National Sun Yat-sen University

Abstract:

The Quantum Tensor Train (QTT) provides an efficient framework for solving high-dimensional linear differential equations because increasing the spatial meshgrids expnonentialy by adding linear sites in the Matrix product state (MPS). By reformulating these differential equations as eigenvalue problems, they become amenable to convergent solutions via the Density Matrix Renormalization Group (DMRG) algorithm. In this work, we extend the QTT methodology to the nonlinear Schrödinger equation or Gross-Pitaevskii Equation (GPE) governing Bose-Einstein Condensates at ultracold temperatures. We focus on computing the ground state of rotational BECs, which exhibit intricate vortex lattice structures (Abrikosov lattices) highly sensitive to numerical discretization and physical parameters. Our approach combines gradient descent with line search and imaginary time evolution via the time-dependent variational principle (TDVP) within the QTT manifold. Furthermore, we validate our framework by simulating a simple breathing mode using TDVP in GPE to do the evolution, demonstrating consistently low and stable QTT bond dimensions throughout the dynamics. These results establish QTT as a powerful tool for high-fidelity simulations of nonlinear quantum systems.

Contact: Lei Wang 9853

Spacetime: M830