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:1608.06239 · Physical review. B./Physical review. B

Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting SU(2N) Dirac fermions

Zhichao Zhou, Da Wang, Congjun Wu, Yu Wang

Published Feb 21, 2017• 17 citations
arXivHTMLPDF

Abstract

We investigate the $\mathrm{SU}(2N)$ symmetry effects with $2N>2$ on the two-dimensional interacting Dirac fermions at finite temperatures, including the valence-bond-solid transition, the Pomeranchuk effect, the compressibility, and the uniform spin susceptibility, by performing the determinant quantum Monte Carlo simulations of the half-filled $\mathrm{SU}(2N)$ Hubbard model on a honeycomb lattice. The columnar valence-bond-solid (cVBS) phase only breaks the threefold discrete symmetry and thus can survive at finite temperatures. The disordered phase in the weak coupling regime is the thermal Dirac semi-metal state, while in the strong coupling regime it is largely a Mott state in which the cVBS order is thermally melted. The calculated entropy-temperature relations for various values of the Hubbard interaction $U$ show that the Pomeranchuk effect occurs when the specific entropy is below a characteristic value of ${S}^{*}$---the maximal entropy per particle from the spin channel of local moments. The $\mathrm{SU}(2N)$ symmetry enhances the Pomeranchuk effect, which facilitates the interaction-induced adiabatic cooling. Our work sheds light on future explorations of novel states of matter with ultracold large-spin alkaline fermions.

DOI
10.1103/physrevb.95.085128

Related papers

Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions

Zhichao Zhou, Da Wang, Zi Yang Meng +2 more

The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled $\mathrm{SU}(2N)$ Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.

arXiv:1512.03994•Physical review. B./Physical review. B•Jun 29, 2016•69 citations

Quantum Monte Carlo simulations of thermodynamic properties of SU(2N) ultracold fermions in optical lattices

Zhichao Zhou, Zi Cai, Congjun Wu +1 more

We have systematically studied the thermodynamic properties of a two-dimensional half-filled $\mathrm{SU}(2N)$ Hubbard model on a square lattice by using the determinant quantum Monte Carlo method. The entropy-temperature relation, the isoentropy curve, and the probability distribution of the on-site occupation number are calculated in both SU(4) and SU(6) cases, which exhibit prominent features of the Pomeranchuk effect. We analyze these thermodynamic behaviors based on energy scales in the density and spin channels. In the density channel, the interaction strength that marks the crossover from the weak to strong interaction regimes increases with the number of fermion components. In the spin channel, increasing the number of fermion components enhances quantum spin fluctuations, which is shown in the simulations of uniform spin susceptibilities and antiferromagnetic structure factors.

arXiv:1410.5922•Physical Review B•Dec 22, 2014•35 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

Pomeranchuk Cooling of SU(2N) Ultracold Fermions in Optical Lattices

Zi Cai, Hsiang-Hsuan Hung, Lei Wang +2 more

We investigate the thermodynamic properties of a half-filled SU(2N) Hubbard model in the two-dimensional square lattice by the method of the determinant quantum Monte Carlo simulation, which is free of the fermion "sign problem." The large number of hyperfine-spin components enhances spin fluctuations, which facilitates the Pomeranchuk cooling to temperatures comparable to the superexchange energy scale in the case of SU(6). Various physical quantities including entropy, charge fluctuations, and spin correlations are calculated.

arXiv:1202.6323•Physical Review Letters•May 29, 2013•41 citations

Dimerized Solids and Resonating Plaquette Order in SU(N) -Dirac Fermions

Thomas C. Lang, Zi Yang Meng, Alejandro Muramatsu +2 more

We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.

arXiv:1306.3258•Physical Review Letters•Aug 9, 2013•73 citations

Finite-temperature properties of strongly correlated fermions in the honeycomb lattice

Baoming Tang, Thereza Paiva, Ehsan Khatami +1 more

We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. We examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. For the homogeneous case, this process is found to be more efficient at finite doping than at half filling. That, in turn, leads to an efficient adiabatic cooling in the presence of a trap, which, starting with even relatively high entropies, can drive the system to have a Mott insulating phase with substantial antiferromagnetic correlations.

arXiv:1307.1707•Physical Review B•Sep 18, 2013•20 citations
We investigate the SU(2N)\mathrm{SU}(2N)SU(2N) symmetry effects with 2N>22N>22N>2 on the two-dimensional interacting Dirac fermions at finite temperatures, including the valence-bond-solid transition, the Pomeranchuk effect, the compressibility, and the uniform spin susceptibility, by performing the determinant quantum Monte Carlo simulations of the half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a honeycomb lattice. The columnar valence-bond-solid (cVBS) phase only breaks the threefold discrete symmetry and thus can survive at finite temperatures. The disordered phase in the weak coupling regime is the thermal Dirac semi-metal state, while in the strong coupling regime it is largely a Mott state in which the cVBS order is thermally melted. The calculated entropy-temperature relations for various values of the Hubbard interaction UUU show that the Pomeranchuk effect occurs when the specific entropy is below a characteristic value of S∗{S}^{*}S∗---the maximal entropy per particle from the spin channel of local moments. The SU(2N)\mathrm{SU}(2N)SU(2N) symmetry enhances the Pomeranchuk effect, which facilitates the interaction-induced adiabatic cooling. Our work sheds light on future explorations of novel states of matter with ultracold large-spin alkaline fermions.
The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with ultracold large-spin alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semimetals to the gapped Mott insulating phases in the SU(4) and SU(6) cases. Both of these Mott insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic N\'eel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves nonmonotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a nonanalytic term in the free energy. Our simulations provide important guidance for the experimental explorations of novel states of matter with ultracold alkaline-earth fermions.
We have systematically studied the thermodynamic properties of a two-dimensional half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a square lattice by using the determinant quantum Monte Carlo method. The entropy-temperature relation, the isoentropy curve, and the probability distribution of the on-site occupation number are calculated in both SU(4) and SU(6) cases, which exhibit prominent features of the Pomeranchuk effect. We analyze these thermodynamic behaviors based on energy scales in the density and spin channels. In the density channel, the interaction strength that marks the crossover from the weak to strong interaction regimes increases with the number of fermion components. In the spin channel, increasing the number of fermion components enhances quantum spin fluctuations, which is shown in the simulations of uniform spin susceptibilities and antiferromagnetic structure factors.
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 investigate the thermodynamic properties of a half-filled SU(2N) Hubbard model in the two-dimensional square lattice by the method of the determinant quantum Monte Carlo simulation, which is free of the fermion "sign problem." The large number of hyperfine-spin components enhances spin fluctuations, which facilitates the Pomeranchuk cooling to temperatures comparable to the superexchange energy scale in the case of SU(6). Various physical quantities including entropy, charge fluctuations, and spin correlations are calculated.
We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.
We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. We examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. For the homogeneous case, this process is found to be more efficient at finite doping than at half filling. That, in turn, leads to an efficient adiabatic cooling in the presence of a trap, which, starting with even relatively high entropies, can drive the system to have a Mott insulating phase with substantial antiferromagnetic correlations.