Solution to sign problems in half-filled spin-polarized electronic systems

  title={Solution to sign problems in half-filled spin-polarized electronic systems},
  author={Emilie Huffman and Shailesh Chandrasekharan},
  journal={Physical Review B},
We solve the sign problem in a particle-hole symmetric spin-polarized fermion model on bipartite lattices using the idea of fermion bags. The solution can be extended to a class of models at half filling but without particle-hole symmetry. Attractive Hubbard models with an odd number of fermion species can also be solved. The new solutions should allow us to study quantum phase transitions that have remained unexplored so far due to sign problems. 

Figures from this paper

Solution to new sign problems with Hamiltonian Lattice Fermions
We present a solution to the sign problem in a class of particle-hole symmetric Hamiltonian lattice fermion models on bipartite lattices using the idea of fermion bags. The solution remains valid
Solution to the sign problem in a frustrated quantum impurity model
In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end.
Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations.
This proof provides a unified description for all the interacting lattice fermion models previously known to be free of the sign problem based on the auxiliary field quantum Monte Carlo method and identifies a number of new sign-problem-free interacting fermions.
Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions
In the Hamiltonian picture, free spin-1/2 Dirac fermions on a bipartite lattice have an O (4) (spincharge) symmetry. Here we construct an interacting lattice model with an interaction V , which is
Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations.
This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of theSign problem.
Solution of the sign problem for the half-filled Hubbard-Holstein model
We show that, by an appropriate choice of auxiliary fields and exact integration of the phonon degrees of freedom, it is possible to define a 'sign-free' path integral for the so called
Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets.
We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S=1/2 antiferromagnets using the basis of spin eigenstates of clusters to
Quantum Criticality of Anti-ferromagnetism and Superconductivity with Relativity
We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum Monte Carlo
Fermion Bag Approach to Lattice Hamiltonian Field Theories
Using a model in the Gross-Neveu Ising universality class, we show how the fermion bag idea can be applied to develop algorithms to Hamiltonian lattice field theories. We argue that fermion world
Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction.
An analytical expression is derived that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results and discussing the computational complexity of the fermion sign problem and methods for alleviating its severity.


  • Phys. J., A49, 90
  • 2013
  • Rev. X, 3, 031010
  • 2013
I and J
  • Rev. D, 85 091502
  • 2012
  • Mod. Phys., 83 349
  • 2011
  • Rev. A, 82, 053621
  • 2010
  • Rev. D, 82, 025007
  • 2010
  • Jurǐ cić, and O. Vafek, Phys. Rev. B, 80, 075432
  • 2009
  • Prokof’ev, B. Svistunov, and M. Troyer, Phys. Rev. Lett., 101, 090402
  • 2008
and C
  • Strouthos, Phys.Rev., D75, 101701
  • 2007