Pure state thermodynamics with matrix product states

We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite temperature properties of quantum systems are derived without the need of statistical mechanics ensembles, but instead using typical properties of random pure states. We show that this formalism can be useful from the computational point of view when combined with tensor network algorithms. In particular, a recently introduced Monte Carlo algorithm is considered which samples matrix product states at random for the estimation of finite temperature observables. Here we characterize this algorithm as an $(\epsilon, \delta)$-approximation scheme and we analytically show that sampling one single state is sufficient to obtain a very good estimation of finite temperature expectation values. These results provide a substantial computational improvement with respect to similar algorithms for one-dimensional quantum systems based on uniformly distributed pure states. The analytical calculations are numerically supported simulating finite temperature interacting spin systems of size up to 100 qubits.Comment: 20 pages, 3 figures; comments are welcom

Phase transition of light on complex quantum networks

Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is non-trivial and well defined in the thermodynamic limit only if the hopping coefficient scales like the inverse of the maximal eigenvalue of the adjacency matrix of the network. Furthermore we provide numerical evidences that, for some complex network topologies, this scaling implies an asymptotically vanishing hopping coefficient in the limit of large network sizes. The latter result suggests the interesting possibility of observing quantum phase transitions of light on complex quantum networks even with very small couplings between the optical cavities.Comment: 8 pages, 5 figure

Quantum automata, braid group and link polynomials

The spin--network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah--Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this combinatorial framework we implement families of finite--states and discrete--time quantum automata capable of accepting the language generated by the braid group, and whose transition amplitudes are colored Jones polynomials. The automaton calculation of the polynomial of (the plat closure of) a link L on 2N strands at any fixed root of unity is shown to be bounded from above by a linear function of the number of crossings of the link, on the one hand, and polynomially bounded in terms of the braid index 2N, on the other. The growth rate of the time complexity function in terms of the integer k appearing in the root of unity q can be estimated to be (polynomially) bounded by resorting to the field theoretical background given by the Chern-Simons theory.Comment: Latex, 36 pages, 11 figure

Fidelity approach to the disordered quantum XY model

We study the random XY spin chain in a transverse field by analyzing the susceptibility of the ground state fidelity, numerically evaluated through a standard mapping of the model onto quasi-free fermions. It is found that the fidelity susceptibility and its scaling properties provide useful information about the phase diagram. In particular it is possible to determine the Ising critical line and the Griffiths phase regions, in agreement with previous analytical and numerical results.Comment: 4 pages, 3 figures; references adde

Microscopic electronic configurations after ultrafast magnetization dynamics

We provide a model for the prediction of the electronic and magnetic configurations of ferromagnetic Fe after an ultrafast decrease or increase of magnetization. The model is based on the well-grounded assumption that, after the ultrafast magnetization change, the system achieves a partial thermal equilibrium. With statistical arguments it is possible to show that the magnetic configurations are qualitatively different in the case of reduced or increased magnetization. The predicted magnetic configurations are then used to compute the dielectric response at the 3p (M) absorption edge, which can be related to the changes observed in the experimental T-MOKE data. The good qualitative agreement between theory and experiment offers a substantial support to the existence of an ultrafast increase of magnetisation, which has been fiercely debated in the last years.Comment: Main text 10 pages including 7 figures. Supplemental material 5 pages including 1 figur

Probability density of quantum expectation values

We consider the quantum expectation value \mathcal{A}=\ of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for non-degenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we comment on the relevance of the central limit theorem and draw some results on an alternative statistical mechanics based on the uniform measure on the energy shell.Comment: Substantial revision. References adde