289 research outputs found
Critical behavior of Dirac fermions from perturbative renormalization
Gapless Dirac fermions appear as quasiparticle excitations in various
condensed-matter systems. They feature quantum critical points with critical
behavior in the 2+1 dimensional Gross-Neveu universality class. The precise
determination of their critical exponents defines a prime benchmark for
complementary theoretical approaches, such as lattice simulations, the
renormalization group and the conformal bootstrap. Despite promising recent
developments in each of these methods, however, no satisfactory consensus on
the fermionic critical exponents has been achieved, so far. Here, we perform a
comprehensive analysis of the Ising Gross-Neveu universality classes based on
the recently achieved four-loop perturbative calculations. We combine the
perturbative series in spacetime dimensions with the one for the
purely fermionic Gross-Neveu model in dimensions by employing
polynomial interpolation as well as two-sided Pad\'e approximants. Further, we
provide predictions for the critical exponents exploring various resummation
techniques following the strategies developed for the three-dimensional scalar
universality classes. We give an exhaustive appraisal of the current
situation of Gross-Neveu universality by comparison to other methods. For large
enough number of spinor components as well as for the case of
emergent supersymmetry , we find our renormalization group estimates to be
in excellent agreement with the conformal bootstrap, building a strong case for
the validity of these values. For intermediate as well as in comparison
with recent Monte Carlo results, deviations are found and critically discussed.Comment: 21 pages, 7 figures, 6 table
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Investigating Absorptive Capacity Strategies via Simulation
Absorptive capacity, defined as the organizational capability to identify, absorb and exploit knowledge, is one of the most discussed topics in the management literature. Yet, its complex nature makes it almost impossible to empirically test it. This paper develops SimAC, an agent-based simulation tool that enables studying and comparing different absorptive capacity strategies, their related financial payoffs, and their knowledge creation potential through time
Deconfined criticality from the QED-Gross-Neveu model at three loops
The QED-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory
involving Dirac fermions and a critical real scalar field. This theory has
recently been argued to represent a dual description of the deconfined quantum
critical point between Neel and valence bond solid orders in frustrated quantum
magnets. We study the critical behavior of the QED-Gross-Neveu model by
means of an epsilon expansion around the upper critical space-time dimension of
up to the three-loop order. Estimates for critical exponents in 2+1
dimensions are obtained by evaluating the different Pade approximants of their
series expansion in epsilon. We find that these estimates, within the spread of
the Pade approximants, satisfy a nontrivial scaling relation which follows from
the emergent SO(5) symmetry implied by the duality conjecture. We also
construct explicit evidence for the equivalence between the QED-Gross-Neveu
model and a corresponding critical four-fermion gauge theory that was
previously studied within the 1/N expansion in space-time dimensions 2<D<4.Comment: 16 pages, 4 figures, 4 tables; v2: additional comments, published
versio
A Decision Support Tool for the Strategic Assessment of Transport Policies : Structure of the Tool and Key Features
On the Complexity of Case-Based Planning
We analyze the computational complexity of problems related to case-based
planning: planning when a plan for a similar instance is known, and planning
from a library of plans. We prove that planning from a single case has the same
complexity than generative planning (i.e., planning "from scratch"); using an
extended definition of cases, complexity is reduced if the domain stored in the
case is similar to the one to search plans for. Planning from a library of
cases is shown to have the same complexity. In both cases, the complexity of
planning remains, in the worst case, PSPACE-complete
Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
Two-dimensional spin-orbital magnets with strong exchange frustration have recently been predicted to facilitate the realization of a quantum critical point in the Gross-Neveu-SO(3) universality class. In contrast to previously known Gross-Neveu-type universality classes, this quantum critical point separates a Dirac semimetal and a long-range-ordered phase, in which the fermion spectrum is only partially gapped out. Here, we characterize the quantum critical behavior of the Gross-Neveu-SO(3) universality class by employing three complementary field-theoretical techniques beyond their leading orders. We compute the correlation-length exponent nu, the order-parameter anomalous dimension eta(phi), and the fermion anomalous dimension eta(psi) using a three-loop epsilon expansion around the upper critical space-time dimension of four, a second-order large-N expansion (with the fermion anomalous dimension obtained even at the third order), as well as a functional renormalization group approach in the improved local potential approximation. For the physically relevant case of N = 3 flavors of two-component Dirac fermions in 2 + 1 space-time dimensions, we obtain the estimates 1/nu = 1.03(15), eta(phi) = 0.42(7), and eta(psi) = 0.180(10) from averaging over the results of the different techniques, with the displayed uncertainty representing the degree of consistency among the three methods
Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations
Coherent state theory is shown to reproduce three categories of
representations of the spectrum generating algebra for an algebraic model: (i)
classical realizations which are the starting point for geometric quantization;
(ii) induced unitary representations corresponding to prequantization; and
(iii) irreducible unitary representations obtained in geometric quantization by
choice of a polarization. These representations establish an intimate relation
between coherent state theory and geometric quantization in the context of
induced representations.Comment: 29 pages, part 1 of two papers, published versio
Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
Two-dimensional spin-orbital magnets with strong exchange frustration have recently been predicted to facilitate the realization of a quantum critical point in the Gross-Neveu-SO(3) universality class. In contrast to previously known Gross-Neveu-type universality classes, this quantum critical point separates a Dirac semimetal and a long-range-ordered phase, in which the fermion spectrum is only partially gapped out. Here, we characterize the quantum critical behavior of the Gross-Neveu-SO(3) universality class by employing three complementary field-theoretical techniques beyond their leading orders. We compute the correlation-length exponent , the order-parameter anomalous dimension , and the fermion anomalous dimension using a three-loop expansion around the upper critical space-time dimension of four, a second-order large- expansion (with the fermion anomalous dimension obtained even at the third order), as well as a functional renormalization group approach in the improved local potential approximation. For the physically relevant case of flavors of two-component Dirac fermions in 2+1 space-time dimensions, we obtain the estimates , , and from averaging over the results of the different techniques, with the displayed uncertainty representing the degree of consistency among the three methods
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