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Holographic quantum states.

Tobias J Osborne1, Jens Eisert, Frank Verstraete

  • 1Wissenschaftskolleg zu Berlin, Berlin, Germany.

Physical Review Letters
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

Continuous quantum fields are equivalent to boundary field dynamics. This connection links quantum measurement theory with quantum field theory, enabling new renormalization group methods and interpretations of cavity QED experiments.

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Area of Science:

  • Quantum Field Theory
  • Quantum Measurement Theory
  • Condensed Matter Physics

Background:

  • Continuous matrix product states (MPS) are crucial for describing quantum many-body systems.
  • Understanding the dynamics of quantum fields, especially in nonequilibrium states, is a significant challenge.
  • The relationship between quantum field theory and quantum measurement is an active area of research.

Purpose of the Study:

  • To establish an equivalence between continuous matrix product states of quantum fields and dissipative dynamics of a lower-dimensional boundary field.
  • To provide a novel framework for applying real-space renormalization group methods to quantum field theories.
  • To offer a new perspective on cavity quantum electrodynamics (QED) experiments and their connection to quantum phase transitions.

Main Methods:

  • Describing continuous matrix product states (MPS) of quantum fields.
  • Analyzing the dissipative nonequilibrium dynamics of an auxiliary boundary field.
  • Demonstrating the correspondence between spatial correlation functions of the bulk field and temporal statistics of the boundary field.

Main Results:

  • An explicit construction of the boundary field is provided.
  • The spatial correlations of the bulk field are shown to equal the temporal statistics of the boundary field.
  • This equivalence allows for lattice-free real-space renormalization group methods in arbitrary dimensions.

Conclusions:

  • A deep connection exists between continuous quantum measurement theory and quantum field theory.
  • The developed framework facilitates the study of quantum field theories without lattice discretization.
  • This work offers a new interpretation for cavity QED experiments, potentially leading to the observation of quantum phase transitions in driven quantum systems.