Fractional Statistics and Quantum Scaling Properties of the Hubbard Chain with Bond-Charge Interaction

Abstract

We present a detailed study of the ground state and low-temperature properties of the integrable Hubbard model with bond-charge interaction, including its conducting properties and scaling behavior near the U-driven quantum phase transitions. Remarkably, the model displays fractional statistical properties, which enlighten the nature of various physical properties, such as the fractional elementary excitations, and give rise to a disordered condensate and phase separation in k space, as well as to a topological change in the generalized Fermi surface at half filling.

Fractional statistics and quantum scaling properties of the integrable Penson-Kolb-Hubbard chain

“…In Ref. 26, the authors have pointed out that the thermodynamic properties of the model in Eq. ͑2͒ is that of an ideal excluson gas with three fractional species, ͗n k,␣ ͘,…”

“…14 Further, other Hamiltonian models obeying fractional exclusion statistics have been studied, such as: multicomponent Sutherland model, 15 quantum Calogero model, 16 model describing onedimensional relativistic fermions interacting with the Toda array of N scalar fields, 17 Hubbard model with infinite-range interaction, 18 exclusion statistics and signature of strongly interacting anyons, 19 strongly interacting one-dimensional Bose gas, 20 gas of neutral fermionic atoms at ultralow temperatures with the attractive interaction tuned to Feshbach resonance, 21 phase transitions and pairing signature in strongly attractive Fermi atomic gases, 22 entanglement entropy in the Calogero-Sutherland model, 23 statistical correlations in an ideal gas of particles, 24 and many-spinon states and representations of Yangians in the SU͑n͒ HaldaneShastry model. 25 Recently, the authors 26 have shown that the exactly solvable Hubbard chain with bond-charge interaction is mapped onto an ideal gas of three species of exclusons. Remarkably, the statistical matrix for this model with on-site interaction is the same found for the Hubbard model with infinite-range interaction.…”

“…26, the scaling analysis of the model allows us to predict power law or logarithmic singularities associated with the critical lines using the scaling form for the free energy in Eq. ͑83͒:…”

Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of thes-wave scattering length

“…Later on, such terms were reconsidered as an alternative scheme for high-T c superconductivity [28,29]. For particular parameter values the Hamiltonian for a Hubbard chain turns out to be integrable [30] and displays fractional statistics [31]. The occupation-number sensitivity of tunnelling was even implemented experimentally by employing the high-resolution quantum gas microscope technique [32].…”

Quantum discord and classical correlations in the bond-charge Hubbard model: Quantum phase transitions, off-diagonal long-range order, and violation of the monogamy property for discord

“…The present work is intended to fill this gap, by investigating the behavior of QD and CC for the ground states of the one-dimensional bond-charge extended Hubbard model 32,33 , which is a reference model in correlated-electron theory. The model has an integrable point, and its entanglement properties have been the subject of recent studies [34][35][36][37][38] where use of two-point and multipartite entanglement measures led to a classification of QPTs into multipartite or two-point driven. These studies left open the problem of addressing the general role of bipartite correlations for all twopoints driven QPTs, as well as their relation with the presence of off diagonal long range order (ODLRO) which characterizes some ordered phases of the model.…”