The gas-liquid transition is a first-order transition terminating at a finite-temperature critical point with diverging density fluctuations. Mott transition, a metal-insulator transition driven by Coulomb repulsion between electrons, has been identified with this textbook transition. However, the critical temperature of the Mott transition can be suppressed, resulting in unusual quantum criticality. It accounts for non-Fermi-liquid-like properties, and strongly momentum dependent quasiparticles as in many materials near the Mott insulator. Among all, the mode-coupling theory of the density fluctuations supports d-wave superconductivity at the order of a hundred Kelvin for relevant parameters of the copper oxide superconductors.The gas-liquid transition is a first-order transition terminating at a finite-temperature critical point with diverging density fluctuations. Mott transition, a metal-insulator transition driven by Coulomb repulsion between electrons, has been identified with this textbook transition. However, the critical temperature of the Mott transition can be suppressed, resulting in unusual quantum criticality. It accounts for non-Fermi-liquid-like properties, and strongly momentum dependent quasiparticles as in many materials near the Mott insulator. Among all, the mode-coupling theory of the density fluctuations supports d-wave superconductivity at the order of a hundred Kelvin for relevant parameters of the copper oxide superconductors.

arXiv:cond-mat/0411217Journal of the Physical Society of JapanMar 1, 200512 citations

Superfluid-Mott-Insulator Transition

Manuel Endres

Springer thesesJan 1, 20142 citations

Quantum criticality of a Bose gas in an optical lattice near the Mott transition

Adam Rançon, N. Dupuis

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.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.

arXiv:1107.1314Physical Review AJan 4, 201213 citations

Universal thermodynamics of the superfluid to Mott insulator transition

N. Dupuis, Adam Rançon

Bulletin of the American Physical SocietyMar 7, 20140 citations

Thermal decoherence in a strongly correlated Bose liquid

Abhishek Joshi, Pinaki Majumdar

We compute the single particle spectral function of a Bose liquid on a lattice, at integer filling, close to the superfluid-Mott transition. We use a `static path approximation' that retains all the classical thermal fluctuations in the problem, and a real space implementation of the random phase approximation (RPA) for the Green's functions on the thermally fluctuating backgrounds. This leads to the standard RPA answers in the ground state but captures the progressive damping of the excitations with increasing temperature. We focus on the momentum resolved lineshape across the superfluid to Bose liquid thermal transition. In the superfluid regime we observe a gapped `amplitude' mode, and gapless `phase' modes of positive and negative energy. The dispersion and weight of these modes changes with interaction but are almost temperature independent, even into the normal state, except near critical coupling. The damping of the modes varies roughly as $T^α f_{\bf k}$ , where $T$ is the temperature and ${\bf k}$ the momentum, with $α\sim 0.5$ and $f_{\bf k}$ having non trivial momentum dependence. The Mott phase has gapped dispersive spectra. Near critical coupling the thermal Bose `liquid' is gapped, with progressive widening of the gap with increasing temperature, a feature that it shares with the Mott insulator.We compute the single particle spectral function of a Bose liquid on a lattice, at integer filling, close to the superfluid-Mott transition. We use a `static path approximation' that retains all the classical thermal fluctuations in the problem, and a real space implementation of the random phase approximation (RPA) for the Green's functions on the thermally fluctuating backgrounds. This leads to the standard RPA answers in the ground state but captures the progressive damping of the excitations with increasing temperature. We focus on the momentum resolved lineshape across the superfluid to Bose liquid thermal transition. In the superfluid regime we observe a gapped `amplitude' mode, and gapless `phase' modes of positive and negative energy. The dispersion and weight of these modes changes with interaction but are almost temperature independent, even into the normal state, except near critical coupling. The damping of the modes varies roughly as $T^α f_{\bf k}$, where $T$ is the temperature and ${\bf k}$ the momentum, with $α\sim 0.5$ and $f_{\bf k}$ having non trivial momentum dependence. The Mott phase has gapped dispersive spectra. Near critical coupling the thermal Bose `liquid' is gapped, with progressive widening of the gap with increasing temperature, a feature that it shares with the Mott insulator.

arXiv:1712.04433Dec 12, 20170 citations

{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.

T^α f_{\bf k}

, where

T

is the temperature and

{\bf k}

the momentum, with

α\sim 0.5

and

f_{\bf k}

having non trivial momentum dependence. The Mott phase has gapped dispersive spectra. Near critical coupling the thermal Bose `liquid' is gapped, with progressive widening of the gap with increasing temperature, a feature that it shares with the Mott insulator.