About

Anders Sandvik is a professor in the Department of Physics at Boston University, specializing in computational research on interacting quantum many-body systems, with a particular focus on quantum spin systems. His research involves developing algorithms for simulations of complex model systems and using these methods to study collective phenomena such as quantum phase transitions. Sandvik has made significant contributions to the understanding of quantum criticality, quantum glass states, and the dynamics of spin systems through his computational approaches. He holds a Master of Science degree from Åbo Akademi University obtained in 1989 and a Ph.D. from the University of California, Santa Barbara, earned in 1993. His work has been recognized with honors including being a Simons Fellow in Theoretical Physics, a Fellow of the American Physical Society, and the Per Brahe Science Prize in 2001. Sandvik is actively involved in the academic community, contributing to research, mentoring students, and advancing the field of condensed matter physics.

Research topics

• Physics
• Quantum mechanics
• Statistical physics
• Condensed matter physics

Selected publications

• Beyond-classical computation in quantum simulation

  Science · 2025-03-12 · 92 citations

  articleOpen access

  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.

  PublisherOA PDFDOI

• Equilibration of topological defects near the deconfined quantum multicritical point

  Nature Communications · 2025-04-10 · 8 citations

  articleOpen access

  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.

  PublisherDOI

• Single-particle dispersion and density of states of the half-filled two-dimensional Hubbard model

  Physical review. B./Physical review. B · 2025-08-07 · 2 citations

  articleSenior author

  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 $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ (the $\mathrm{\ensuremath{\Sigma}}$ points). We find saddle points at $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0),(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$ (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 $\mathrm{\ensuremath{\Sigma}}$. The fraction of quasiparticle states within the ledge is ${n}_{\mathrm{ledge}}\ensuremath{\approx}0.15$. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the $\mathrm{\ensuremath{\Sigma}}$ points, with states around the $X$ points becoming filled only at doping fractions $x\ensuremath{\ge}{n}_{\mathrm{ledge}}$. The high density of states away from the $\mathrm{\ensuremath{\Sigma}}$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.

  PublisherDOI

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

  Physical review. B./Physical review. B · 2025-06-03 · 1 citations

  preprintOpen accessSenior author

  We study the dynamic structure factor $S(k,\ensuremath{\omega})$ of the spin-1/2 chain with long-range, power-law decaying unfrustrated (sign-alternating) Heisenberg interactions ${J}_{r}\ensuremath{\sim}{(\ensuremath{-}1)}^{r\ensuremath{-}1}{r}^{\ensuremath{-}\ensuremath{\alpha}}$ by means of stochastic analytic continuation (SAC) of imaginary-time correlations computed by quantum Monte Carlo (QMC) calculations. We do so in both the long-range antiferromagnetic (AFM, for $\ensuremath{\alpha}\ensuremath{\lesssim}2.23$) and quasi-long-range-ordered (QLRO, for $\ensuremath{\alpha}\ensuremath{\gtrsim}2.23$) ground-state phases, employing different SAC parametrizations of $S(k,\ensuremath{\omega})$ to resolve sharp edges characteristic of fractional quasiparticles and sharp peaks expected with conventional quasiparticles. 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 $\ensuremath{\delta}$-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 $S(k,\ensuremath{\omega})$ agrees well with known Bethe-ansatz results. In the AFM phase the low-energy dispersion relation is known to be nonlinear, ${\ensuremath{\omega}}_{k}\ensuremath{\sim}{k}^{z}$, and we extract the corresponding dynamic exponent $z(\ensuremath{\alpha})$, 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 and QMC studies of systems with a transition from conventional to fractionalized quasiparticles.

  PublisherOA PDFDOI

• Ground State of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> Heisenberg Spin Chain with Random Ferromagnetic and Antiferromagnetic Couplings

  Physical Review Letters · 2025-02-24 · 2 citations

  articleSenior author

  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≪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.

  PublisherDOI

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

  ArXiv.org · 2025-03-25

  preprintOpen access

  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.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-12-02

  preprintOpen accessSenior author

  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.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-04-03

  preprintOpen accessSenior author

  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.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-07-12

  preprintOpen accessSenior author

  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.

  PublisherOA PDFDOI

• Using operator covariance to disentangle scaling dimensions in lattice models

  arXiv (Cornell University) · 2024-06-18

  preprintOpen access1st authorCorresponding

  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.

  PublisherOA PDFDOI

Recent grants

• Simulation studies of ground state phases and criticality in correlated quantum matter

  NSF · $375k · 2011–2014

• Simulation Studies of Ground State Phases and Criticality in Correlated Quantum Matter

  NSF · $426k · 2017–2020

• PIF: Quantum Monte Carlo Methods for Non-Equilibrium Dynamics of Interacting Quantum Many-Body Systems

  NSF · $345k · 2012–2015

• Simulation Studies of Ground State Phases and Criticality in Correlated Quantum Matter

  NSF · $246k · 2005–2008

• Simulation studies of ground state phases and criticality in correlated quantum matter

  NSF · $396k · 2014–2017

Frequent coauthors

• Wenan Guo

  72 shared

• Hui Shao

  Beijing Normal University

  62 shared

• Shiliang Li

  55 shared

• Zi Yang Meng

  51 shared

• Jun Takahashi

  37 shared

• Ling Wang

  Zhejiang University

  33 shared

• Nvsen Ma

  Beihang University

  31 shared

• Elbio Dagotto

  University of Tennessee at Knoxville

  29 shared

Education

• Ph.D., Physics

  University of California, Santa Barbara

  1995

• M.S., Physics

  University of California, Santa Barbara

  1991

• B.S., Physics

  University of California, Santa Barbara

  1989

Awards & honors

• Simons Fellow in Theoretical Physics
• Fellow of the American Physical Society
• Per Brahe Science Prize (2001)