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Corner-Space Renormalization Method for Driven-Dissipative Two-Dimensional Correlated Systems.

S Finazzi1, A Le Boité1, F Storme1

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We developed a new theoretical method to study 2D quantum systems. This approach efficiently solves the master equation in a corner of the Hilbert space for driven-dissipative systems.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Quantum optics

Background:

  • Studying driven-dissipative quantum systems is crucial for understanding complex phenomena.
  • Simulating these systems on two-dimensional (2D) lattices presents significant computational challenges.

Purpose of the Study:

  • To present a novel theoretical method for studying 2D driven-dissipative correlated quantum systems.
  • To demonstrate the efficiency and accuracy of the proposed method.

Main Methods:

  • Solving the master equation within a specifically defined 'corner of the Hilbert space'.
  • Iteratively determining the states spanning this corner space using eigenvectors of smaller subsystems.
  • Merging subsystems and selecting states based on joint probability maximization.
  • Improving accuracy by increasing the dimension of the corner space until convergence.

Main Results:

  • The proposed method provides an efficient pathway to obtain the steady-state density matrix for 2D lattice systems.
  • The method was successfully applied to the driven-dissipative 2D Bose-Hubbard model.
  • Demonstrated the convergence and accuracy of the approach with increasing corner space dimension.

Conclusions:

  • The developed theoretical method offers an efficient and accurate way to study complex 2D driven-dissipative quantum systems.
  • This approach is particularly useful for systems with quantum optical nonlinearities, such as coupled cavity arrays.