| 1. |
- Bagrov, Andrey A., et al.
(författare)
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Multiscale structural complexity of natural patterns
- 2020
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Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : NATL ACAD SCIENCES. - 0027-8424 .- 1091-6490. ; 117:48, s. 30241-30251
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Tidskriftsartikel (refereegranskat)abstract
- Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is "complex" and what is "simple" but also, can be used to accurately detect different phase transitions and gain information about dynamics of nonequilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.
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| 2. |
- Ageev, Dmitry S., et al.
(författare)
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Coleman-Weinberg potential in p-adic field theory
- 2020
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Ingår i: European Physical Journal C. - : SPRINGER. - 1434-6044 .- 1434-6052. ; 80:9
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study lambda phi(4) scalar field theory defined on the unramified extension of p-adic numbers Q(pn). For different "space-time" dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman-Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, p -> 1 and p -> infinity. We show that the p -> 1 limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the p -> infinity limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.
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| 3. |
- Ageev, Dmitry S., et al.
(författare)
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Deterministic chaos and fractal entropy scaling in Floquet conformal field theories
- 2021
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 103:10
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Tidskriftsartikel (refereegranskat)abstract
- In this Letter, we study two-dimensional Floquet conformal field theory, where the external periodic driving is described by iterated logistic or tent maps. These maps are known to be typical examples of dynamical systems exhibiting the order-chaos transition, and we show that, as a result of such driving, the entanglement entropy scaling develops fractal features when the corresponding dynamical system approaches the chaotic regime. For the driving set by the logistic map, the fractal contribution to the scaling dominates, making entanglement entropy a highly oscillating function of the subsystem size.
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| 4. |
- Bagrov, Andrey A., et al.
(författare)
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Kinetic samplers for neural quantum states
- 2021
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 104:10
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Tidskriftsartikel (refereegranskat)abstract
- Neural quantum states are a recently introduced class of variational many-body wave functions that are very flexible in approximating diverse quantum states. Optimization of an NQS ansatz requires sampling from the corresponding probability distribution defined by squared wave function amplitude. For this purpose, we propose to use kinetic sampling protocols and demonstrate that in many important cases such methods lead to much smaller autocorrelation times than the Metropolis-Hastings sampling algorithm while still allowing to easily implement lattice symmetries (unlike autoregressive models). We also use uniform manifold approximation and projection algorithm to construct two-dimensional isometric embedding of Markov chains and show that kinetic sampling helps attain a more homogeneous and ergodic coverage of the Hilbert space basis.
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| 5. |
- Bagrov, Andrey A., et al.
(författare)
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Detecting quantum critical points in the t-t ' Fermi-Hubbard model via complex network theory
- 2020
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Ingår i: Scientific Reports. - : NATURE RESEARCH. - 2045-2322. ; 10
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Tidskriftsartikel (refereegranskat)abstract
- A considerable success in phenomenological description of high-Tc superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)-a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-t ' Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped t-t ' Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify precursors of the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed.
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| 6. |
- Bagrov, Andrey A., et al.
(författare)
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Suppressing backscattering of helical edge modes with a spin bath
- 2019
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 100:19
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Tidskriftsartikel (refereegranskat)abstract
- We address the question of stability of protected helical edge states at the boundary of two-dimensional topological insulators upon interactions with the external bath. We study how backscattering amplitude changes when different interaction channels between the system and the environment are present. Drawing an analogy with the concept of pointer states in theory of open quantum systems, we demonstrate that in a certain regime the interplay between the Coulomb and the spin-spin interactions can make the backscattering process strictly irrelevant, and the helical modes become robust states with a well-defined momentum. This opens a possibility to use the external spin bath as a stabilizer that alleviates destructive effects and restores the helicity protection.
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| 7. |
- Iliasov, Askar, et al.
(författare)
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Anisotropic destruction of the Fermi surface in inhomogeneous holographic lattices
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We analyze fermionic response of strongly correlated holographic matter in presence of inhomogeneous periodically modulated potential mimicking the crystal lattice. The modulation is sourced by a scalar operator that explicitly breaks the translational symmetry in one direction. We compute the fermion spectral function and show that it either exhibits a well defined Fermi surface with umklapp gaps opening on the Brillouin zone boundary at small lattice wave vector, or, when the wave vector is large, the Fermi surface is anisotropically deformed and the quasiparticles get significantly broadened in the direction of translation symmetry breaking. Making use of the ability of our model to smoothly extrapolate to the homogeneous Q-lattice like setup, we show that this novel effect is not due to the periodic modulation of the potential and Umklapp physics, but rather due to the anisotropic features of the holographic horizon. That means it encodes novel physics of strongly correlated critical systems which may be relevant for phenomenology of exotic states of electron matter.
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| 8. |
- Verlhac, Benjamin, et al.
(författare)
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Thermally induced magnetic order from glassiness in elemental neodymium
- 2022
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Ingår i: Nature Physics. - : Nature Portfolio. - 1745-2473 .- 1745-2481. ; 18:8, s. 905-911
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Tidskriftsartikel (refereegranskat)abstract
- At finite temperatures, fluctuations invariably introduce disorder and are responsible for ultimately destroying ordered phases. Here we present an unusual magnetic transition in elemental neodymium where, with increasing temperature, long-range multiply periodic 'multi-Q' magnetic order emerges from a self-induced spin glass. Using temperature-dependent spin-polarized scanning tunnelling microscopy, we characterize the local order of a previously reported spin glass phase, and quantify the emergence of long-range multi-Q order with increasing temperature. We develop two analysis tools that allow us to determine the glass transition temperature from measurements of the spatially dependent magnetization. We compare these observations with atomistic spin dynamics simulations, which reproduce the qualitative observation of a phase transition from a low-temperature spin glass phase to an intermediate ordered multi-Q phase. These simulations trace the origin of the unexpected high-temperature order in weakened frustration driven by temperature-dependent sublattice correlations. These findings constitute an example of order from disorder, and provide a platform to study the rich magnetization dynamics of a self-induced spin glass.Thermal fluctuations associated with higher temperatures normally destroy long-range order, but in some circumstances they can stabilize new ordered phases. This 'order by disorder' phenomenon has now been observed in the magnetic phases of neodymium.
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| 9. |
- Westerhout, Tom, et al.
(författare)
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Generalization properties of neural network approximations to frustrated magnet ground states
- 2020
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Ingår i: Nature Communications. - : Springer Science and Business Media LLC. - 2041-1723. ; 11:1
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Tidskriftsartikel (refereegranskat)abstract
- Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.
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