Quantum Monte Carlo study of systems interacting via long-range interactions mediated by a cavity

We study one-dimensional quantum gases in continuous space with cavity-mediated infinite-range interactions using variational and diffusion Monte Carlo methods. Starting from the exact two-body solution, we construct a non-translationally invariant Jastrow wavefunction that accurately captures the spatial structure induced by the cavity field and provides an efficient many-body ansatz for both bosonic and fermionic systems. We analize properties of three characteristic quantum systems, subject to long-range interactions: (i) ideal Bose gas (ii) interacting Bose gas (iii) ideal Fermi gas. In the absence of short-range interactions, we identify a crossover from a stable, weakly modulated phase realized for repulsive interactions to a delocalized bound state for attractive interactions, marked by clustering, loss of superfluidity, and the absence of a thermodynamic limit. Introducing short-range repulsion, either through contact interactions or fermionic statistics, leads to the formation of a mesoscopic gas-like regime that disappears in the thermodynamic limit. A qualitative phase diagram is proposed to illustrate the combined effects of short- and long-range interactions, highlighting the emergence of distinct regimes with characteristic structural properties.

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