Quantum Critical Points and the Sign Problem

Abstract

The "sign problem" (SP) is the fundamental limitation to simulations of strongly correlated materials in condensed matter physics, solving quantum chromodynamics at finite baryon density, and computational studies of nuclear matter. As a result, it is part of the reason fields such as ultra-cold atomic physics are so exciting: they can provide quantum emulators of models that could not otherwise be solved, due to the SP. For the same reason, it is also one of the primary motivations behind quantum computation. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians, since the details of how it onsets, and its eventual occurrence, can be altered by the choice of algorithm or many-particle basis. Despite that, we show that the SP in determinant quantum Monte Carlo (DQMC) is quantitatively linked to quantum critical behavior. We demonstrate this via simulations of a number of fundamental models of condensed matter physics, including the spinful and spinless Hubbard Hamiltonians on a honeycomb lattice and the ionic Hubbard Hamiltonian, all of whose critical properties are relatively well understood. We then propose a reinterpretation of the low average sign for the Hubbard model on the square lattice when away from half-filling, an important open problem in condensed matter physics, in terms of the onset of pseudogap behavior and exotic superconductivity. Our study charts a path for exploiting the average sign in QMC simulations to understand quantum critical behavior, rather than solely as an obstacle that prevents quantum simulations of many-body Hamiltonians at low temperature.

11+13 pages, 4+11 Figures

References in corpus (101)

• Quantum Computing in the NISQ era and beyond
• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Cluster Theories
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Quantum Monte Carlo methods for nuclear physics
• The QCD phase diagram for small densities from imaginary chemical potential
• Continuous Time Quantum Monte Carlo method for fermions
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• The QCD thermal phase transition in the presence of a small chemical potential
• Fermi-Hubbard physics with atoms in an optical lattice
• Interactions and phase transitions on graphene's honeycomb lattice
• Tools for quantum simulation with ultracold atoms in optical lattices
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Quantum Monte Carlo calculations of A=8 nuclei
• A Constrained Path Monte Carlo Method for Fermion Ground States
• Quantum Algorithms for Fermionic Simulations
• High density QCD on a Lefschetz thimble?
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• The Dynamical Cluster Approximation: Non-Local Dynamics of Correlated Electron Systems
• Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
• Meron-Cluster Solution of Fermion Sign Problems
• Imaginary chemical potential and finite fermion density on the lattice
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Pressure and non-linear susceptibilities in QCD at finite chemical potentials
• Deviations from Fermi-liquid behavior above $T_c$ in 2D short coherence length superconductors
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• From band insulator to Mott insulator in one dimension
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards quantitative theory
• A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
• Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Diagrammatic Monte Carlo
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Variational and Diffusion Quantum Monte Carlo Calculations with the CASINO Code
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• Nature of the spin liquid state of the Hubbard model on honeycomb lattice
• Strange metallicity in the doped Hubbard model
• Recent Developments of World-Line Monte Carlo Methods
• Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
• Using Quantum Computers for Quantum Simulation
• Can correlations drive a band insulator metallic?
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Quantum critical behavior of the one-dimensional ionic Hubbard model
• Quantum Monte Carlo Methods in Nuclear Physics: Recent Advances
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Lowering qubit requirements for quantum simulations of fermionic systems
• Geometry Dependence of the Sign Problem
• Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
• Exact Quantum Monte Carlo Process for the Statistics of Discrete Systems
• Quantum Monte Carlo Study of an Interaction-Driven Band Insulator to Metal Transition
• Topological phase transitions in the repulsively interacting Haldane-Hubbard model
• Quantum Critical Points and the Sign Problem
• The fermion bag approach to lattice field theories
• Ab initio effective Hamiltonians for cuprate superconductors
• Easing the Monte Carlo sign problem
• Solution to sign problems in half-filled spin-polarized electronic systems
• Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Conducting phase in the two-dimensional disordered Hubbard model
• Atomic nuclei from quantum Monte Carlo calculations with chiral EFT interactions
• Nature of the insulating phases in the half-filled ionic Hubbard model
• Metallic phase in the two-dimensional ionic Hubbard model
• Finite-temperature Auxiliary-Field Quantum Monte Carlo: Self-Consistent Constraint and Systematic Approach to Low Temperatures
• Symmetry-projected Wave Functions in Quantum Monte Carlo Calculations
• The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations
• Effective Hamiltonian for cuprate superconductors derived from multi-scale ab initio scheme with level renormalization
• Unified quantitative model for magnetic and electronic spectra of the undoped cuprates
• The 2D Hubbard model on the honeycomb lattice
• Lifshitz Transition in the Two Dimensional Hubbard Model
• Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator
• Electronic phase transitions in the half-filled ionic Hubbard model
• Lefschetz thimbles decomposition for the Hubbard model on the hexagonal lattice
• Applying the tempered Lefschetz thimble method to the Hubbard model away from half-filling
• Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory
• Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder
• Negative sign problem in continuous-time quantum Monte Carlo: optimal choice of single-particle basis for impurity problems
• Multi-orbital cluster dynamical mean-field theory with an improved continuous-time quantum Monte Carlo algorithm
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Effect of Disorder on Charge Density Wave and Superconducting Order in the Half-Filled Attractive Hubbard Model
• Interacting electrons in a two-dimensional disordered environment: Effect of a Zeeman magnetic field
• Doping a correlated band insulator: A new route to half metallic behaviour
• Phase Diagram of the Half-Filled Ionic Hubbard Model
• Topological Origin of the Fermion Sign Problem
• Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets
• Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models
• Auxiliary Field Quantum Monte Carlo for Multiband Hubbard Models: Controlling the Sign and Phase Problems to Capture Hund's Physics
• Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians
• Quantum computation of thermal averages in the presence of a sign problem
• Complex Langevin Equation and the Many-Fermion Problem
• Is there a superconducting phase in the half-filled ionic Hubbard model ?
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Intertwined states at finite temperatures in the Hubbard model
• Reduction of the sign problem using the meron-cluster approach

Cited by in corpus (24)

• Quantum Critical Points and the Sign Problem
• Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives
• On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem
• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• A perspective on machine learning and data science for strongly correlated electron problems
• Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state
• Universality and Critical Exponents of the Fermion Sign Problem
• Fermion sign bounds theory in quantum Monte Carlo simulation
• On the thermodynamics of fermions at any temperature based on parametrized partition function
• Sign Problem in Quantum Monte Carlo Simulation
• Bilayer Hubbard model: Analysis based on the fermionic sign problem
• Thermodynamics of correlated electrons in a magnetic field
• Unusual Hole-doping-dependent Electronic Instability and Electron-Phonon Coupling in Infinite-layer Nickelates
• A flexible class of exact Hubbard-Stratonovich transformations
• Charge excitations across a superconductor-insulator transition
• Defining a universal sign to strictly probe a phase transition
• Sketching phase diagrams using low-depth variational quantum algorithms
• Charge Singlets and Orbital-Selective Charge Density Wave Transitions
• Hamming Distance and the onset of quantum criticality
• Confinement-Induced Enhancement of Superconductivity in a Spin-$\frac{1}{2}$ Fermion Chain Coupled to a ${\mathbb{Z}}_2$ Lattice Gauge Field
• The competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Site-resolved observables in the doped spin-imbalanced triangular Hubbard model
• Dressing due to correlations strongly reduces the effect of electron-phonon coupling