Kinetic energy driven phase transitions in Bose superfluids occur at low values of the repulsion when the values of the next-to-nearest and next-to-next-to-nearest hopping term attain certain critical values, resulting in alterations in the wavevector of the condensate. We map out the space of possible phases allowed by particular forms of the single-particle energy dispersion in the superfluid state, noting the appearance of a new phase, and examine in more detail the effects of additional repulsive terms on the form of the condensate wavefunction. We also examine the effect of these additional hopping terms on the formation of inhomogeneities in the condensate.
We investigate how strongly interacting bosons, described by the Bose-Hubbard Hamiltonian, transition from the Mott insulator to the superfluid phase and, ultimately, to a regime of vanishing interaction where the system smoothly transitions to an ensemble of free bosons undergoing Bose-Einstein condensation. Our study focuses on bosons residing on a three-dimensional simple cubic lattice, with tight-binding interactions characterized by the kinetic energy
t between neighboring lattice sites and on-site repulsion
U. To achieve this, we develop a formalism based on mapping the original quantum mechanical Hamiltonian onto an effective quantum spherical model. This approach is nonperturbative in interaction energy and spans the entire range of the interaction parameter
U. Our findings are presented through a series of multiparameter phase diagrams that include temperature, interaction energy, chemical potential, and particle density, highlighting the corresponding critical surfaces and lines. In this context, we address the issue of quantum critical points at fixed densities, which appear as endpoints in the temperature-interaction phase diagram. We also compare our theoretical results, where applicable, with other approaches, including quantum Monte Carlo simulations.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
We study the quantum phase transitions and identify a tricritical point between a normal Bose superfluid, a superfluid that breaks additional Z(2) Ising symmetry, and a Mott insulator in a recent shaken optical lattice experiment. We show that near the transition between normal and Z(2) symmetry breaking superfluids, bosons can condense into a momentum state with high or even locally maximum kinetic energies due to the interaction effect. We present a general low-energy effective field theory that treats both the superfluid transition and the Ising transition in a uniform framework. Using the perturbative renormalization group method, we find that the critical behavior of the quantum phase transition belongs to a universality class different from that of a dilute Bose gas.
Recent advances in cooling techniques make possible the experimental study of quantum phase transitions, which are transitions near absolute zero temperature accessed by varying a control parameter. A paradigmatic example is the superfluid-Mott transition of interacting bosons on a periodic lattice. From the relativistic Ginzburg-Landau action of this superfluid-Mott transition we derive the elementary excitations of the bosonic system, which contain in the superfluid phase a gapped Higgs mode and a gapless Goldstone mode. We show that this energy spectrum is in good agreement with the available experimental data and we use it to extract, with the help of dimensional regularization, meaningful analytical formulas for the beyond-mean-field equation of state in two and three spatial dimensions. We find that, while the mean-field equation of state always gives a second-order quantum phase transition, the inclusion of Gaussian quantum fluctuations can induce a first-order quantum phase transition. This prediction is a strong benchmark for future experiments on quantum phase transitions.
We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure $P(\ensuremath{\mu},T)$ versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass
m∗ and scattering length
a∗. Here
m∗ is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while
a∗ is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio
t/U between hopping amplitude and on-site repulsion.