SciPost Phys. 10, 087 (2021) ·
published 23 April 2021
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We solve the quantum-mechanical antiferromagnetic Heisenberg model with spins positioned on vertices of the truncated icosahedron using the density-matrix renormalization group (DMRG). This describes magnetic properties of the undoped C$_{60}$ fullerene at half filling in the limit of strong on-site interaction $U$. We calculate the ground state and correlation functions for all possible distances, the lowest singlet and triplet excited states, as well as thermodynamic properties, namely the specific heat and spin susceptibility. We find that unlike smaller C$_{20}$ or C$_{32}$ that are solvable by exact diagonalization, the lowest excited state is a triplet rather than a singlet, indicating a reduced frustration due to the presence of many hexagon faces and the separation of the pentagonal faces, similar to what is found for the truncated tetrahedron. This implies that frustration may be tuneable within the fullerenes by changing their size. The spin-spin correlations are much stronger along the hexagon bonds and exponentially decrease with distance, so that the molecule is large enough not to be correlated across its whole extent. The specific heat shows a high-temperature peak and a low-temperature shoulder reminiscent of the kagomé lattice, while the spin susceptibility shows a single broad peak and is very close to the one of C$_{20}$.
SciPost Phys. 10, 086 (2021) ·
published 22 April 2021
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Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz equation arise as coherent macroscopic low-energy fluctuations of the ferromagnetic ground state. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves. The internal magnon structure of classical spin waves is resolved by performing the semi-classical quantisation using the Riemann-Hilbert problem approach. We present an expression for the overlap of two semi-classical eigenstates and discuss how correlation functions at the semi-classical level arise from classical phase-space averaging.
SciPost Phys. 10, 085 (2021) ·
published 22 April 2021
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We study 3+1 dimensional $SU(N)$ Quantum Chromodynamics (QCD) with $N_f$ degenerate quarks that have a spatially varying complex mass. It leads to a network of interfaces connected by interface junctions. We use anomaly inflow to constrain these defects. Based on the chiral Lagrangian and the conjectures on the interfaces, characterized by a spatially varying $\theta$-parameter, we propose a low-energy description of such networks of interfaces. Interestingly, we observe that the operators in the effective field theories on the junctions can carry baryon charges, and their spin and isospin representations coincide with baryons. We also study defects, characterized by spatially varying coupling constants, in 2+1 dimensional Chern-Simons-matter theories and in a 3+1 dimensional real scalar theory.
SciPost Phys. 10, 084 (2021) ·
published 22 April 2021
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Semi-visible jets arise in strongly interacting dark sectors, where parton evolution includes dark sector emissions, resulting in jets overlapping with missing transverse momentum. The implementation of semi-visible jets is done using the Pythia Hidden valley module to duplicate the QCD sector showering. In this work, several jet substructure observables have been examined to compare semi-visible jets and light quark/gluon jets. These comparisons were performed using different dark hadron fraction in the semi-visible jets (signal). The extreme scenarios where signal consists either of entirely dark hadrons or visible hadrons offers a chance to understand the effect of the specific dark shower model employed in these comparisons. We attempt to decouple the behaviour of jet-substructure observables due to inherent semi-visible jet properties, from model dependence owing to the existence of only one dark shower model as mentioned above.
SciPost Phys. 10, 083 (2021) ·
published 15 April 2021
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Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of $5/2$. We consider the FQHE at another even denominator fraction, namely $\nu=2+3/8$, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the "$\bar{3}\bar{2}^{2}1^{4}$" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at $\nu=2+3/8$. We make predictions for experimentally measurable properties of the $\bar{3}\bar{2}^{2}1^{4}$ state that can reveal its underlying topological structure.
David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr
SciPost Phys. 10, 082 (2021) ·
published 14 April 2021
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We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-P\'ech\'e (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.
SciPost Phys. 10, 081 (2021) ·
published 13 April 2021
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The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension $d \geq 3$ (including non-integer $d$). Each conformal partial wave is expressed as a sum over ordinary spin partial waves, and the coefficients of this sum factorize into a product of vertex functions that only depend on the conformal data of the incoming, respectively outgoing operators. As a simple example, we apply this conformal partial wave decomposition to the scalar box integral in $d = 4$ dimensions.
