Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1912.11233 · Physical Review Research

Trion states and quantum criticality of attractive SU(3) Dirac fermions

Han Xu, Xiang Li, Zhichao Zhou, Xin Wang, Lei Wang, Congjun Wu, Yu Wang

Published Jun 22, 2023• 13 citations
arXivHTMLPDF

Abstract

We perform the projector quantum Monte Carlo (QMC) simulation to study the trion formation and quantum phase transition in the half filled attractive SU(3) Hubbard model on a honeycomb lattice. With increasing attractive Hubbard interaction, our simulations demonstrate a continuous quantum phase transition from the semimetal to charge-density wave (CDW) at the critical coupling ${U}_{c}/t=\ensuremath{-}1.52(2)$. The critical exponents $\ensuremath{\nu}=0.82(3)$ and $\ensuremath{\eta}=0.58(4)$ determined by the QMC simulation remarkably disagree with those of the $N=3$ chiral Ising universality class suggested by the effective Gross-Neveu-Yukawa (GNY) theory, but coincide with the $N=1$ chiral Ising universality class. In the CDW phase, we show that on-site and off-site trions coexist and the off-site trion forms a local bond state. Our work not only illustrates the formation of off-site trions in two-dimensional Hubbard model but also raises doubts about the extent of applicability of GNY model on attractive SU(3) Dirac fermions.

DOI
10.1103/physrevresearch.5.023180

Related papers

Quantum Monte Carlo simulations of the attractive SU(3) Hubbard model on a honeycomb lattice

Xu Han, Zhichao Zhou, Xin Wang +2 more

We perform the projector quantum Monte Carlo simulation of the half-filled attractive SU(3) Hubbard model on a honeycomb lattice, exploring the effects of SU(3) symmetry on the correlated attractive Dirac fermions. Our simulation indicates the absence of pairing order in the system and shows a quantum phase transition from the semimetal to charge density wave (CDW) at the critical point $U_c=-1.52(2)$. We demonstrate that this quantum phase transition belongs to the chiral Ising universality class according to the numerically determined critical exponents $\nu=0.82(3)$ and $\eta=0.58(4)$. With the increase of coupling strength, the trion formation is investigated, and the change in probability of the on-site trion occupancy infers the coexistence of on-site trionic and off-site trionic CDW states at half-filling.

•Dec 24, 2019•2 citations

Quantum Monte Carlo simulations of thermodynamic properties of attractive SU(3) Dirac fermions

Xiang Li, Han Xu, Yu Wang

We employ the determinant quantum Monte Carlo method to study the finite-temperature properties of the half-filled attractive $\mathrm{SU}(3)$ Hubbard model on a honeycomb lattice. We calculate the phase diagram in which the phase boundary separates the disordered phase and the charge density wave (CDW) phase and the transition temperature ${T}_{\text{tr}}(|U|)$ varies nonmonotonically with attractive Hubbard interaction $|U|$. As the Hubbard $|U|$ increases at constant temperature $T<\text{max}({T}_{\text{tr}}(|U|))$, the system first undergoes a transition from thermal Dirac semimetal phase to CDW phase, and eventually the CDW state is thermally melted at a strong Hubbard $|U|$ where the system enters a trion liquid phase. In between the two transition points the nonmonotonic $|U|$ dependence of CDW order strength is strikingly different from the zero-temperature monotonic behavior. In the trion CDW state where off-site trions arise from quantum fluctuations (a fermion inside an on-site trion hops to a nearest-neighbor site), the simulated triple occupancy at constant Hubbard $|U|$ surprisingly increases with temperature, implying that the formation of off-site trions is suppressed by the thermal delocalization of on-site trions. We have also calculated the entropy-temperature relations for various attractive Hubbrad interactions, which exhibit the prominent characteristic of the Pomeranchuk effect. Our work has revealed that the formation of on-site and off-site trions has significant consequences for thermodynamic properties of SU(3) Dirac fermions.

arXiv:2101.00804•Physical review. B./Physical review. B•Oct 2, 2023•4 citations

Thermal charge-density-wave transition and trion formation in the attractive SU(3) Hubbard model on a honeycomb lattice

Xiang Li, Xu Han, Yu Wang

We employ the determinant quantum Monte Carlo method to study the thermodynamic properties of the attractive SU(3) Hubbard model on a honeycomb lattice. The thermal charge density wave (CDW) transition, the trion formation, the entropy-temperature relation and the density compressibility are simulated at half filling. The CDW phase only breaks the lattice inversion symmetry on the honeycomb lattice and thus can survive at finite temperatures. The disordered phase is the thermal Dirac semi-metal state in the weak coupling regime, while in the strong coupling regime it is mainly a Mott-insulated state in which the CDW order is thermally melted. The formation of trions is greatly affected by thermal fluctuations. The calculated entropy-temperature relations exhibit prominent features of the Pomeranchuk effect which is related to the distribution of trions. Our simulations show that the density compressibility is still nonzero immediately after the CDW phase appears, but vanishes when the long-range order of trions forms.

•Jan 4, 2021•0 citations

Coexisting Néel and charge density wave orders in attractive three-color fermions

Xiang Li, Yu Wang

In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on the interactions---unbound fermions, on-site trions, and off-site trions---leading to the coexistence of multiple fermionic species in the ordered phase, which demonstrates that the attractive three-color fermions are unique from other correlated fermion systems and may host intriguing phases and phase transitions. At temperatures below the superexchange energy scale, we employ the determinant quantum Monte Carlo (QMC) method to investigate the phases and phase transitions in the half-filled attractive three-color Hubbard model on a honeycomb lattice where the Hubbard interactions are color dependent (anisotropic interactions) and the coupling between color 3 and colors (1, 2) serves as a control parameter. In the coupling regime where on-site and off-site trions coexist, our QMC simulations demonstrate coexisting N\'eel and charge density wave (CDW) orders which are common in condensed matter but rare in ultracold atoms. At weak coupling where the color superfluid (CSF) order is scattered by color-3 fermions, we find that very small coupling of color 3 with colors (1, 2) can destroy the CSF order and that the vanishing of the CSF order is not immediately accompanied by the emergence of the on-site trionic phase, which strikingly disagrees with the prevalent results of dynamical mean-field theory. The underlying mechanisms of the coexisting N\'eel/CDW orders and of the CSF order breaking are also presented based on intuitive physical pictures.

arXiv:2205.10225•Physical review. B./Physical review. B•Sep 3, 2024•2 citations

QMC study of the chiral Heisenberg Gross-Neveu universality class

Yuichi Otsuka, Kazuhiro Seki, Sandro Sorella +1 more

Abstract We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a d-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the d-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number N of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.

arXiv:2111.08220•Journal of Physics Conference Series•Mar 1, 2022•2 citations

Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice

Yuichi Otsuka, Kazuhiro Seki, Sandro Sorella +1 more

We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic $\ensuremath{\pi}$ flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the $U(1)$ symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the $s$-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekul\'e valence bond solid, where an emergent $U(1)$ symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].

arXiv:1803.02001•Physical review. B./Physical review. B•Jul 18, 2018•31 citations
We perform the projector quantum Monte Carlo (QMC) simulation to study the trion formation and quantum phase transition in the half filled attractive SU(3) Hubbard model on a honeycomb lattice. With increasing attractive Hubbard interaction, our simulations demonstrate a continuous quantum phase transition from the semimetal to charge-density wave (CDW) at the critical coupling Uc/t=\ensuremath−1.52(2){U}_{c}/t=\ensuremath{-}1.52(2)Uc​/t=\ensuremath−1.52(2). The critical exponents \ensuremathν=0.82(3)\ensuremath{\nu}=0.82(3)\ensuremathν=0.82(3) and \ensuremathη=0.58(4)\ensuremath{\eta}=0.58(4)\ensuremathη=0.58(4) determined by the QMC simulation remarkably disagree with those of the N=3N=3N=3 chiral Ising universality class suggested by the effective Gross-Neveu-Yukawa (GNY) theory, but coincide with the N=1N=1N=1 chiral Ising universality class. In the CDW phase, we show that on-site and off-site trions coexist and the off-site trion forms a local bond state. Our work not only illustrates the formation of off-site trions in two-dimensional Hubbard model but also raises doubts about the extent of applicability of GNY model on attractive SU(3) Dirac fermions.
We perform the projector quantum Monte Carlo simulation of the half-filled attractive SU(3) Hubbard model on a honeycomb lattice, exploring the effects of SU(3) symmetry on the correlated attractive Dirac fermions. Our simulation indicates the absence of pairing order in the system and shows a quantum phase transition from the semimetal to charge density wave (CDW) at the critical point Uc=−1.52(2)U_c=-1.52(2)Uc​=−1.52(2). We demonstrate that this quantum phase transition belongs to the chiral Ising universality class according to the numerically determined critical exponents ν=0.82(3)\nu=0.82(3)ν=0.82(3) and η=0.58(4)\eta=0.58(4)η=0.58(4). With the increase of coupling strength, the trion formation is investigated, and the change in probability of the on-site trion occupancy infers the coexistence of on-site trionic and off-site trionic CDW states at half-filling.
We employ the determinant quantum Monte Carlo method to study the finite-temperature properties of the half-filled attractive SU(3)\mathrm{SU}(3)SU(3) Hubbard model on a honeycomb lattice. We calculate the phase diagram in which the phase boundary separates the disordered phase and the charge density wave (CDW) phase and the transition temperature Ttr(∣U∣){T}_{\text{tr}}(|U|)Ttr​(∣U∣) varies nonmonotonically with attractive Hubbard interaction ∣U∣|U|∣U∣. As the Hubbard ∣U∣|U|∣U∣ increases at constant temperature T<max(Ttr(∣U∣))T<\text{max}({T}_{\text{tr}}(|U|))T<max(Ttr​(∣U∣)), the system first undergoes a transition from thermal Dirac semimetal phase to CDW phase, and eventually the CDW state is thermally melted at a strong Hubbard ∣U∣|U|∣U∣ where the system enters a trion liquid phase. In between the two transition points the nonmonotonic ∣U∣|U|∣U∣ dependence of CDW order strength is strikingly different from the zero-temperature monotonic behavior. In the trion CDW state where off-site trions arise from quantum fluctuations (a fermion inside an on-site trion hops to a nearest-neighbor site), the simulated triple occupancy at constant Hubbard ∣U∣|U|∣U∣ surprisingly increases with temperature, implying that the formation of off-site trions is suppressed by the thermal delocalization of on-site trions. We have also calculated the entropy-temperature relations for various attractive Hubbrad interactions, which exhibit the prominent characteristic of the Pomeranchuk effect. Our work has revealed that the formation of on-site and off-site trions has significant consequences for thermodynamic properties of SU(3) Dirac fermions.
We employ the determinant quantum Monte Carlo method to study the thermodynamic properties of the attractive SU(3) Hubbard model on a honeycomb lattice. The thermal charge density wave (CDW) transition, the trion formation, the entropy-temperature relation and the density compressibility are simulated at half filling. The CDW phase only breaks the lattice inversion symmetry on the honeycomb lattice and thus can survive at finite temperatures. The disordered phase is the thermal Dirac semi-metal state in the weak coupling regime, while in the strong coupling regime it is mainly a Mott-insulated state in which the CDW order is thermally melted. The formation of trions is greatly affected by thermal fluctuations. The calculated entropy-temperature relations exhibit prominent features of the Pomeranchuk effect which is related to the distribution of trions. Our simulations show that the density compressibility is still nonzero immediately after the CDW phase appears, but vanishes when the long-range order of trions forms.
In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on the interactions---unbound fermions, on-site trions, and off-site trions---leading to the coexistence of multiple fermionic species in the ordered phase, which demonstrates that the attractive three-color fermions are unique from other correlated fermion systems and may host intriguing phases and phase transitions. At temperatures below the superexchange energy scale, we employ the determinant quantum Monte Carlo (QMC) method to investigate the phases and phase transitions in the half-filled attractive three-color Hubbard model on a honeycomb lattice where the Hubbard interactions are color dependent (anisotropic interactions) and the coupling between color 3 and colors (1, 2) serves as a control parameter. In the coupling regime where on-site and off-site trions coexist, our QMC simulations demonstrate coexisting N\'eel and charge density wave (CDW) orders which are common in condensed matter but rare in ultracold atoms. At weak coupling where the color superfluid (CSF) order is scattered by color-3 fermions, we find that very small coupling of color 3 with colors (1, 2) can destroy the CSF order and that the vanishing of the CSF order is not immediately accompanied by the emergence of the on-site trionic phase, which strikingly disagrees with the prevalent results of dynamical mean-field theory. The underlying mechanisms of the coexisting N\'eel/CDW orders and of the CSF order breaking are also presented based on intuitive physical pictures.
Abstract We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a d-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the d-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number N of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.
We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic $\ensuremath{\pi}$ flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the U(1)U(1)U(1) symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the sss-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekul\'e valence bond solid, where an emergent U(1)U(1)U(1) symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].