Interplay of localisation and competing interaction channels: cascade of quantum phase transitions

TL;DR

This paper explores how the competition between localization, interactions, and spin degrees of freedom induces a sequence of quantum phase transitions in lattice particles, with implications for cold atom systems.

Contribution

It demonstrates that tuning the relative strength of density-density and spin interactions drives multiple quantum phase transitions, revealing new frustrated phases and critical behavior.

Findings

Quantum phase transitions driven by competing interactions.

Singularities in effective exchange integrals at critical points.

Sign change in spin interaction induces phase transition even at zero spin coupling.

Abstract

We investigate the interplay of localization, interactions and (pseudo)spin degrees of freedom on quantum states of particles on the lattice. Our results show that breaking the paradigm density-density interaction $U_0\gg$ (pseudo)spin-(pseudo)spin interaction $U_s$ will drive the sequence of quantum phase transitions (QPT), where (pseudo)spin state and particle ordering, in case of several particle species, on the lattice are strongly changed. QPT driven by competing interactions, $|U_s|\sim U_0$, manifest itself in singularities of effective exchange integrals. $|U_s|\sim U_0$ implies a frustration when the interactions standing alone drive the system to different phases. Even at $U_s=0$, there is typically a QPT induced by $U_s$ sign change. Vector cold atoms, Fermions or Bosons, on optical lattices are the state-of-the-art realization of our system where $U_s$ is tunable \textit{in situ}.