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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

Continuous matrix product states for quantum fields.

F Verstraete1, J I Cirac

  • 1University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Wien, Austria.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We introduce matrix product states for continuum models, extending density matrix renormalization group methods to quantum field theories in one spatial dimension. This approach is demonstrated using the Lieb-Liniger model.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Quantum Field Theory

Background:

  • Matrix product states (MPS) are a powerful tool for simulating one-dimensional quantum systems.
  • Existing MPS formalisms typically rely on a discrete lattice structure.
  • Extending these methods to continuum models and quantum field theories remains a challenge.

Purpose of the Study:

  • To define matrix product states in a continuum limit, independent of lattice discretization.
  • To generalize the density matrix renormalization group (DMRG) and variational MPS (V MPS) methods for continuum systems.
  • To apply the developed formalism to a relevant physical model.

Main Methods:

  • Formulation of matrix product states directly in the continuum.
  • Adaptation of DMRG and V MPS algorithms for continuum Hamiltonians.
  • Numerical implementation and testing on the Lieb-Liniger model.

Main Results:

  • A rigorous definition of matrix product states for continuum models was established.
  • The formalism successfully extends DMRG and V MPS to quantum field theories in 1 spatial dimension.
  • The Lieb-Liniger model was accurately reproduced using the new continuum MPS approach.

Conclusions:

  • The developed continuum matrix product state formalism provides a versatile framework for studying 1D quantum field theories.
  • This method overcomes limitations of lattice-based approaches, enabling broader applications.
  • The successful application to the Lieb-Liniger model validates the approach for complex quantum systems.