Class Of Quantum Spin Systems Research Articles

Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature

We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on combining the contour representation of quantum spin systems of this type due to Borgs, Kotecký, and Ueltschi with the algorithmic framework developed by Helmuth, Perkins, and Regts, and Borgs et al.

The free energy in a class of quantum spin systems and interchange processes

We study a class of quantum spin systems in the mean-field setting of the complete graph. For spin S=12, the model is the Heisenberg ferromagnet, and for general spin S∈12N, it has a probabilistic representation as a cycle-weighted interchange process. We determine the free energy and the critical temperature (recovering results by Tóth and by Penrose when S=12). The critical temperature is shown to coincide (as a function of S) with that of the q = 2S + 1 state classical Potts model, and the phase transition is discontinuous when S ≥ 1.

Decay of transverse correlations in quantum Heisenberg models

We study a class of quantum spin systems that include the S=12 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 representations of the correlation functions, on stochastic domination and on first-passage percolation.

Semi-Classical Dynamics in Quantum Spin Systems

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes.

Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Parts III and IV

This is the continuation of a series of articles concerning a class of quantum spin systems with Hamiltonian operators of the form $$H_\lambda = \sum\limits_{x \in \Lambda } {s_x + } \sum\limits_{yo \subset \Lambda } {\lambda ^{\left| {yo} \right|_c - 1} } t_{yo} $$ where Λ is a graph, λ is a small parameter andsx has a gap≥1 for all x e Λ\I In the singular setI ⊂ Λ, the gap ofsx can be arbitrarily small. Part III is devoted to the proof of a preliminary result, while in Part IV we consider the case in whichI is a subset of finite density of Λ. This completes the first iteration step of the deterministic part of the proof of localization in the ground state of the random field quantumXY model.

Uniqueness of the translationally invariant ground state in quantum spin systems

We introduce a class of quantum spin systems on ℤd. We show that the translationally invariant ground state is unique for this system if it is in a strong external field.

Exact ground state of a class of quantum spin systems.

We present some exact results for the ground-state wave function and the energy of disordered quantum-mechanical spin systems in any dimensions. The system contains all nearest- and some of the next-nearest-neighbor interactions. The solution is also available for some range of anisotropy. In all the cases the ground-state wave function is insensitive to the disorder.

On the classical limit and the problem of phase transitions

Some aspects of the relation between proofs of both absence and existence of phase transitions for a class of quantum spin systems and their classical counterparts are discussed. The results of absence of phase transitions apply to a large class of classical systems with special symmetry already considered by Vuillermot and Romerio (1975), and to their quantum mechanical analogues.