Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
arXiv:2410.18854 · doi:10.1126/sciadv.adz4856
Abstract
The notorious fermion sign problem, arising from fermion statistics, presents a fundamental obstacle to the numerical simulation of quantum many-body systems. Here, we introduce a framework that circumvents the sign problem in the studies of quantum criticality and its associated phases by leveraging imaginary-time nonequilibrium critical dynamics. We demonstrate that the critical properties can be accurately determined from the system's short-time relaxation, a regime where the sign problem remains manageable for quantum Monte-Carlo (QMC) simulations. After validating this approach on two benchmark fermionic models, we apply it to the sign-problematic Hubbard model hosting SU(3)-symmetric Dirac fermions. We present the first numerically exact characterization of its quantum phase diagram, revealing a continuous transition between a Dirac semi-metal and a SU(3) antiferromagnetic phase. This transition defines an unconventional Gross-Neveu universality class that fundamentally reshapes current understanding of Gross-Neveu criticality. Our work provides a powerful tool for investigating sign-problematic systems and quantum criticality.
6+22 pages, 3+19 figures
References in corpus (54)
- A Common Thread: the pairing interaction for the unconventional superconductors
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- The Hubbard Model
- Enhancement of superconductivity near a nematic quantum critical point
- A sufficient condition for the absence of the sign problem in the fermionic quantum Monte-Carlo algorithm
- Linear in Temperature Resistivity and Associated Mysteries
- Solving fermion sign problem in quantum Monte Carlo by Majorana representation
- Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
- Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations
- Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
- Fermion-induced quantum critical points
- Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
- Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
- Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
- Antiferromagnetic spin correlation of SU() Fermi gas in an optical super-lattice
- Geometry Dependence of the Sign Problem
- Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
- Observation of antiferromagnetic correlations in an ultracold SU() Hubbard model
- Monte Carlo Studies of Quantum Critical Metals
- Easing the Monte Carlo sign problem
- Solution to sign problems in half-filled spin-polarized electronic systems
- Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
- Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
- Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
- Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
- Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations
- Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
- Multi-meson Yukawa interactions at criticality
- Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
- How Quantum Are Non-Negative Wavefunctions?
- Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
- Confinement transition in the QED-Gross-Neveu-XY universality class
- Universal short-time quantum critical dynamics in imaginary time
- Mitigating the Sign Problem Through Basis Rotations
- Mott transition in the -flux SU() Hubbard model on a square lattice
- Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
- Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
- Metal-insulator transition and magnetism of SU(3) fermions in the square lattice
- Intrinsic sign problem in fermionic and bosonic chiral topological matter
- Fermion sign bounds theory in quantum Monte Carlo simulation
- Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid
- Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
- Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
- Quantum Monte Carlo Simulation of Generalized Kitaev Models
- An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo
- Universal short time quantum critical dynamics of finite size systems
- Mitigating the fermion sign problem by automatic differentiation
- Trion states and quantum criticality of attractive SU(3) Dirac fermions
- Robust Fermi liquid instabilities in sign problem-free models
- Gross-Neveu-Yukawa theory of spontaneous symmetry breaking
- Boosting quantum Monte Carlo and alleviating sign problem by Gutzwiller projection
- Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
- Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
- Gross-Neveu-Yukawa SO(2) and SO(3) tensorial criticality
Cited by in corpus (4)
- Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
- Relaxation Critical Dynamics in Measurement-induced Phase Transitions
- Short-time critical dynamics in the classical cubic dimer model
- Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states