Exponential decay in O(n)-invariant quantum spin systems

2025/06/27 by Björnberg, Jakob E., Ryan, Kieran
#60K35 #82B10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.22254

Abstract

We consider O(n)-invariant and reflection-positive quantum spin systems on the integer lattice in any dimension, and prove that spin-spin correlations decay exponentially fast provided n is large enough. This answers a question of Ueltschi, who proved that for small n there is instead long-range order (for d at least 3).

Citations

• Dimerization in O(n)-invariant quantum spin chains
• Improved bounds for connection probabilities in random loop models
• Reflection positivity and infrared bounds for quantum spin systems

Cited by

• Dimerization in O(n)-invariant quantum spin chains

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