Mesoscopic effects in quantum phases of ultracold quantum gases in optical lattices

Abstract

We present a wide array of quantum measures on numerical solutions of 1D Bose-and FermiHubbard Hamiltonians for finite-size systems with open boundary conditions. Finite size effects are highly relevant to ultracold quantum gases in optical lattices, where an external trap creates smaller effective regions in the form of the celebrated "wedding cake" structure and the local density approximation is often not applicable. Specifically, for the Bose-Hubbard Hamiltonian we calculate number, quantum depletion, local von-Neumann entropy, generalized entanglement or Q-measure, fidelity, and fidelity susceptibility; for the Fermi-Hubbard Hamiltonian we also calculate the pairing correlations, magnetization, charge-density correlations, and antiferromagnetic structure factor. Our numerical method is imaginary time propagation via time-evolving block decimation. As part of our study we provide a careful comparison of canonical vs. grand canonical ensembles and Gutzwiller vs. entangled simulations. The most striking effect of finite size occurs for bosons: we observe a strong blurring of the tips of the Mott lobes accompanied by higher depletion, and show how the location of the first Mott lobe tip approaches the thermodynamic value as a function of system size.

Quantifying Complexity in Quantum Phase Transitions via Mutual Information Complex Networks

“…Physically this could be because the length scale of correlations has become as long as one lattice spacing but not two, resulting in a period of rapid increase in mutual information between nearest neighbors relative to second nearest neighbors. In strong Bose Hubbard model describing massive particles for commensurate lattice filling, with BKT crossover occurring in the limit L → ∞ at a ratio of tunneling J to interaction U of (J/U )BKT = 0.305; for smaller system sizes, the effective critical point [29] can be as small as (J/U )BKT 0.2. The density and clustering coefficient grow as spatial correlations develop in the superfluid phase.…”

“…Our simulations are converged up to a variance tolerance of 10 −10 (10 −8 ) in the TIM (BHM). Mesoscopic corrections have been explored for the BHM in detail in our previous work [29].…”

Thermal entanglement of Hubbard dimers in the nonextensive statistics

“…It has been shown that entanglement of two neighboring sites shows a sharp peak either near or at the critical point where the phase transition takes place [5][6][7]14]. This suggests an intimate relation between quantum entanglement and quantum phase transition [2,19,21,20,26].…”

“…Small-scale systems belong to nonextensive systems as mentioned above. It is necessary to take into account the effect of nonextensivity, when we study the properties of quantum information of qubits, which have been mainly investigated within the BGS [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In recent years, the NES has been applied to the study on quantum information [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53].…”

“…Quantum entanglement is expected to play an essential role as a resource in quantum communication and information processing. Many studies have been made on quantum entanglement with quantum spin models [3][4][5][6][7][8][9][10][11] and fermion systems [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] to clarify both its qualitative and quantitative aspects. The interface between the quantum information and statistical mechanics has been considerably investigated in recent years.…”