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Causality and quantum criticality in long-range lattice models.

Mohammad F Maghrebi1, Zhe-Xuan Gong1, Michael Foss-Feig1

  • 1Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA; Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.

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Long-range quantum lattice systems can exhibit relativistic behavior. Our study shows that beyond a critical coupling exponent, these systems develop emergent relativistic dynamics, influencing their causal structure.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Long-range quantum lattice systems differ from short-range ones.
  • They may not satisfy Lieb-Robinson theorem conditions, lacking emergent relativistic structure.
  • Understanding their behavior is crucial for quantum many-body systems.

Purpose of the Study:

  • Investigate critical and near-critical behavior in long-range interacting quantum models.
  • Characterize the response of these systems to local perturbations.
  • Determine conditions for emergent relativistic dynamics.

Main Methods:

  • Field-theoretic approach.
  • Renormalization group theory up to two-loop order.
  • Analysis of one-dimensional transverse-field Ising and fermionic models.

Main Results:

  • Deduced the dynamic critical exponent for emergent causal behavior.
  • Identified a critical power-law exponent for long-range couplings.
  • Showed that dynamics become effectively relativistic beyond this critical value.
  • Calculated critical exponents for ground-state correlations and causal cone deviations.

Conclusions:

  • Long-range interactions can lead to emergent relativistic behavior in quantum lattice systems.
  • The dynamic critical exponent governs the transition to relativistic dynamics.
  • System behavior is tunable via the power-law exponent of interactions.