Decay of transverse correlations in quantum Heisenberg models

Abstract

We study a class of quantum spin systems that includes the $S=\frac{1}{2}$ Heisenberg and XY-models, and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily constant, it may be random, and it points in the same direction. Our proof is entirely probabilistic and it relies on a random-loop-representation of the correlation functions, on stochastic domination, and on first-passage percolation.

arXiv comment9 pages

References in corpus (6)

• Geometric Aspects of Quantum Spin States
• Random loop representations for quantum spin systems
• The phase transition of the quantum Ising model is sharp
• Some Applications of the Lee-Yang Theorem
• Vanishing critical magnetization in the quantum Ising model
• Infrared bound and mean-field behaviour in the quantum Ising model

Cited by in corpus (6)

• The free energy in a class of quantum spin systems and interchange processes
• Dimerization and Néel order in different quantum spin chains through a shared loop representation
• Critical temperature of Heisenberg models on regular trees, via random loops
• Large cycles in random permutations related to the Heisenberg model
• A direct proof of dimerization in a family of SU(n)-invariant quantum spin chains
• On a class of orthogonal-invariant quantum spin systems on the complete graph