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arXiv:2101.00804 · Physical review. B./Physical review. B

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

Xiang Li, Han Xu, Yu Wang

Published Oct 2, 2023• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.108.165102

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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.
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 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=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.
Recent advances in microwave shielding have increased the stability and control of large numbers of polar molecules, allowing for the first realization of a molecular Bose-Einstein condensate. Remarkably, it was also recently realized that shielded polar molecules exhibit an SU(N) symmetry among their hyperfine states, opening the door to SU(N) systems with larger N, bosonic particle statistics, and tunable interactions-both repulsive and attractive. Motivated by these results, we have studied the SU(3) attractive Fermi-Hubbard model (FHM) on a square lattice. Using the determinant quantum Monte Carlo (DQMC) method, we explore the finite temperature phase diagram and provide evidence for three distinct regions-a three-component Fermi liquid (FL) region, a "trion" liquid (TL) region, and an ordered charge density wave (CDW) phase. The CDW phase is stable at finite temperature [in contrast to the SU(2) CDW], while the FL to TL crossover appears to point to a quantum phase transition at zero temperature. Our method extends straightforwardly to larger N and is sign problem free for even values of N. With these results, we demonstrate the potential physics enabled by using polar molecules as a quantum simulation platform for the attractive SU(N) FHM.
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength UUU (relative to the hopping parameter ttt) at half filling and zero temperature, the system undergoes a quantum phase transition at 5.0<Uc/t<5.15.0<{U}_{c}/t<5.15.0<Uc​/t<5.1 from a semimetal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half filling, and increasing the interaction strength at finite but low temperature TTT, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as UUU is increased and TTT is lowered.
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.