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arXiv:2212.07113 · SciPost Physics

Interaction quenches in Bose gases studied with a time-dependent hypernetted-chain Euler-Lagrange method

Mathias Gartner, David Miesbauer, Michael Kobler, Julia Freund, Giuseppe Carleo, Robert E. Zillich

Published Apr 9, 2025• 0 citations
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Abstract

We present a new variational method to study the dynamics of a closed bosonic many-body system, the time-dependent hypernetted-chain Euler-Lagrange method, tHNC. Based on the Jastrow ansatz, it accounts for quantum fluctuations in a non-perturbative way. The tHNC method scales well with the number of dimensions, as demonstrated by our results on one-, two-, and three-dimensional systems. We apply the tHNC method to interaction quenches, i.e. sudden changes of the interaction strength, in homogeneous Bose gases. When the quench is strong enough that the final state has roton excitations (as found and predicted for dipolar and Rydberg-dressed Bose-Einstein condensates, respectively), the pair distribution function exhibits stable oscillations. For validation, we compare tHNC results with time-dependent variational Monte Carlo results in one and two dimensions.

DOI
10.21468/scipostphys.18.4.123

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We present a new variational method to study the dynamics of a closed bosonic many-body system, the time-dependent hypernetted-chain Euler-Lagrange method, tHNC. Based on the Jastrow ansatz, it accounts for quantum fluctuations in a non-perturbative way. The tHNC method scales well with the number of dimensions, as demonstrated by our results on one-, two-, and three-dimensional systems. We apply the tHNC method to interaction quenches, i.e. sudden changes of the interaction strength, in homogeneous Bose gases. When the quench is strong enough that the final state has roton excitations (as found and predicted for dipolar and Rydberg-dressed Bose-Einstein condensates, respectively), the pair distribution function exhibits stable oscillations. For validation, we compare tHNC results with time-dependent variational Monte Carlo results in one and two dimensions.
We investigate the ground-state properties and excitations of Rydberg-dressed bosons in both three and two dimensions, using the hypernetted-chain Euler-Lagrange approximation, which accounts for correlations and thus goes beyond the mean-field approximation. The short-range behavior of the pair distribution function signals the instability of the homogeneous system with respect to the formation of droplet crystals at strong couplings and large soft-core radius. This tendency to spatial density modulation coexists with off-diagonal long-range order. The contribution of the correlation energy to the ground-state energy is significant at large coupling strengths and intermediate values of the soft-core radius while for a larger soft-core radius the ground-state energy is dominated by the mean-field (Hartree) energy. We have also performed path integral Monte Carlo simulations at selected system parameters to verify the performance of our hypernetted-chain Euler-Lagrange results in three dimensions. In the homogeneous phase, the two approaches are in very good agreement. Moreover, Monte Carlo simulations predict a first-order quantum phase transition from a homogeneous superfluid phase to the quantum droplet phase with face-centered cubic symmetry for Rydberg-dressed bosons in three dimensions.
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Ground-state properties of a two-dimensional fluid of bosons with repulsive dipole-dipole interactions are studied by means of the Euler-Lagrange hypernetted-chain approximation. We present a self-consistent semianalytical theory of the pair distribution function g(r)g(r)g(r) and ground-state energy of this system. Our approach is based on the solution of a zero-energy scattering Schr\"odinger equation for the ``pair amplitude'' g(r)\sqrt{g(r)}g(r)​ with an effective potential from Jastrow-Feenberg correlations. We find excellent agreement with quantum Monte Carlo results over a wide range of coupling strength, nearly up to the critical coupling for the liquid-to-crystal quantum phase transition. We also calculate the one-body density matrix and related quantities, such as the momentum distribution function and the condensate fraction.