Entropy-driven first-order phase transition in quantum compass model with Ly>3 Tian Liang

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DUALITY TRANSFORMATION Compass model Plaquette model

The plaquette model quantum fluctuation h = 0: classical model of Ising spins one-dimensional nearest-neighbor Ising model Symmetry: system energy remains the same under spin flip for each row and each column Ground state degeneracy: Given arbitrary values of the spins on one row and one column, there is a unique ground of the system compatible with these values. h > K xy : quantum fluctuations leads to proliferation of defects and loss of long-ranged order.

QUANTUM-CLASSICAL MAPPING Path integral representation Self-duality

Numerical Results Two chain problem: Ly=2

Finite size scaling 2D Ising model γ= 1.75 β =0.125 ν = 1

Numerical Results Two chain problem: Ly=3

Finite size scaling Four-state Potts model α = 0.69 γ = 1.17 β =0.085 ν = 0.66

the nature of the disorder transition B. Doucot et al., PRB 71, (2005) S. Wenzel and W. Janke, cond-mat/ v1

Numerical Results Two chain problem: Ly=4

Numerical Results Two chain problem: Ly=Lx (Quantum 2D system )

First-order phase transition for Ly>3

q-state Potts model and coloring entropy continuous mosaic Coloring entropy (q>4) Line tension, vanishes at t = 0

q-state Potts & XY model and coloring entropy vs. Four color theorem The current work

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