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arXiv:1104.5494 · Physical Review A

Thermodynamics of strongly interacting fermions in two-dimensional optical lattices

Ehsan Khatami, Marcos Rigol

Published Nov 14, 2011• 91 citations
arXivHTMLPDF

Abstract

We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the thermodynamic limit. We focus our analysis on the strongly interacting regime, where the on-site repulsion is of the order of or greater than the band width. We compute the equation of state, double occupancy, entropy, uniform susceptibility, and spin correlations for temperatures that are similar to or below the ones achieved in current optical lattice experiments. We provide a quantitative analysis of adiabatic cooling of trapped fermions in two dimensions, by means of both flattening the trapping potential and increasing the interaction strength.

DOI
10.1103/physreva.84.053611

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We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the thermodynamic limit. We focus our analysis on the strongly interacting regime, where the on-site repulsion is of the order of or greater than the band width. We compute the equation of state, double occupancy, entropy, uniform susceptibility, and spin correlations for temperatures that are similar to or below the ones achieved in current optical lattice experiments. We provide a quantitative analysis of adiabatic cooling of trapped fermions in two dimensions, by means of both flattening the trapping potential and increasing the interaction strength.
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.
The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disorder in the onsite energy, the interaction strength, as well as the hopping amplitude and explore how energy, double occupancy, entropy, heat capacity, and magnetic correlations of the system in the thermodynamic limit evolve as the strength of disorder changes. We compare our findings with those obtained from determinant quantum Monte Carlo simulations and discuss the relevance of our results to experiments with cold fermionic atoms in optical lattices.
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.
We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the N\'eel ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods.
We use numerical linked cluster expansions (NLCEs) to study correlated lattice systems in one and two dimensions.For fermions in the honeycomb lattice, we study its finite-temperature properties and short-range spin correlations using NLCEs and determinantal quantum Monte Carlo (DQMC) simulations.For the homogeneous system, 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.Employing a local density approximation (LDA), we examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems.We also use NLCEs to study thermodynamic properties of the two-dimensional spin-1/2 Ising, XY, and Heisenberg models with bimodal random-bond disorder on the square and honeycomb lattices.In all cases, the nearest-neighbor coupling between the spins takes values ±J with equal probability.We obtain the disorder averaged (over all disorder configurations) energy, entropy, specific heat, and uniform magnetic susceptibility in each case.These results are compared with the corresponding ones in the clean models.Analytic expressions are obtained for low orders in the expansion of these thermodynamic quantities in inverse temperature.For many-body localization in disordered isolated systems, we study quantum quenches in the thermodynamic limit.By a quantum quench it is meant that the initial state is stationary with respect iii to an initial Hamiltonian, which is suddenly changed to a new (time-independent) Hamiltonian.The latter then drives the (unitary) dynamics of the system.We are interested in the time average of observables after relaxation following the quench, which can be computed under the so-called diagonal ensemble.
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.