Statistical Mechanics
Quantum thermal absorption machines: refrigerators, engines and clocks (1902.02672v3)
Mark T. Mitchison
2019-02-07
The inexorable miniaturisation of technologies, the relentless drive to improve efficiency and the enticing prospect of boosting performance through quantum effects are all compelling reasons to investigate microscopic machines. Thermal absorption machines are a particularly interesting class of device that operate autonomously and use only heat flows to perform a useful task. In the quantum regime, this provides a natural setting in which to quantify the thermodynamic cost of various operations such as cooling, timekeeping or entanglement generation. This article presents a pedagogical introduction to the physics of quantum absorption machines, covering refrigerators, engines and clocks in detail.
Hilbert Space Fragmentation and Many-Body Localization (1906.05709v2)
Francesca Pietracaprina, Nicolas Laflorencie
2019-06-13
Investigating many-body localization (MBL) using exact numerical methods is limited by the exponential growth of the Hilbert space. However, localized eigenstates display multifractality and only extend over a vanishing fraction of the Hilbert space. Here, building on this remarkable property, we develop a simple yet efficient decimation scheme to discard the irrelevant parts of the Hilbert space of the random-field Heisenberg chain. This leads to an Hilbert space fragmentation in small clusters, allowing to access larger systems at strong disorder. The MBL transition is quantitatively predicted, together with a geometrical interpretation of MBL multifractality.
Equilibrium Microcanonical Annealing for First-Order Phase Transitions (1907.07067v1)
Nathan Rose, Jonathan Machta
2019-07-16
A framework is presented for carrying out simulations of equilibrium systems in the microcanonical ensemble using annealing in an energy ceiling. The framework encompasses an equilibrium version of simulated annealing, population annealing and hybrid algorithms that interpolate between these extremes. These equilibrium, microcanonical annealing algorithms are applied to the thermal first-order transition in the 20-state, two-dimensional Potts model. All of these algorithms are observed to perform well at the first-order transition though for the system sizes studied here, equilibrium simulated annealing is most efficient.
Momentum space conformal three-point functions of conserved currents and a general spinning operator (1903.01110v2)
Hiroshi Isono, Toshifumi Noumi, Toshiaki Takeuchi
2019-03-04
We construct conformal three-point functions in momentum space with a general tensor and conserved currents of spin
and
. While conformal correlators in momentum space have been studied especially in the connection with cosmology, correlators involving a tensor of general spin and scaling dimension have not been studied very much yet. Such a direction is unavoidable when we go beyond three-point functions because general tensors always appear as an intermediate state. In this paper, as a first step, we solve the Ward-Takahashi identities for correlators of a general tensor and conserved currents. In particular we provide their expression in terms of the so-called triple-
integrals and a differential operator which relates triple-
Highly parallel algorithm for the Ising ground state searching problem (1907.05124v2)
A. Yavorsky, L. A. Markovich, E. A. Polyakov, A. N. Rubtsov
2019-07-11
Finding an energy minimum in the Ising model is an exemplar objective, associated with many combinatorial optimization problems, that is computationally hard in general, but occurs in all areas of modern science. There are several numerical methods, providing solution for the medium size Ising spin systems. However, they are either computationally slow and badly parallelized, or do not give sufficiently good results for the large systems. In this paper, we present a highly parallel algorithm, called Mean-field Annealing from a Random State (MARS), incorporating the best features of the classical simulated annealing (SA) and Mean-Field Annealing (MFA) methods. The algorithm is based on the mean-field descent from a randomly selected configuration and temperature. Since a single run requires little computational effort, the effectiveness can be achieved by massive parallelisation. MARS shows excellent performance both on the large Ising spin systems and on the set of exemplary maximum cut benchmark instances in terms of both solution quality and computational time.
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