Large deviations for quantum spin probabilities at temperature zero

Large Deviations for Quantum Spin Systems

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages XΛ := 1 |Λ| ∑ i∈Λ Xi, where the Xi’s are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation p...

Large Deviations in Quantum Spin Chain

We show the full large deviation principle for KMS-states and C∗finitely correlated states on a quantum spin chain. We cover general local observables. Our main tool is Ruelle’s transfer operator method.

Hitting probabilities and large deviations

Let ”Yn•n∈Z+ be a sequence of random variables in R d and let A ⊂ Rd: Then P”Yn ∈ A for some n• is the hitting probability of the set A by the sequence ”Yn•. We consider the asymptotic behavior, as m → ∞, of P”Yn ∈ mA; some n• = P”hitting mA• whenever (1) the probability law of Yn/n satisfies the large deviation principle and (2) the central tendency of Yn/n is directed away from the given set ...

Density Matrix Renormalisation Group for a Quantum Spin Chain at Non-Zero Temperature

We apply a recent adaptation of White’s density matrix renormalisation group (DMRG) method to a simple quantum spin model, the dimerised XY chain, in order to assess the applicabilty of the DMRG to quantum systems at non-zero temperature. We find that very reasonable results can be obtained for the thermodynamic functions down to low temperatures using a very small basis set. Low temperature re...

2078 Hitting Probabilities and Large Deviations