| 1. |
- Andreasson, Philip, et al.
(författare)
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Quantum error correction for the toric code using deep reinforcement learning
- 2019
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Ingår i: Quantum. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 3
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Tidskriftsartikel (refereegranskat)abstract
- We implement a quantum error correction algorithm for bit-flip errors on the topological toric code using deep reinforcement learning. An action-value Q-function encodes the discounted value of moving a defect to a neighboring site on the square grid (the action) depending on the full set of defects on the torus (the syndrome or state). The Q-function is represented by a deep convolutional neural network. Using the translational invariance on the torus allows for viewing each defect from a central perspective which significantly simplifies the state space representation independently of the number of defect pairs. The training is done using experience replay, where data from the algorithm being played out is stored and used for mini-batch upgrade of the Q-network. We find performance which is close to, and for small error rates asymptotically equivalent to, that achieved by the Minimum Weight Perfect Matching algorithm for code distances up to d=7. Our results show that it is possible for a self-trained agent without supervision or support algorithms to find a decoding scheme that performs on par with hand-made algorithms, opening up for future machine engineered decoders for more general error models and error correcting codes.
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| 2. |
- Balabanov, Oleksandr, et al.
(författare)
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Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands
- 2021
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Ingår i: Machine Learning. - : IOP Publishing. - 2632-2153. ; 2:2
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Tidskriftsartikel (refereegranskat)abstract
- Multi-band insulating Bloch Hamiltonians with internal or spatial symmetries, such as particle-hole or inversion, may have topologically disconnected sectors of trivial atomic-limit (momentum-independent) Hamiltonians. We present a neural-network-based protocol for finding topologically relevant indices that are invariant under transformations between such trivial atomic-limit Hamiltonians, thus corresponding to the standard classification of band insulators. The work extends the method of 'topological data augmentation' for unsupervised learning introduced (2020 Phys. Rev. Res. 2 013354) by also generalizing and simplifying the data generation scheme and by introducing a special 'mod' layer of the neural network appropriate for Z ( n ) classification. Ensembles of training data are generated by deforming seed objects in a way that preserves a discrete representation of continuity. In order to focus the learning on the topologically relevant indices, prior to the deformation procedure we stack the seed Bloch Hamiltonians with a complete set of symmetry-respecting trivial atomic bands. The obtained datasets are then used for training an interpretable neural network specially designed to capture the topological properties by learning physically relevant momentum space quantities, even in crystalline symmetry classes.
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| 3. |
- Balabanov, Oleksandr, 1991, et al.
(författare)
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Unsupervised learning using topological data augmentation
- 2020
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Ingår i: PHYSICAL REVIEW RESEARCH. - 2643-1564. ; 2
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Tidskriftsartikel (refereegranskat)abstract
- Unsupervised machine learning is a cornerstone of artificial intelligence as it provides algorithms capable of learning tasks, such as classification of data, without explicit human assistance. We present an unsupervised deep learning protocol for finding topological indices of quantum systems. The core of the proposed scheme is a “topological data augmentation” procedure that uses seed objects to generate ensembles of topologically equivalent data. Such data, assigned with dummy labels, can then be used to train a neural network classifier for sorting arbitrary objects into topological equivalence classes. Importantly, we also show how to retrieve the local quantities corresponding to the learned topological indices from the intermediate outputs of the trained network. Our protocol is explicitly illustrated on two-band insulators in one and two dimensions, characterized by a winding number and a Chern number respectively. Using the augmentation technique also in the classification step, to classify a family of topologically equivalent objects instead of a single object, we can achieve accuracy arbitrarily close to 100% even for indices outside the training regime. Apart from the method's applicability to topological classification, it also provides a new perspective on data augmentation in supervised machine learning, where given sufficient mathematical structure the set of category-preserving deformations can be rigorously defined.
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| 4. |
- Cusumano, Linda, 1981, et al.
(författare)
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Current benefits and future possibilities with digital field reporting
- 2024
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Ingår i: INTERNATIONAL JOURNAL OF CONSTRUCTION MANAGEMENT. - 1562-3599 .- 2331-2327.
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Tidskriftsartikel (refereegranskat)abstract
- Mobile phones and tablets enable contractors to digitally collect large amounts of production remarks and facilitate the acquisition. The increased data access and machine learning techniques allow the construction industry to take a significant step forward in shifting from implicit to explicit knowledge. However, this step requires both standardisation and data quality assurance combined with project incitements ensuring continuous data collection. Therefore, this study examines the current data quality and standardisation of inspection data generated using the production software Dalux Field, mining a dataset of more than 95000 production issues. Additionally, a survey of production software users assesses project and project member benefits and future possibilities with digital inspection reporting. The results show considerable benefits with digital inspection reporting, such as time savings, cost reductions and increased general quality control. However, the standardisation in reporting between projects and team members is low. Finally, this paper suggests methods for improving data quality and standardization for automation of the data analysis, allowing new projects in project-based organisations to benefit from previous project experiences.
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| 5. |
- Cusumano, Linda, 1981, et al.
(författare)
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Intelligent building contract tendering - potential and exploration
- 2022
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Ingår i: IABSE Symposium Prague, 2022: Challenges for Existing and Oncoming Structures - Report. - Zurich, Switzerland : International Association for Bridge and Structural Engineering (IABSE). ; , s. 1902-1909
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Konferensbidrag (refereegranskat)abstract
- Project tendering is the construction business “Tightrope-walking.” It is a time-limited balance act where technical and business specialists find the best technical proposal at the right price. The purpose and aim of this study were to explore artificial intelligence (AI) in the tender work and to identify challenges and possibilities with data-driven decision-making. An AI work support tool was adopted and used to extract and process client requirements. The tool and digital-work procedure were presented and discussed with tender specialists from a large contractor in a workshop. A two-step survey was performed in connection to the workshop, investigating the potential users' insights and attitudes for implementation. The main result and conclusion were that AI and digitalization could support tendering; however, successfully generating business value will require higher levels of digitalization, well-structured databases, and access to historical project data.
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| 6. |
- Cusumano, Linda, 1981, et al.
(författare)
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Natural language processing as work support in project tendering
- 2022
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Ingår i: Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems. - London : CRC Press. - 9781003348443 ; , s. 1583-1588
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Konferensbidrag (refereegranskat)abstract
- When producing a tender, contractors manually analyze client requirements contained within many different text documents. The combination of requirements lead to crucial design decisions and every decision is related to costs and risks. This study explores the possibility of making the client requirement analysis in design-bid contracts automated to reduce the risk of conceptual design mistakes. The research approach chosen includes developing a work support tool based on natural language processing and analyzing its usefulness through a combination of surveys and a workshop for tendering specialist. The results show that applying digitalized working methods and using artificial intelligence in the tender phase can enable data-informed decision making and generate benchmarking and risk management opportunities. The study contributes to insights regarding automation and digitization possibilities in tender projects and how artificial intelligence tools can be designed for supporting data-driven decisions.
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| 7. |
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| 8. |
- Granath, Mats, 1972, et al.
(författare)
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Anharmonic softening of Raman active phonons in iron-pnictides: Estimating the Fe isotope effect due to anharmonic expansion
- 2009
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Ingår i: Physical Review B. - 1098-0121. ; 79:23, s. 235103-
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Tidskriftsartikel (refereegranskat)abstract
- We present Raman measurements on the iron-pnictide superconductors CeFeAsO1-xFx and NdFeAsO1-xFx. Modeling the Fe-As plane in terms of harmonic and a cubic anharmonic Fe-As interactions, we calculate the temperature dependence of the energy and lifetime of the Raman active Fe B-1g mode and fit to the observed energy shift. The shifts and lifetimes are in good agreement with those measured also in other Raman studies which demonstrate that the phonon spectrum, at least at small wave numbers, is well represented by phonon-phonon interactions without any significant electronic contribution. Even at zero temperature there is a non-negligent effect of interactions on the phonon energy, which for the Fe B-1g mode corresponds to 6 cm(-1) or 3% of the total energy of the mode. We also estimate the anharmonic expansion from Fe (56 -> 54) isotope substitution to Delta a approximate to 5.1 x 10(-4) angstrom and Delta d(Fe-As) approximate to 2.5 x 10(-4) angstrom and the shift of harmonic zero-point fluctuations of bond lengths less than or similar to 3 x 10(-5) angstrom(2), giving a total relative average decrease in electronic hopping integrals of vertical bar delta vertical bar/t less than or similar to 2.0 x 10(-4). For a nonphonon-mediated weak-coupling superconductor this gives an isotope exponent alpha similar to 10(-2). The results pose a serious challenge for any theory of superconductivity in the pnictides that does not include electron-phonon interactions to produce a sizable Fe isotope effect.
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| 9. |
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| 10. |
- Granath, Mats, 1972, et al.
(författare)
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Diffusion and Localization of Relative Strategy Scores in The Minority Game
- 2016
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 165:1, s. 94-114
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Tidskriftsartikel (refereegranskat)abstract
- We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase (α≡P/N≳1) of the basic Minority Game using sign-payoff, with N agents holding two strategies over P histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent’s strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score x∈Z of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities, leading either to a static and asymmetric exponential distribution centered at x=0 for fickle agents or to diffusion with a positive or negative drift for frozen agents. In terms of scaled coordinates x/N−−√ and t / N the distributions are uniquely given by α and in quantitative agreement with direct simulations of the game. As the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic Minority Game in the asymmetric phase.
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| 11. |
- Granath, Mats, 1972, et al.
(författare)
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Discretized thermal Green’s functions
- 2012
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Ingår i: Annalen der Physik. - : Wiley - VCH Verlag GmbH. - 0003-3804 .- 1521-3889. ; 524:3-4, s. 147-152
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Tidskriftsartikel (refereegranskat)abstract
- We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time t and thus periodic in imaginary (Matsubara) frequency i pi n. The formalism requires a generalization of the Dyson equation G (G0, S) and the Baym-Kadanoff-Luttinger-Ward functional for the free energy beta O = G (G). A conformal transformation is used to analytically continue the periodized Matsubara Green's function to real frequencies in a way that conserves the discontinuity at t = 0 of the corresponding real-time Green's function. This allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation in the t discretization. The formalism is tested on dynamical mean field theory calculations of the paramagnetic Hubbard model.
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| 12. |
- Granath, Mats, 1972, et al.
(författare)
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Distributional exact diagonalization formalism for quantum impurity models
- 2012
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Ingår i: Physical Review B. - : American Physical Society. - 1098-0121 .- 2469-9950 .- 2469-9969. ; 86:11
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Tidskriftsartikel (refereegranskat)abstract
- We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single-impurity Anderson model and the two-orbital Hubbard model within dynamical mean-field theory (DMFT) as well as real frequency data for self-energy of the single-band Hubbard model within DMFT using the numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought.
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| 13. |
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| 14. |
- Granath, Mats, 1972, et al.
(författare)
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Modeling a striped pseudogap state
- 2010
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Ingår i: Physical Review B. - 1098-0121. ; 81:2
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Tidskriftsartikel (refereegranskat)abstract
- We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local d-wave or s-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.
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| 15. |
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| 16. |
- Granath, Mats, 1972, et al.
(författare)
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Signatures of Coherent Electronic Quasiparticles in the Paramagnetic Mott Insulator.
- 2014
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 90
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Tidskriftsartikel (refereegranskat)abstract
- We study the Mott insulating state of the half-filled paramagnetic Hubbard model within dynamical mean field theory using a recently formulated stochastic and non-perturbative quantum impurity solver. The method is based on calculating the impurity self energy as a sample average over a representative distribution of impurity models solved by exact diagonalization. Due to the natural parallelization of the method, millions of poles are readily generated for the self energy which allows to work with very small pole-broadening $\eta$. Solutions at small and large $\eta$ are qualitatively different; solutions at large $\eta$ show featureless Hubbard bands whereas solutions at small $\eta\leq 0.001$ (in units of half bare band width) show a band of electronic quasiparticles with very small quasiparticle weight at the inner edge of the Hubbard bands. The validity of the results are supported by agreement within statistical error $\sigma_{\text{QMC}}\sim 10^{-4}$ on the imaginary frequency axis with calculations using a continuous time quantum Monte Carlo solver. Nevertheless, convergence with respect to finite size of the stochastic exact diagonalization solver remains to be rigourously established.
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| 17. |
- Hammar, Karl, et al.
(författare)
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Error-rate-agnostic decoding of topological stabilizer codes
- 2022
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Ingår i: Physical Review A. - 2469-9934 .- 2469-9926. ; 105
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Tidskriftsartikel (refereegranskat)abstract
- Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold maximum-likelihood decoders require an explicit error model for Pauli errors to decode a specific syndrome, whereas lower-threshold heuristic approaches such as minimum-weight matching are error agnostic. Here we consider an intermediate approach, formulating a decoder that depends on the bias, i.e., the relative probability of phase-flip to bit-flip errors, but is agnostic to error rate. Our decoder is based on counting the number and effective weight of the most likely error chains in each equivalence class of a given syndrome. We use Metropolis-based Monte Carlo sampling to explore the space of error chains and find unique chains that are efficiently identified using a hash table. Using the error-rate invariance, the decoder can sample chains effectively at an error rate which is higher than the physical error rate and without the need for thermalization between chains in different equivalence classes. Applied to the surface code and the XZZX code, the decoder matches maximum-likelihood decoders for moderate code sizes or low error rates. We anticipate that, because of the compressed information content per syndrome, it can be taken full advantage of in combination with machine-learning methods to extrapolate Monte Carlo-generated data.
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| 18. |
- Holmlund, Joakim, 1968, et al.
(författare)
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Two-magnon Raman scattering from the Cu3O4 layers in (Sr-2,Ba-2)Cu3O4Cl
- 2009
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Ingår i: Physical Review B - Condensed Matter and Materials Physics. - 2469-9950 .- 2469-9969 .- 1098-0121 .- 1550-235X. ; 79:8
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Tidskriftsartikel (refereegranskat)abstract
- (Sr-2,Ba-2)Cu3O4Cl2 are antiferromagnetic insulators which are akin to the parent compounds of the cuprate superconductors but with two distinct magnetic ordering temperatures related to two magnetic Cu-I and Cu-II spin sublattices. Here we present a study of these materials by means of Raman spectroscopy. Following the temperature and polarization dependence of the data, we readily identify two distinct features at around 3000 and 300 cm(-1) that are related to two-magnon scattering from the two sublattices. The estimated spin-exchange coupling constants for the Cu-I and Cu-II sublattices are found to be J(I)similar to 139-143(132-136) meV and J(II)similar to 14 (11) meV for Sr(Ba) compounds. Moreover, we observe modes at around 480 and 445 cm(-1) for the Sr and Ba containing samples, respectively, which disappears at the ordering temperature of the Cu-II. We argue that these modes may also be of magnetic origin and possibly related to interband transitions between the Cu-I-Cu-II sublattices.
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| 19. |
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| 20. |
- Karypidis, Dimitrios, 1991, et al.
(författare)
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Structural Health Monitoring of RC structures using optic fiber strain measurements: a deep learning approach
- 2019
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Ingår i: 20th Congress of IABSE, New York City 2019: The Evolving Metropolis - Report. ; 114
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Konferensbidrag (refereegranskat)abstract
- This paper reports the early findings of an ongoing project aimed at developing new methods to upgrade the current maintenance strategies of the civil and transport infrastructure. As part of these new methods, the use of Machine Learning (ML) algorithms is being investigated to constitute the core of a new generation of more accurate and robust structural health monitoring (SHM) systems for concrete structures. Unlike most of the existing SHM systems, relying on the analysis of the natural frequencies of the structure based on data obtained from accelerometers, the present study uses a distributed optic fiber system to monitor the strain distribution along steel reinforcing bars. The preliminary results of the study indicate that a semi-supervised Deep Autoencoder algorithm (DAE) can successfully quantify the damage attributable to transverse cracks in a reinforced concrete beam subjected to three-point loading. Future applications will feature the determination of crack locations, early detection of reinforcement corrosion as well as other types of damage such as splitting cracks or surface spalling.
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| 21. |
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| 22. |
- Sabashvili, Andro, 1984, et al.
(författare)
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Bilayer graphene spectral function in the random phase approximation and self-consistent GW approximation
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121. ; 88
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Tidskriftsartikel (refereegranskat)abstract
- We calculate the single-particle spectral function for doped bilayer graphene in the low energy limit, described by two parabolic bands with zero band gap and long range Coulomb interaction. Calculations are done using thermal Green's functions in both the random phase approximation (RPA) and the fully self-consistent GW approximation. Consistent with previous studies RPA yields a spectral function which, apart from the Landau quasiparticle peaks, shows additional coherent features interpreted as plasmarons, i.e., composite electron-plasmon excitations. In the GW approximation the plasmaron becomes incoherent and peaks are replaced by much broader features. The deviation of the quasiparticle weight and mass renormalization from their noninteracting values is small which indicates that bilayer graphene is a weakly interacting system. The electron energy loss function, Im[−εq−1(ω)] shows a sharp plasmon mode in RPA which in the GW approximation becomes less coherent and thus consistent with the weaker plasmaron features in the corresponding single-particle spectral function.
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| 23. |
- Srivastava, Basudha, 1996, et al.
(författare)
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The XYZ^2 hexagonal stabilizer code
- 2022
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Ingår i: Quantum. - : Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. - 2521-327X. ; 6
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Tidskriftsartikel (refereegranskat)abstract
- We consider a topological stabilizer code on a honeycomb grid, the "XYZ2" code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor. 48, 215302 (2015)], with a specific implementation of the boundary. It utilizes weight-six (XYZXYZ) plaquette stabilizers and weight-two (XX) link stabilizers on a planar hexagonal grid composed of 2d2 qubits for code distance d, with weight-three stabilizers at the boundary, stabilizing one logical qubit. We study the properties of the code using maximum-likelihood decoding, assuming perfect stabilizer measurements. For pure X, Y, or Z noise, we can solve for the logical failure rate analytically, giving a threshold of 50%. In contrast to the rotated surface code and the XZZX code, which have code distance d2 only for pure Y noise, here the code distance is 2d2 for both pure Z and pure Y noise. Thresholds for noise with finite Z bias are similar to the XZZX code, but with markedly lower sub-threshold logical failure rates. The code possesses distinctive syndrome properties with unidirectional pairs of plaquette defects along the three directions of the triangular lattice for isolated errors, which may be useful for efficient matching-based or other approximate decoding.
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| 24. |
- Strand, Hugo, 1983, et al.
(författare)
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The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
- 2011
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Ingår i: Phys. Rev. B. - : American Physical Society. - 1098-0121. ; 83:20
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Tidskriftsartikel (refereegranskat)abstract
- We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition.
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| 25. |
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| 26. |
- Wårdh, Jonatan, 1990, et al.
(författare)
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Effective model for a supercurrent in a pair-density wave
- 2017
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Ingår i: Physical Review B Condensed Matter. - 0163-1829. ; 96:22
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Tidskriftsartikel (refereegranskat)abstract
- We extend the standard effective model of d-wave superconductivity of a single band tight-binding Hamiltonian with a nearest-neighbor attraction to include finite range periodically modulated pair hopping. The pair hopping is characterized by a fixed wave number Q=Qx̂ breaking lattice rotational symmetry. Within self-consistent BCS theory we study the general variational state consisting of two incommensurate singlet pair amplitudes ΔQ1 and ΔQ2 and find two types of ground states; one of the Larkin-Ovchnnikov (LO) or pair-density wave (PDW) type with ΔQ1=ΔQ2 and Q1=−Q2≈Q, and one of the Fulde-Ferrell (FF) type with ΔQ2=0 and Q1≈±Q. An anomalous term in the static current operator arising from the pair hopping ensures that Bloch's theorem on ground state current is enforced also for the time-reversal and parity breaking FF state, despite no spin-population imbalance. We also consider a supercurrent by exploring the space of pair momenta Q1 and Q2 and identify characteristics of a state with multiple finite momentum order parameters. This includes the possibility of phase separation of current densities and spontaneous mirror-symmetry breaking manifested in the directional dependence of the depairing current.
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| 27. |
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| 28. |
- Wårdh, Jonatan, 1990, et al.
(författare)
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Suppression of superfluid stiffness near a Lifshitz-point instability to finite-momentum superconductivity
- 2018
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Ingår i: Physical Review B Condensed Matter. - 0163-1829. ; 98
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Tidskriftsartikel (refereegranskat)abstract
- We derive the effective Ginzburg-Landau (GL) theory for finite-momentum [Fulde-Ferrell-Larkin-Ovchinnikov/pair-density wave (FFLO/PDW)] superconductivity without spin population imbalance from a model with local attraction and repulsive pair hopping. We find that the GL free energy must include up to sixth-order derivatives of the order parameter, providing a unified description of the interdependency of zero and finite-momentum superconductivity. For weak pair hopping the phase diagram contains a line of Lifshitz points where vanishing superfluid stiffness induces a continuous change to a long wavelength FF state. For larger pair hopping there is a bicritical region where the pair momentum changes discontinuously. Here the FF type state is near degenerate with the LO or PDW type state. At the intersection of these two regimes there is a “super-Lifshitz” point with extra soft fluctuations. The instability to finite-momentum superconductivity occurs for arbitrarily weak pair hopping for sufficiently large attraction suggesting that even a small repulsive pair hopping may be significant in a microscopic model of strongly correlated superconductivity. Several generic features of the model may have bearing on the cuprate superconductors, including the suppression of superfluid stiffness in proximity to a Lifshitz point as well as the existence of subleading FFLO order (or vice versa) in the bicritical regime.
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| 29. |
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