In the Hamiltonian picture, free spin- $1/2$ Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction $V$ , which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling $V$ , we show that we can study the phase transition between the massless fermion phase at small- $V$ and a massive fermion phase at large- $V$ . We construct a fermion bag algorithm to study this phase transition and find evidence for it to be second order. Numerical study shows that the universality class of the transition is different from the one studied earlier involving the Hubbard coupling $U$ . Here we obtain some critical exponents using lattices up to $L=48$ .In the Hamiltonian picture, free spin-$1/2$ Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction $V$, which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling $V$, we show that we can study the phase transition between the massless fermion phase at small-$V$ and a massive fermion phase at large-$V$. We construct a fermion bag algorithm to study this phase transition and find evidence for it to be second order. Numerical study shows that the universality class of the transition is different from the one studied earlier involving the Hubbard coupling $U$. Here we obtain some critical exponents using lattices up to $L=48$.

arXiv:2112.15511International Symposium on Lattice Field Theory (LATTICE)May 16, 20220 citations

Quantum criticality in the two-dimensional Hubbard model

Mathias Pelz

Jul 10, 20260 citations

Dirac electrons in the square-lattice Hubbard model with a d -wave pairing field: The chiral Heisenberg universality class revisited

Yuichi Otsuka, Kazuhiro Seki, Sandro Sorella +1 more

We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components $N=8$ in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a $d$ -wave pairing field, inducing Dirac cones in the single-particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, which is the canonical model for graphene, despite the unit cells being apparently different (e.g., they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting $N$ and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the $N=8$ chiral Heisenberg universality class are $\ensuremath{\nu}=1.05(5)$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}=0.75(4)$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.23(4)$, which are compared with the previous numerical estimations.We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components $N=8$ in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a $d$-wave pairing field, inducing Dirac cones in the single-particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, which is the canonical model for graphene, despite the unit cells being apparently different (e.g., they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting $N$ and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the $N=8$ chiral Heisenberg universality class are $\ensuremath{\nu}=1.05(5)$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}=0.75(4)$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.23(4)$, which are compared with the previous numerical estimations.

arXiv:2009.04685Physical review. B./Physical review. BDec 1, 202035 citations

Quantum Criticality of Antiferromagnetism and Superconductivity with Relativity

Hanqing Liu, Emilie Huffman, Shailesh Chandrasekharan A +1 more

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 simulations. Importantly, interactions in our model are not only invariant under SU(2) symmetries of spin and charge like the Hubbard model, but they also preserve an Ising-like electron spin-charge flip symmetry. From unbiased fermion bag Monte Carlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either antiferromagnetism or superconductivity, and that the transition at which both orders are simultaneously quantum critical belongs to a new "chiral spin-charge symmetric" universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.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 simulations. Importantly, interactions in our model are not only invariant under SU(2) symmetries of spin and charge like the Hubbard model, but they also preserve an Ising-like electron spin-charge flip symmetry. From unbiased fermion bag Monte Carlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either antiferromagnetism or superconductivity, and that the transition at which both orders are simultaneously quantum critical belongs to a new "chiral spin-charge symmetric" universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.

arXiv:2109.06059Physical Review LettersMar 15, 202211 citations

Quantum Criticality Due to Incipient Phase Separation in the Two-dimentional Hubbard Model

Ehsan Khatami, Karlis Mikelsons, Alexandru Macridin +4 more

Bulletin of the American Physical SocietyMar 17, 20100 citations

In the Hamiltonian picture, free spin-

1/2

Dirac fermions on a bipartite lattice have an

O(4)

(spin-charge) symmetry. Here we construct an interacting lattice model with an interaction

V

, which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling

V

, we show that we can study the phase transition between the massless fermion phase at small-

V

and a massive fermion phase at large-

V

. We construct a fermion bag algorithm to study this phase transition and find evidence for it to be second order. Numerical study shows that the universality class of the transition is different from the one studied earlier involving the Hubbard coupling

U

. Here we obtain some critical exponents using lattices up to

L=48

We numerically investigate the quantum criticality of the chiral Heisenberg universality class with the total number of fermion components

N=8

in terms of the Gross-Neveu theory. Auxiliary-field quantum Monte Carlo simulations are performed for the square lattice Hubbard model in the presence of a

d

-wave pairing field, inducing Dirac cones in the single-particle spectrum. This property makes the model particularly interesting because it turns out to belong to the same universality class of the Hubbard model on the honeycomb lattice, which is the canonical model for graphene, despite the unit cells being apparently different (e.g., they contain one and two sites, respectively). We indeed show that the two phase transitions, expected to occur on the square and on the honeycomb lattices, have the same quantum criticality. We also argue that details of the models, i.e., the way of counting

N

and the anisotropy of the Dirac cones, do not change the critical exponents. The present estimates of the exponents for the

N=8

chiral Heisenberg universality class are $\ensuremath{\nu}=1.05(5)$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}=0.75(4)$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.23(4)$, which are compared with the previous numerical estimations.