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arXiv:1410.5922 · Physical Review B

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

Zhichao Zhou, Zi Cai, Congjun Wu, Yu Wang

Published Dec 22, 2014• 35 citations
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Abstract

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.

DOI
10.1103/physrevb.90.235139

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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 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 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.
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 present a numerically exact study of the Hubbard model with spin-dependent anisotropic hopping on the square lattice using auxiliary-field quantum Monte Carlo method. At half filling, the system undergoes Ising phase transitions on cooling, leading to the formation of Ising-type antiferromagnetic order for repulsive interactions and charge-density wave order for attractive interactions at finite temperatures. By elegantly implementing the sign-problem-free condition and Hubbard-Stratonovich transformations, we achieve significant improvements in precision control of the numerical calculations and obtain highly accurate results of the transition temperatures from weak to strong interactions across representative anisotropies. We further characterize the system by examining the temperature dependence of various thermodynamic properties, including the energy, double occupancy, specific heat, and charge susceptibility. Specifically, we provide unbiased numerical results of the entropy map on temperature-interaction plane, the critical entropy, and the spin, singlon and doublon correlations, all of which are directly measurable in optical lattice experiments. Away from half filling, we explore the behavior of the sign problem and investigate the possible emergence of stripe spin-density wave order in the system with repulsive interaction.
We study the thermodynamics of the three-dimensional Hubbard model at half filling on approach to the N\'eel transition by means of large-scale unbiased diagrammatic determinant Monte Carlo simulations. We obtain the transition temperature in the strongly correlated regime, as well as the temperature dependence of the energy, entropy, double occupancy, and nearest-neighbor spin correlation function. Our results improve the accuracy of previous unbiased studies and present accurate benchmarks in the ongoing effort to realize the antiferromagnetic state of matter with ultracold atoms in optical lattices.
We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half filling: A maximum in the entropy at nonzero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can, therefore, be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.