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dimensions. At the critical point, an algebraic decay of the form ~ 1/rη is found, with a decay exponent being approximately η ≈ 2+2d.
Quantum XX model with competing short- and long-range interactions. — We considered the quantum XX model with competing short- and global-range interactions in a one-dimensional lattice, defined by the Hamiltonian:
The nearest-neighbor coupling constant and the strength of the transverse field are denoted by J and h, respectively, and the last term of the r.h.s. represents a global-range antiferromagnetic interaction of strength ε. It is expressed as the square of the staggered magnetization operator:
This model is equivalent to a Bose-Hubbard model with cavity-mediated global-range interactions in the hard-core-boson limit, which has experimental relevance in terms of cold atoms in an optical lattice in the presence of a high-finesse optical resonator, an optical cavity.
Using fermionic techniques, the problem was solved exactly in one dimension in the thermodynamic limit. The ground-state phase diagram consists of two ordered phases:
ferromagnetic (F) and antiferromagnetic (AF), as well as an XY phase having quasi-long-range order, see Fig. 1. We have also studied quantum relaxation after sudden quenches. Quenching from the AF phase to the XY region, remanent AF order is observed below a dynamical transition line. In the opposite quench, from the XY region to the AF phase beyond a static
Figure 1. Phase diagram of the quantum XX model with cavity-induced global-range interactions of strength ε = 1. The color codes indicate the value of the staggered magnetization, x, and that of the longitudinal magnetization, mz.
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metastability line, AF order arises on top of a remanent XY quasi-long-range order, which corresponds to a dynamically generated supersolid state in the equivalent Bose-Hubbard model with hard-core bosons.
Entanglement entropy of disordered quantum wire junctions. — The entanglement properties of extended quantum systems have attracted much interest in the recent decade.
One reason for this is that various entanglement measures turned out be sensitive to whether the underlying model is critical or not, moreover, some of these showed universal scaling in critical points. For a subsystem A of a closed system in a pure state, the natural entanglement measure is the entanglement entropy, which is the von Neumann entropy of the reduced density matrix corresponding to the subsystem. An important question is how the inhomogeneities, which break translational invariance, and which are present almost inevitably in real systems, affect the entanglement properties. As a contribution to this field, we considered different disordered lattice models composed of M linear chains glued together in a star-like manner, and studied the scaling of the entanglement between one arm and the rest of the system using a numerical strong-disorder renormalization group (SDRG) method. We pointed out that the random XX model and the free-fermion (FF) model with random nearest-neighbor hopping obey different SDRG rules at a junction as opposed to a linear geometry, which is illustrated in Fig. 2. For all studied models, the random transverse-field Ising model (RTIM), the XX spin model, and the FF model, the average entanglement entropy is found to increase with the length L of the arms according to the form S(L)=ceff/6lnL + const. For the RTIM and the XX model, the effective central charge ceff is universal with respect to the details of junction, and only depends on the number M of arms. Interestingly, for the RTIM, ceff decreases with M, whereas for the XX model it increases. For the latter model, the numerical estimates fit accurately to a form linear in 1/M: ceff(M)=2ln2(1-1/M).
For the free-fermion model, ceff depends also on the details of the junction, which is related to the sublattice symmetry of the model. In this case, both increasing and decreasing tendency with M can be realized with appropriate junction geometries. We have also established upper bounds on the average entanglement entropy of a chain of length L for all the three models under study, which hold universally, irrespective of the other subsystem to which the chain is coupled.
Figure 2. SDRG steps for the XX model (XX) and free fermions (FF) in the case of two elementary geometries. The sites coupled by the strongest bond (shown in red) are eliminated, while the remaining sites are connected by a weak, effective coupling obtained perturbatively. For the linear configuration the steps for the XX and FF models essentially agree with each other, while for the T shaped geometry they differ.
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Network-based prediction of protein interactions. — As biological function emerges through interactions between a cell's molecular constituents, understanding cellular mechanisms requires us to catalogue all physical interactions between proteins. Despite spectacular advances in high-throughput mapping, the number of missing human protein-protein interactions (PPIs) continues to exceed the experimentally documented interactions.
Computational tools that exploit structural, sequence or network topology information are increasingly used to fill in the gap, using the patterns of the already known interactome to predict undetected, yet biologically relevant interactions. Such network-based link prediction tools rely on the Triadic Closure Principle (TCP), stating that two proteins likely interact if they share multiple interaction partners. TCP is rooted in social network analysis, namely the observation that the more common friends two individuals have, the more likely that they know each other. We offered direct empirical evidence across multiple datasets and organisms that, despite its dominant use in biological link prediction, TCP is not valid for most protein pairs. We showed that this failure is fundamental - TCP violates both structural constraints and evolutionary processes. This understanding allowed us to propose a link-prediction principle, consistent with both structural and evolutionary arguments, that predicts yet uncovered protein interactions based on paths of length three (L3). A systematic computational cross-validation showed that the L3 principle significantly outperformed existing link-prediction methods. To experimentally test the L3 predictions, we performed both large-scale high-throughput and pairwise tests, finding that the predicted links test positively at the same rate as previously known interactions, suggesting that most (if not all) predicted interactions are real. Combining L3 predictions with experimental tests provided new interaction partners of FAM161A, a protein linked to retinitis pigmentosa, offering novel insights into the molecular mechanisms that lead to the disease. Because L3 is rooted in a fundamental biological principle, we expect it to have a broad applicability, enabling us to better understand the emergence of biological function under both healthy and pathological conditions.
Collective nonlinear Thomson back-scattering for generating phase-controlled isolated attosecond pulses in the nm wavelength range. — We have studied the collectively emitted radiation of a relativistic electron bunch of 106 – 108 electrons colliding with an intense femtosecond (few-cycle) near-infrared laser pulse. By analytically solving the equation of motion of the electrons interacting with the incoming laser field of arbitrarily high intensity, the exact radiation field stemming from Thomson back-scattering has been calculated in the head-on collision geometry. On the basis of our results, the collective spectrum (containing very high-order harmonics) and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch has been determined. It has turned out that for certain, realistic input parameters, single-cycle isolated pulses of ca. 20 attoseconds duration can be generated in the XUV – soft x-ray spectral range, including the 2.33–4.37 nm water window.
We have also shown that the generated collective radiation is almost linearly polarized, and it is extremely well collimated around the initial velocity of the electron bunch. Moreover, this radiation has a considerable intensity and its carrier envelope phase difference (CEP) is locked to that of the incoming femtosecond laser pulse. The results of the present study allow us to propose a novel source of isolated attosecond XUV – soft x-ray pulses with a well-controlled CEP. Such sources of radiation may be of importance because isolated attosecond XUV pulses make possible to investigate the real-time electron dynamics in atoms, molecules and solids experimentally. Besides, the CEP of the incoming femtosecond laser pulse affects
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various processes in atomic or molecular systems on this time scale, as has been observed in most of the pioneering experiments. The proposed novel source of isolated attosecond pulses may have several scientific applications, e.g. in performing pump–probe experiments on the attosecond time scale. Fig. 3 illustrates the CEP phase locking which manifests itself in the temporal evolution of the isolated attosecond pulses generated by the Thomson back-scattering of the incoming single-cycle laser pulses with different CEP values.
Figure 3. Temporal pulse shapes of the isolated attosecond pulses (at distance R0=2 m from the interaction region), stemming from nonlinear Thomson back-scattering along the polar angle of 180°, for different values of the carrier-envelope phase difference (CEP) of the near-infrared (NIR) laser pulse given in the legend. The inset shows the incoming NIR pulse shapes of different CEP with the corresponding colors. We have considered an 8nm electron bunch of 108 electrons, whose initial relativistic factor has been assumed to be γ0=10. The assumed parameters of the counter-propagating, almost single-cycle laser pulse are λL=800 nm, E0=4×1012 V/m.This figure shows that the CEP of the attosecond pulse perfectly follows the CEP of the NIR laser pulse with a phase difference of π. This very simple relationship makes the CEP of these attosecond pulses easily controllable through the CEP of the NIR laser pulse, which is expected to have an importance in attosecond pump-probe experiments.
Grants
OTKA K-109577: Ordering and dynamics in many-body systems (F. Iglói, 2014-2017)
K_18 (NKFIH) K128989: Many-body systems in and out of equilibrium (R. Juhász, 2018-2022)
International cooperation
Saarland University (Saarbrücken, Germany), Nonequilibrium quench dynamics of quantum systems (F. Iglói, G. Roósz)
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National Chengchi University (Taipei, Taiwan), Critical quench dynamics of random spin chains (F. Iglói, G. Roósz)
Northeastern University (Boston, USA), Network-based prediction of protein interactions (I.
Kovács)
Kuwait University (Safat, Kuwait), Phase diagram of random, antiferromagnetic spin chains (F.
Iglói)
Institut Néel (Grenoble, France) Critical behavior of systems with long-range interactions (F.
Iglói)
Université Saclay, CEA, CNRS (Saclay, France) Dynamics of random quantum systems (F. Iglói) TU München (München, Germany), Entanglement entropy of disordered quantum wire junctions (R. Juhász)
Universität Ulm, Institut für Quantenphysik, Institut für Quantenoptik (Ulm, Germany), Wigner function description of tunneling, focussing waves in quantum mechanics, nano-emitters and single-photon switches (S. Varró)
Publications
Articles
1. Blass B, Rieger H, Roósz G, Iglói F: Quantum relaxation and metastability of lattice bosons with cavity-induced long-range interactions. PHYS REV LETT 121:9 095301/1-6 (2018)
2. Iglói F, Monthus C: Strong disorder RG approach - a short review of recent developments. EUR PHYS J B 91:11 290/1-25 (2018)
3. Iglói F, Kovács IA: Transverse spin correlations of the random transverse-field Ising model. PHYS REV B 97:9 094205/1-6 (2018)
4. Iglói F, Blaß B, Roósz G, Rieger H: Quantum XX model with competing short- and long-range interactions: Phases and phase transitions in and out of equilibrium. PHYS REV B 98:18 184415/1-15 (2018)
5. Juhász R, Oberreuter JM, Zimborás Z: Entanglement entropy of disordered quantum wire junctions. J STAT MECH-THEORY E 123106/1-19 (2018)
6. Juhász R, Iglói F: Nonuniversal and anomalous critical behavior of the contact process near an extended defect. PHYS REV E 97:1 012111/1-8 (2018)
7. Hack S, Varró S, Czirják A: Carrier-envelope phase controlled isolated attosecond pulses in the nm wavelength range, based on coherent nonlinear Thomson-backscattering.
NEW J PHYS 20: 073043/1-10 (2018) See also: R-N.2
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