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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • The Mermin-Wagner theorem prohibits continuous symmetry breaking (CSB) in low-dimensional systems with short-range interactions.
  • Long-range interactions, however, may allow for CSB, but critical decay rates remain undefined for 1D quantum systems at zero temperature.

Purpose of the Study:

  • Investigate the possibility of CSB in a 1D quantum spin chain with U(1) symmetry and power-law interactions V(r)∼1/r^{α}.
  • Determine the critical exponent governing the decay of interactions for CSB.
  • Characterize the phase transition and its universality class.

Main Methods:

  • Analytical techniques
  • Numerical simulations
  • Renormalization group analysis (implied)

Main Results:

  • CSB occurs for interaction decay exponents α below a critical value α_{c}(≤3).
  • The transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal and Lorentz symmetries.
  • The transition belongs to a universality class similar to, yet distinct from, the Berezinskii-Kosterlitz-Thouless transition.

Conclusions:

  • Long-range interactions enable CSB in 1D quantum systems, contrary to predictions for short-range forces.
  • A critical interaction decay exponent defines the boundary between phases.
  • Experimental signatures of the CSB phase are predicted to be observable in trapped-ion systems.