aiqbench analysis
This study applies Path Integral Monte Carlo methods to simulate quantum fluids on a curved surface, specifically investigating how positive curvature influences thermodynamic properties and superfluid transitions. By addressing the sign problem for fermions and anyons, the research provides exact numerical solutions for models relevant to quantum general relativity and strongly correlated electron systems. The findings offer fundamental insights into the interplay between geometry and many-body physics, advancing theoretical frameworks in condensed matter theory rather than presenting new AI algorithms or quantum hardware products.
Path Integral Monte Carlo on a Sphere
arXiv:2603.22338v2 Announce Type: replace-cross Abstract: We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant positive curvature. We use path integral Monte Carlo to measure the kinetic energy, the internal energy and the static structure of a bosons, fermions and anyons fluid at low temperatures on the sphere. For bosons we also measure the superfluid fraction and compare its behavior at the critical temperature with the universal jump predicted by Nelson and Kosterlitz in flat space in the thermodynamic limit at the superfluid phase transition. For fermions and anyons it is necessary to use the restricted path integral recipe in order to overcome the sign problem. Even if this recipe is exact for the non interacting fluid it reduces to just an approximation for an interacting system. And we make the example of the electron gas at low temperature. Snapshots of the many body path configuration during the evolution of the computer experiment show that the ``speed'' of the single particle path near the poles slows down as a consequence of the ``hairy ball theorem'' of Poincar\'e. The influence of curvature on the thermodynamic and structural properties of the many body fluid is also studied.
Abstract:We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant positive curvature. We use path integral Monte Carlo to measure the kinetic energy, the internal energy and the static structure of a bosons, fermions and anyons fluid at low temperatures on the sphere. For bosons we also measure the superfluid fraction and compare its behavior at the critical temperature with the universal jump predicted by Nelson and Kosterlitz in flat space in the thermodynamic limit at the superfluid phase transition. For fermions and anyons it is necessary to use the restricted path integral recipe in order to overcome the sign problem. Even if this recipe is exact for the non interacting fluid it reduces to just an approximation for an interacting system. And we make the example of the electron gas at low temperature. Snapshots of the many body path configuration during the evolution of the computer experiment show that the ``speed'' of the single particle path near the poles slows down as a consequence of the ``hairy ball theorem'' of Poincaré. The influence of curvature on the thermodynamic and structural properties of the many body fluid is also studied.
Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)
arXiv:2603.22338 [cond-mat.quant-gas]
(or arXiv:2603.22338v2 [cond-mat.quant-gas] for this version)
https://doi.org/10.1103/y457-glbg DOI(s) linking to related resources
From: Riccardo Fantoni Dr. [view email] [v1] Sat, 21 Mar 2026 06:39:29 UTC (224 KB) [v2] Fri, 21 Aug 2026 21:48:30 UTC (226 KB)
Full text under the publisher's open licence · 274 words
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