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Area of Science:

  • Theoretical Physics
  • Quantum Many-Body Systems
  • Computational Physics

Background:

  • Matrix product states (MPS) are effective for 1D quantum spin systems.
  • Continuous matrix product states (cMPS) represent 1D quantum field theories.
  • Optimizing cMPS for inhomogeneous potentials has been a significant challenge.

Purpose of the Study:

  • To develop a robust method for optimizing continuous matrix product states (cMPS).
  • To enable accurate calculations for 1D interacting field theories in external potentials.
  • To provide a computationally efficient approach for determining ground states and energies.

Main Methods:

  • Introduced a piecewise linear parameterization for matrix-valued functions in cMPS.
  • Utilized high-order Taylor expansions for exact calculation of reduced density matrices.
  • Developed a variational algorithm for exact energy and derivative computation.

Main Results:

  • The new method allows exact calculation of energies and their derivatives.
  • Computational cost scales cubically with the bond dimension.
  • Successfully applied to find ground states of interacting bosons in potentials.

Conclusions:

  • The piecewise linear parameterization resolves cMPS optimization issues for inhomogeneous systems.
  • Enables efficient and exact computation of key physical quantities.
  • Applicable to calculating boundary/Casimir energy corrections in open boundary systems.