Quantum spin liquids of Rydberg excitations in a honeycomb lattice induced by density-dependent Peierls phases

TL;DR

This paper investigates how density-dependent Peierls phases in Rydberg atom honeycomb lattices induce disordered quantum phases, including potential quantum spin liquids and bosonic integer quantum Hall states, through complex transport phenomena.

Contribution

It introduces a detailed numerical study of phase transitions and novel disordered phases arising from density-dependent complex hopping in Rydberg systems, revealing potential quantum spin liquids and topological states.

Findings

Identification of a disordered phase with finite spin gap and non-trivial Chern number.

Evidence for a bosonic integer-quantum Hall phase protected by U(1) symmetry.

Discovery of a gapless spin-liquid-like regime at strong nonlinear hoppings.

Abstract

We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit coupled Rydberg atoms gives rise to disordered quantum phases which are candidates for quantum spin liquids. As recently demonstrated in [Lienhard et al. Phys. Rev. X, 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of the hard-core bosons or equivalently to complex XY spin interactions. Using exact diagonalization (ED) we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms. In mean-field approximation there is a phase transition from a quasi-condensate to a 120{\deg} phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase with a finite spin gap emerges close to the mean-field critical point as a result of quantum fluctuations induced by the density-dependence of the complex hopping. We show that this phase is a genuine disordered one, has a non-vanishing spin chirality and is characterized by a non-trivial many-body Chern number. ED simulations of small lattices with up to 28 lattice sites point to a non-degenerate ground state and thus to a bosonic integer-quantum Hall (BIQH) phase, protected by U(1) symmetry. The Chern number of C = 1, which is robust to disorder, is however different from the even Chern numbers found in BIQH phases. For very strong, nonlinear hoppings of opposite sign we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin-liquid but lies outside the parameter regime accessible in the Rydberg system.