for describing the annealing process. We introduce the concept of dual asymmetric KZS, where both a pseudocritical relaxation time and the deconfinement time enter and the scaling also depends on the driving direction according to a duality principle connecting the topological defects in the two phases. These defects require a much longer time scale for equilibration than the amplitude of the order parameter. Beyond advancing the DQC scenario, our scaling approach provides a new window into out-of-equilibrium criticality with multiple length and time scales.

cond-mat.str-el↗

arXiv2025

Comment on: "Dynamics of disordered quantum systems with two- and three-dimensional tensor networks" arXiv:2503.05693

In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in some cases show lower errors than recent simulations of quantum dynamics using a quantum annealer [2] (King et al., Science, eado6285, 2025). However, of the simulations in Ref. [2], Ref. [1] did not attempt the most complex lattice geometry, nor reproduce the largest simulations in 3D lattices, nor simulate the longest simulation times, nor simulate the low-precision ensembles in which correlations grow the fastest, nor produce the full-state and fourth-order observables produced by Ref. [2]. Thus this work should not be misinterpreted as having overturned the claim of Ref. [2]: the demonstration of quantum simulations beyond the reach of classical methods. Rather, these classical advances narrow the parameter space in which beyond-classical computation has been demonstrated. In the near future these classical methods can be combined with quantum simulations to help sharpen the boundary between classical and quantum simulability.

quant-ph↗

arXiv2025

Ground state of the S = 1/2 Heisenberg spin chain with random ferro- and antiferromagnetic couplings

We study the Heisenberg $S=1/2$ chain with random ferro- and antiferromagnetic couplings using quantum Monte Carlo simulations at ultra-low temperatures, converging to the ground state. Finite-size scaling of correlation functions and excitation gaps demonstrate an exotic critical state in qualitative agreement with previous strong-disorder renormalization group calculations but with scaling exponents depending on the coupling distribution. We find dual scaling regimes of the transverse correlations versus the distance, with an $L$ independent form $C(r)=r^{-μ}$ for $r \ll L$ and $C(r,L)=L^{-η}f(r/L)$ for $r/L > 0$, where $μ> η$ and the scaling function is delivered by our analysis. These results are at variance with previous spin-wave and density-matrix renormalization group calculations, thus highlighting the power of unbiased quantum Monte Carlo simulations.

cond-mat.str-el↗

arXiv2024

Cross Validation in Stochastic Analytic Continuation

Stochastic Analytic Continuation (SAC) of Quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experimentally measurable dynamic response functions. Recent developments of the SAC method have allowed for spectral functions with sharp features, e.g. narrow peaks and divergent edges, to be resolved with unprecedented fidelity. Often times, it is not known what exact sharp features, if any, are present \textit{a priori}, and, due to the ill-posed nature of the analytic continuation problem, multiple spectral representations may be acceptable. In this work, we borrow from the machine learning and statistics literature and implement a cross validation technique to provide an unbiased method to identify the most likely spectrum amongst a set obtained with different spectral parameterizations and imposed constraints. We demonstrate the power of this method with examples using imaginary-time data generated by QMC simulations and synthetic data generated from artificial spectra. Our procedure, which can be considered a form of model selection, can be applied to a variety of numerical analytic continuation methods, beyond just SAC.

cond-mat.str-el↗

arXiv2024

Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition

We study the Rényi entanglement entropy (EE) of the two-dimensional $J$-$Q$ model, the emblematic quantum spin model of deconfined criticality at the phase transition between antiferromagnetic and valence-bond-solid ground states. State-of-the-art quantum Monte Carlo calculations of the EE reveal critical corner contributions that scale logarithmically with the system size, with a coefficient in remarkable agreement with the form expected from a large-$N$ conformal field theory with SO($N=5$) symmetry. However, details of the bipartition of the lattice are crucial in order to observe this behavior. If the subsystem for the reduced density matrix does not properly accommodate valence-bond fluctuations, logarithmic contributions appear even for corner-less bipartitions. We here use a $45^\circ$ tilted cut on the square lattice. Beyond supporting an SO($5$) deconfined quantum critical point, our results for both the regular and tilted cuts demonstrate important microscopic aspects of the EE that are not captured by conformal field theory.

cond-mat.str-el↗

arXiv2024

Unconventional U(1) to $\mathbf{Z_q}$ cross-over in quantum and classical ${\bf q}$-state clock models

We consider two-dimensional $q$-state quantum clock models with quantum fluctuations connecting states with clock transitions with different choices for matrix elements. We study the quantum phase transitions in these models using quantum Monte Carlo simulations, with the aim of characterizing the cross-over from emergent U(1) symmetry at the transition (for $q \ge 4$) to $Z_q$ symmetry of the ordered state. We also study classical three-dimensional clock models with spatial anisotropy corresponding to the space-time anisotropy of the quantum systems. The U(1) to ${Z_q}$ symmetry cross-over in all these systems is governed by a dangerously irrelevant operator. We specifically study $q=5$ and $q=6$ models with different forms of the quantum fluctuations and different anisotropies in the classical models. We find the expected classical XY critical exponents and scaling dimensions $y_q$ of the clock fields. However, the initial weak violation of the U(1) symmetry in the ordered phase, characterized by a $Z_q$ symmetric order parameter $ϕ_q$, scales in an unexpected way. As a function of the system size $L$, close to the critical temperature $ϕ_q \propto L^p$, where the known value of the exponent is $p=2$ in the classical isotropic clock model. In contrast, for strongly anisotropic classical models and the quantum models we find $p=3$. For weakly anisotropic classical models we observe a cross-over from $p=2$ to $p=3$ scaling. The exponent $p$ directly impacts the exponent $ν'$ governing the divergence of the U(1) to $Z_q$ cross-over length scale $ξ'$ in the thermodynamic limit, according to the relationship $ν'=ν(1+|y_q|/p)$, where $ν$ is the conventional correlation length exponent. We present a phenomenological argument based on an anomalous renormalization of the clock field in the presence of anisotropy, possibly as a consequence of topological (vortex) line defects.

cond-mat.str-el↗