Abstract We consider
O(n) O ( n ) -invariant and reflection-positive quantum spin systems on the integer lattice in any dimension, and prove that at low temperatures, 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 at low temperatures (for
d≥3 d ≥ 3 ).
Abstract: We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins S satisfy β ≪ √ S. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with S ≫ 1. The most notable examples are the quantum orbital-compass model on Z 2 and the quantum 120-degree model on Z 3 which are shown to exhibit symmetry breaking at low-temperatures despite
Recent work by Greenblatt, Lange, Marcelli, and Porta (Commun. Math. Phys. 2024) provides the first rigorous justification of adiabatic theory for interacting quantum systems at positive temperature. Their analysis treats weakly interacting lattice fermions and combines a rigorous Wick rotation with fermionic cluster expansion techniques. Here, we study a class of weakly interacting quantum spin systems and derive response theory at positive temperature, thereby covering non-Fermi systems for the first time. Our proof identifies and exploits the locality property of local indistinguishability as a key ingredient in carrying out low-temperature adiabatic expansions. The fact that these systems satisfy local indistinguishability was recently established jointly with Adhikari (arXiv:2508.15907) using cluster expansion methods together with a probabilistic swapping trick.
We investigate entanglement generation in one-dimensional quantum spin systems with the sinusoidal deformation. In the system, the energy scale of each local term in the Hamiltonian is modified according to a position-dependent function ${\mathrm{sin}}^{\ensuremath{\alpha}}[\frac{\ensuremath{\pi}}{N}(x\ensuremath{-}\frac{1}{2})]$, where
x is the position of the local term and
N is the length of the system. We show that at zero temperature the system with $\ensuremath{\alpha}\ensuremath{\ge}2$ is able to generate a sizable entanglement between two spins at open edges, even when the two spins are infinitely far apart. This long-distance entanglement is rather robust against thermal fluctuations and survives up to a temperature that decays with the system size slowly, in an algebraic form.