Sutirtha Paul, Matthias Thamm, Rahul Soni, Paul E. Sokol, and Adrian Del Maestro
While the canonical and grand canonical ensembles both describe equilibrium statistical mechanics in the thermodynamic limit, their distinct constraints can lead to differences in finite systems, especially in one spatial dimension where quantum and thermal fluctuations are enhanced. To probe the interplay between number fluctuations and strong correlations, we analytically compute grand canonical corrections to the density-density correlation function and one body density matrix of a Tomonaga–Luttinger liquid via bosonization. We identify a regime where these corrections are non-negligible and benchmark our findings using both Monte Carlo simulations of bosonic quantum liquids and density matrix renormalization group calculations of interacting spinless fermions in one spatial dimension. Our results demonstrate a measurable difference between the two ensembles in a regime with tunable density. We find that in practice, this difference can lead to complications when extracting the effective parameters of low-energy quantum hydrodynamic descriptions with experimental consequences for confined low dimensional superfluid $^4$He.
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The QMC data was generated with quantum Monte Carlo using our open source path integral software also available on github. DMRG data was generated using .. Processed data is included in the data directory and the full raw simulation data set is available online at
This work was performed with support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0024333.
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