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Register a new userQuantum and thermal melting of stripe forming systems with competing long ranged interactions
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We study the quantum melting of stripe phases in models with competing short range and long range interactions decaying with distance as $1/r^{sigma}$ in two space dimensions. At zero temperature we find a two step disordering of the stripe phases with the growth of quantum fluctuations. A quantum critical point separating a phase with long range positional order from a phase with long range orientational order is found when $sigma leq 4/3$, which includes the Coulomb interaction case $sigma=1$. For $sigma > 4/3$ the transition is first order, which includes the dipolar case $sigma=3$. Another quantum critical point separates the orientationally ordered (nematic) phase from a quantum disordered phase for any value of $sigma$. Critical exponents as a function of $sigma$ are computed at one loop order in an $epsilon$ expansion and, whenever available, compared with known results. For finite temperatures it is found that for $sigma geq 2$ orientational order decays algebraically with distance until a critical Kosterlitz-Thouless line. Nevertheless, for $sigma < 2$ it is found that long range orientational order can exist at finite temperatures until a critical line which terminates at the quantum critical point at $T=0$. The temperature dependence of the critical line near the quantum critical point is determined as a function of $sigma$.
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We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $alpha geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($alpha=1$) and dipolar magnetic films ($alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.
Work fluctuations and work probability distributions are fundamentally different in systems with short- ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with shortranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet , well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short-ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behaviour of the work probability distribution and the associated fluctuations is presented.
We state and prove four types of Lieb-Robinson bounds valid for many-body open quantum systems with power law decaying interactions undergoing out of equilibrium dynamics. We also provide an introductory and self-contained discussion of the setting and tools necessary to prove these results. The results found here apply to physical systems in which both long-ranged interactions and dissipation are present, as commonly encountered in certain quantum simulators, such as Rydberg systems or Coulomb crystals formed by ions.
The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from the classical $O(N)$ spin models and we then move to quantum spin systems.
Frustration in quantum many body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, to the ground states of the local interaction terms and the global ground state of the total many-body Hamiltonian. This universal measure is bounded from below by the ground-state bipartite block entanglement. For many-body Hamiltonians that are sums of two-body interaction terms, a further inequality relates quantum frustration to the pairwise entanglement between the constituents of the local interaction terms. This additional bound is a consequence of the limits imposed by monogamy on entanglement shareability. We investigate the behavior of local pair frustration in quantum spin models with competing interactions on different length scales and show that valence bond solids associated to exact ground-state dimerization correspond to a transition from generic frustration, i.e. geometric, common to classical and quantum systems alike, to genuine quantum frustration, i.e. solely due to the non-commutativity of the different local interaction terms. We discuss how such frustration transitions separating genuinely quantum orders from classical-like ones are detected by observable quantities such as the static structure factor and the interferometric visibility.
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