Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors

TL;DR

This paper reveals that infinite-range interactions in a quantum Heisenberg chain induce long-range $XY$ order and symmetry breaking, violating the Mermin-Wagner theorem, with potential verification in quantum emulators.

Contribution

It demonstrates the emergence of long-range order and symmetry breaking in a Heisenberg chain with infinite-range interactions, supported by analytical and numerical methods.

Findings

Long-range $XY$ order induced by weak infinite-range interactions.

Violation of the Mermin-Wagner theorem in this system.

Logarithmic violation of the area law in entanglement entropy.

Abstract

Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity mediated infinite range interactions can induce fast scrambling in a Heisenberg $XXZ$ spin chain (Phys. Rev. Research {\bf 2}, 043399 (2020)). In this work, we analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions. Employing both analytical spin-wave theory as well as numerical DMRG calculations, we find that there is a large parameter regime where the continuous $U(1)$ symmetry of this model is spontaneously broken and the ground state of the system exhibits $XY$ order. This kind of symmetry breaking and the consequent long range order is forbidden for short range interacting systems by the Mermin-Wagner theorem. Intriguingly, we find that the $XY$ order can be induced by even an infinitesimally weak infinite range interaction. Furthermore, we demonstrate that in the $U(1)$ symmetry broken phase, the half chain entanglement entropy violates the area law logarithmically. Finally, we discuss a proposal to verify our predictions in state-of-the-art quantum emulators.