Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice

Abstract

We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice experiments.

Optimization of finite-size errors in finite-temperature calculations of unordered phases

“…In Fig. 5, we show results for δE l for the 2D Heisenberg model in four different lattice geometriessquare [12], honeycomb [16,17], kagome, and triangular [5]. In all cases, the error is once again seen to decrease exponentially fast with increasing the number of sites in the clusters considered.…”

Lanczos-boosted numerical linked-cluster expansion for quantum lattice models

“…The calculation of properties P (c) using ED is the most computationally expensive part of the NLCEs. For example, in a site expansion, for which order l of the series includes all clusters up to l sites, calculations for the square or honeycomb lattice Fermi-Hubbard models have so far been limited to l = 9 [7,8,19,20]. Even though there are only 112 topologically-distinct clusters to diagonalize for the square lattice in the 9th order in that case, the calculations are limited by memory and time requirements for diagonalization of the largest matrices for clusters with a size larger than 9 sites.…”

Thermodynamics of the Hubbard model on stacked honeycomb and square lattices

“…47 For the Hubbard model in the context of optical lattice experiments, the presence of the effect was numerically observed both for square and honeycomb lattices. 29,48 0.65 0.70 0.75 We here investigate this effect for the stacked lattices in a homogeneous system. Figure 5 shows the adiabatic cooling effect at half filling and at entropy per site s = 0.7 at a range of anisotropies, with cooling persisting up to U/t ≈ 6.…”

“…23 Motivated by the physics of graphene and by the search for a spin liquid state at low temperature, [25][26][27] experimental realizations of the model on a honeycomb geometry have appeared 28 and provided results in agreement with numerical calculations of the 2d model. 29,30 Complementary to studies on isotropic lattices, anisotropic lattices of various types, e.g. with couplings in the vertical axis chosen differently from in-plane couplings, can be realized.…”