skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

Journal Article · · Physical Review. D.
 [1];  [2]
  1. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  2. Duke Univ., Durham, NC (United States)

Motivated by the fermion-bag approach, in this work we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points, particularly those with four-fermion interactions. Although these theories are constructed in discrete time with a finite temporal lattice spacing ϵ, when ϵ → 0, conventional continuous-time Hamiltonian lattice field theories are recovered. The fermion-bag algorithms run relatively faster when ϵ = 1 as compared to ϵ → 0 but still allow us to compute universal quantities near the quantum critical point even at such a large value of ϵ. As an example of this new approach, here we study the $$N_f$$ = 1 Gross-Neveu chiral-Ising universality class in 2 + 1 dimensions by calculating the critical scaling of the staggered mass order parameter. We show that we are able to study lattice sizes up to 1002 sites when ϵ = 1, while with comparable resources we can reach lattice sizes of only up to 642 when ϵ → 0. The critical exponents obtained in both these studies match within errors.

Research Organization:
Duke Univ., Durham, NC (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP); Innovation, Science and Economic Development Canada (ISED); National Science Foundation (NSF)
Grant/Contract Number:
FG02-05ER41368; ACI-1548562
OSTI ID:
1800275
Alternate ID(s):
OSTI ID: 1608078
Journal Information:
Physical Review. D., Vol. 101, Issue 7; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

References (90)

Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry journal October 2015
From domain wall to overlap in 2 + 1 d journal March 2016
Lattice fermions: Species doubling, chiral invariance and the triangle anomaly journal May 1981
Chiral anomalies and rooted staggered fermions journal May 2007
Asymptotically safe and free chiral theories with and without scalars journal September 2017
Hybrid Monte Carlo journal September 1987
Benchmark results in the 2D lattice Thirring model with a chemical potential journal March 2018
Revisiting the hybrid quantum Monte Carlo method for Hubbard and electron-phonon models journal February 2018
Monte Carlo simulation of the semimetal-insulator phase transition in monolayer graphene journal March 2010
Fermion bag solutions to some sign problems in four-fermion field theories journal May 2012
Symmetric Fermion Mass Generation as Deconfined Quantum Criticality journal February 2018
Real-time evolution of strongly coupled fermions driven by dissipation journal September 2016
Fermion bag approach to fermion sign problems: New opportunities in lattice fermion field theories journal July 2013
Dynamical symmetry breaking in asymptotically free field theories journal November 1974
Universal Quantum Criticality in the Metal-Insulator Transition of Two-Dimensional Interacting Dirac Electrons journal March 2016
Chiral determinant as an overlap of two vacua journal January 1994
Fermion Bags, Duality, and the Three Dimensional Massless Lattice Thirring Model journal April 2012
Relativistic Mott criticality in graphene journal August 2009
Dynamical generation of topological masses in Dirac fermions journal February 2018
A method for simulating chiral fermions on the lattice journal August 1992
Bootstrapping 3D fermions with global symmetries journal January 2018
On theO(1/N 2)β-function of the Nambu-Jona-Lasinio model with non-abelian chiral symmetry journal March 1994
Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions journal August 2015
XSEDE: Accelerating Scientific Discovery journal September 2014
Critical flavor number in the three dimensional Thirring model journal May 2007
COMPUTATION OF CRITICAL EXPONENT η AT O(1/N 3 ) IN THE FOUR-FERMI MODEL IN ARBITRARY DIMENSIONS journal February 1994
Dirac Fermions in Solids: From High-T c Cuprates and Graphene to Topological Insulators and Weyl Semimetals journal March 2014
From bosonic topological transition to symmetric fermion mass generation journal March 2018
Theory of interacting electrons on the honeycomb lattice journal February 2009
Monte Carlo calculations of coupled boson-fermion systems. I journal October 1981
Fermion bag approach to Hamiltonian lattice field theories in continuous time journal December 2017
Fermionic quantum criticality in honeycomb and π -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo journal April 2015
Quantum Monte Carlo Simulation of the Chiral Heisenberg Gross-Neveu-Yukawa Phase Transition with a Single Dirac Cone journal September 2019
Yukawa conformal field theories and emergent supersymmetry journal November 2016
Critical chiral Heisenberg model with the functional renormalization group journal February 2018
Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations journal December 2015
Solution to sign problems in half-filled spin-polarized electronic systems journal March 2014
Fermion bag approach to lattice field theories journal July 2010
Ising and Gross-Neveu model in next-to-leading order journal December 2016
Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study journal June 2009
Superconductivity from the condensation of topological defects in a quantum spin-Hall insulator journal June 2019
Bootstrapping 3D fermions journal March 2016
The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code journal January 2017
Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach journal May 2014
Critical behavior of Dirac fermions from perturbative renormalization journal September 2018
Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation journal June 2015
Fermion-induced quantum critical points journal August 2017
Interplay of universality classes in a three-dimensional Yukawa model journal April 1996
Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications journal March 2019
Critical exponents of new universality classes journal September 1993
Efficient continuous-time quantum Monte Carlo method for the ground state of correlated fermions journal June 2015
Designer Monte Carlo simulation for the Gross-Neveu-Yukawa transition journal February 2020
Strong-coupling field theories. II. Fermions and gauge fields on a lattice journal September 1976
A soluble relativistic field theory journal January 1958
Solution to sign problems in models of interacting fermions and quantum spins journal October 2016
Absence of neutrinos on a lattice journal July 1981
Dynamical symmetry breaking in four-fermion interaction models journal June 1991
Masses in graphenelike two-dimensional electronic systems: Topological defects in order parameters and their fractional exchange statistics journal November 2009
Three dimensional four-fermion models—A Monte Carlo study journal May 2007
Critical flavor number of the Thirring model in three dimensions journal November 2017
Origin of fermion masses without spontaneous symmetry breaking journal April 2016
Thermal Ising transitions in the vicinity of two-dimensional quantum critical points journal April 2016
Updating the Inverse of a Matrix journal June 1989
Stochastic series expansion simulation of the t V model journal April 2016
The three-dimensional Thirring model for and journal July 1999
Fluctuation-induced continuous transition and quantum criticality in Dirac semimetals journal September 2017
Anomalous mass dimension at O(1/N2) in the O(N) Gross-Neveu model journal December 1992
Fermionic quantum critical point of spinless fermions on a honeycomb lattice journal October 2014
Critical behaviour of the three-dimensional Gross-Neveu and Higgs-Yukawa models journal March 1994
Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations journal June 2016
Fermion-induced quantum criticality with two length scales in Dirac systems journal March 2018
Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations journal December 2016
Four-loop critical exponents for the Gross-Neveu-Yukawa models journal November 2017
Large Nf quantum field theory journal December 2018
Four-fermion interaction near four dimensions journal December 1991
Quantum critical behavior in three dimensional lattice Gross-Neveu models journal July 2013
Meron-Cluster Solution of Fermion Sign Problems journal October 1999
Large N critical exponents for the chiral Heisenberg Gross-Neveu universality class journal May 2018
Phase diagram of electronic systems with quadratic Fermi nodes in 2 < d < 4 : 2 + ε expansion, 4 ε expansion, and functional renormalization group journal February 2017
Actions for dynamical fermion simulations: are we ready to go? journal March 2004
Hybrid Monte Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice journal December 2018
Towards critical physics in 2+1d with U(2N )-invariant fermions journal November 2016
Chiral symmetry restoration in the three-dimensional four-fermion model at nonzero temperature and density journal January 2001
Lattice non-local chiral fermions journal February 1988
Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields journal January 2007
Novel phases in strongly coupled four-fermion theories journal August 2017
Hybrid Monte Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density journal November 2017
Four-Fermi Theories in Fewer Than Four Dimensions journal May 1993
Compatible orders and fermion-induced emergent symmetry in Dirac systems journal January 2018
Yukawa CFTs and Emergent Supersymmetry preprint January 2016

Cited By (1)


Similar Records

Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
Journal Article · Thu Mar 25 00:00:00 EDT 2021 · Physical Review D · OSTI ID:1800275

Quantum Criticality of Antiferromagnetism and Superconductivity with Relativity
Journal Article · Tue Mar 15 00:00:00 EDT 2022 · Physical Review Letters · OSTI ID:1800275

Antiferromagnetic transitions of Dirac fermions in three dimensions
Journal Article · Fri Oct 30 00:00:00 EDT 2020 · Physical Review. B · OSTI ID:1800275