Equivalence and Divergence of Imaginary-Time Evolution and Gradient Descent for Gaussian Variational States

Imaginary-time evolution (ITE) is one of the most widely used numerical techniques for obtaining ground states of many-body Hamiltonians. In this work, we compare ITE with gradient descent (GD) within the framework of Gaussian wavefunction ansatze. We show that while ITE and GD are formally equivalent for fermionic systems, GD exhibits consistently faster convergence for bosonic systems, challenging the common assumption of their complete equivalence.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-11-09

• Fields of study

  Physics

• Identifiers
  arXiv 2511.06364
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Kondo impurity in an attractive Fermi-Hubbard bath: Equilibrium and dynamics

  2025cited by this paper
• Scalable imaginary time evolution with neural network quantum states

  2023cited by this paper
• Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions.

  2021cited by this paper
• Zero-temperature phases of the two-dimensional Hubbard-Holstein model: A non-Gaussian exact diagonalization study

  2019cited by this paper
• Variational ansatz-based quantum simulation of imaginary time evolution

  2018cited by this paper
• Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications

  2017influential reference
• Generation of Bose-Einstein Condensates’ Ground State Through Machine Learning

  2017cited by this paper
• The Hubbard dimer: a density functional case study of a many-body problem

  2015cited by this paper
• Electronic structure calculations with dynamical mean-field theory

  2005cited by this paper
• Density Matrix Approach to Local Hilbert Space Reduction

  1997cited by this paper
• Density-matrix renormalization-group study of the polaron problem in the Holstein model

  1997cited by this paper
• Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

  1996cited by this paper
• Density-matrix algorithms for quantum renormalization groups.

  1993cited by this paper

• No citing papers are available for this paper.