The first-order phase transition in the large polaron ground state

R. Mańka, Maciej Suffczynski

The large polaron first-order phase transition from the mobile to the self-trapped phase is determined from a variational principal. The transition is a spontaneous transition to a coherent state breaking the translational invariance of the polaron Hamiltonian.

A. N. Das, Sanchita Sil

H. L�wen

Laurent Proville, S. Aubry

The bound states of two electrons in the adiabatic Holstein-Hubbard model are studied numerically in one and two dimensions from the anticontinuous limit. This model involves a competition between a local electron-phonon coupling (with a classical lattice) which tends to form pairs of electrons and the repulsive Hubbard interaction $U \geq 0$ which tends to break them. In 1D, the ground-state always consists in a pair of localized polarons in a singlet state. They are located at the same site for U=0. Increasing U, there is a first order transition at which the bipolaron becomes a spin singlet pair of two polarons bounded by a magnetic interaction. The pinning mode of the bipolaron soften in the vicinity of this transition leading to a higher mobility of the bipolaron which is tested numerically. In 2D, and for any $U$, the electron-phonon coupling needs to be large enough in order to form small polarons or bipolarons instead of extended electrons. We calculate the phase diagram of the bipolaron involving first order transitions lines with a triple point. A pair of polarons can form three types of bipolarons: a) on a single site at small $U$, b) a spin singlet state on two nearest neighbor sites for larger $U$ as in 1D and c) a new intermediate state obtained as the resonant combination of four 2-sites singlet states sharing a central site, called quadrisinglet. The breathing and pinning internal modes of bipolarons in 2D generally only weakly soften and thus, they are practically not mobile. On the opposite, in the vicinity of the triple point involving the quadrisinglet, both modes exhibit a significant softening. However, it was not sufficient for allowing the existence of a classical mobile bipolaron (at least in that model).

Wei Yi, Wei Zhang

We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for an arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological superfluid state and the normal state for a highly polarized Fermi gas in the thermodynamic limit. As polarization in a Fermi gas with SOC is induced by the effective Zeeman field, we also discuss the influences of the effective Zeeman field on the ground state of the system. Our findings may be tested directly in future experiments.

Feng Qiao, Qiu-Yi Chen, Zu-Jian Ying

The experimental access to ultra-strong couplings in light-matter interactions has made the quantum phase transition (QPT) in the quantum Rabi model practically relevant, while the physics of the QPT has not yet been fully explored. The polaron picture is a method capable of analyzing in the entire coupling regime and extracting the essential physics behind the QPT. However, the asymmetric deformation of polarons is missing in the current polaron picture. In the present work we propose an improved variational method in asymmetric polaron picture (APP). Our APP not only increases the method accuracy but also reveals more underlying physics concerning the QPT. We find that in the ground state both the polarons and antipolarons are asymmetrically deformed to a large extent, which leads to a richer phase diagram. We also analyze the first excited state in which we unveil an asymmetry direction reversal for the polarons and an attraction/replusion transition differently from the ground state. Finally, we apply the APP in quantum Fisher information analysis and critical coupling extraction, the improvements indicate that the polaron asymmetry makes a considerable contribution to the quantum resource in quantum metrology and plays an unnegligible role in the QPT. Our results and mechanism clarifications expose more subtle energy competitions and abundant physics, and the method potentially might have broader applications in light-matter interactions.