Waterlike anomalies in the Bose–Hubbard model

Abstract

Although well-researched as a prototype Hamiltonian for strongly interacting quantum systems, the Bose-Hubbard model has not so far been explored as a fluid system with waterlike anomalies. In this work we show that this model supports, in the limit of a strongly localizing confining potential, density anomalies which can be traced back to ground state (zero-temperature) phase transitions between different Mott insulators. This key finding opens a new pathway for theoretical and experimental studies of liquid water and, in particular, we propose a test of our predictions that can be readily implemented in a ultra-cold atom platform.

Double-peak specific heat anomaly and correlations in the Bose-Hubbard model

“…1(a) portrays the specific heat c µ as a function of the temperature T in a three-dimensional diagram including a wide range of chemical potential values (in different colors), with the loci of maxima represented as dotted and continuous black lines in the µT plane. At zero temperature, there are ground-state phase transitions (GSPT) between Mott insulators of successive occupation numbers whenever the chemical potential µ takes on integer values of the local interaction U [52,61], shown as red dots. At higher temperatures, it is observed a maximum at any value of fixed µ, symbolized by dotted lines.…”

Quantum density anomaly in optically trapped ultracold gases

“…The density anomalies in the normal fluid can be traced back to the ground-state phase transitions between Mott insulators of successive occupation numbers [62]. This anomalous behavior, present even in the absence of hopping, arises from the competition between the chemical potential, which promotes the boson occupation in the lattice, with the on-site repulsion interaction U , which favors the boson removal.…”

Quantum density anomaly in optically trapped ultracold gases

“…At such transition points two states are equally accessible and this degeneracy accounts for an observed macroscopic residual entropy of s 0 = k B ln 2. For finite temperatures, zero point entropies produce peaks near those points as the chemical potential is varied [40]. By turning on the tunneling probability adiabatically the superfluid phase emerges exactly from Mott Insulator transition points, mitigating residual entropies, as should be expected through the third law of thermodynamics.…”

“…The numerical analysis concerning the stationary solutions ∇Γ SF T [F ′ , ∆ 00 , ∆ 01 ] = 0 and their agreement with the results exposed in reference [30] ∂T µ is the entropy per volume. Hence, the coefficients α and α µ are interchangeable to investigate waterlike anomalies near the ground state [40]. The pressure is fixed employing the Gibbs-Duhem relation dP = ρdµ + sdT = 0, where P is related to the grandcanonical potential according to −P V = Ω = Γ SF T .…”

“…Density anomalies in the normal fluid can be traced back to the ground state phase transitions between Mott Insulators of successive occupation numbers [40]. This anomalous behavior, present even in the absence of hopping, arises from the competition between the chemical potential, which promotes the boson occupation in the lattice, with the on site repulsion interaction U , which favors the boson removal.…”