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SciPost Physics

SciPost Physics Vol. 6 issue 2 (February 2019)

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A simple mechanism for unconventional superconductivity in a repulsive fermion model

Kevin Slagle, Yong Baek Kim

SciPost Phys. 6, 016 (2019) · published 1 February 2019 | · pdf

Motivated by a scarcity of simple and analytically tractable models of superconductivity from strong repulsive interactions, we introduce a simple tight-binding lattice model of fermions with repulsive interactions that exhibits unconventional superconductivity (beyond BCS theory). The model resembles an idealized conductor-dielectric-conductor trilayer. The Cooper pair consists of electrons on opposite sides of the dielectric, which mediates the attraction. In the strong coupling limit, we use degenerate perturbation theory to show that the model reduces to a superconducting hard-core Bose-Hubbard model. Above the superconducting critical temperature, an analog of pseudo-gap physics results where the fermions remain Cooper paired with a large single-particle energy gap.
Sigma models on flags

Kantaro Ohmori, Nathan Seiberg, Shu-Heng Shao

SciPost Phys. 6, 017 (2019) · published 4 February 2019 | · pdf

We study (1+1)-dimensional non-linear sigma models whose target space is the flag manifold $U(N)\over U(N_1)\times U(N_2)\cdots U(N_m)$, with a specific focus on the special case $U(N)/U(1)^{N}$. These generalize the well-known $\mathbb{CP}^{N-1}$ model. The general flag model exhibits several new elements that are not present in the special case of the $\mathbb{CP}^{N-1}$ model. It depends on more parameters, its global symmetry can be larger, and its 't Hooft anomalies can be more subtle. Our discussion based on symmetry and anomaly suggests that for certain choices of the integers $N_I$ and for specific values of the parameters the model is gapless in the IR and is described by an $SU(N)_1$ WZW model. Some of the techniques we present can also be applied to other cases.
Superconductivity in the Hubbard model: a hidden-order diagnostics from the Luther-Emery phase on ladders

Luca F. Tocchio, Federico Becca, Arianna Montorsi

SciPost Phys. 6, 018 (2019) · published 5 February 2019 | · pdf

Short-range antiferromagnetic correlations are known to open a spin gap in the repulsive Hubbard model on ladders with $M$ legs, when $M$ is even. We show that the spin gap originates from the formation of correlated pairs of electrons with opposite spin, captured by the hidden ordering of a spin-parity operator. Since both spin gap and parity vanish in the two-dimensional limit, we introduce the fractional generalization of spin parity and prove that it remains finite in the thermodynamic limit. Our results are based upon variational wave functions and Monte Carlo calculations: performing a finite size-scaling analysis with growing $M$, we show that the doping region where the parity is finite coincides with the range in which superconductivity is observed in two spatial dimensions. Our observations support the idea that superconductivity emerges out of spin gapped phases on ladders, driven by a spin-pairing mechanism, in which the ordering is conveniently captured by the finiteness of the fractional spin-parity operator.
Coexistence of valence-bond formation and topological order in the Frustrated Ferromagnetic $J_1$-$J_2$ Chain

Cliò Efthimia Agrapidis, Stefan-Ludwig Drechsler, Jeroen van den Brink, Satoshi Nishimoto

SciPost Phys. 6, 019 (2019) · published 6 February 2019 | · pdf

Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena to emerge. We consider an elementary frustrated 1D system: the spin-$\frac{1}{2}$ ferromagnetic ($J_1$) Heisenberg chain with next-nearest-neighbor antiferromagnetic ($J_2$) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at $J_2/|J_1|>1/4$ and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous symmetry breaking through order by disorder. Quite interestingly, this VBS state has a Affleck-Kennedy-Lieb-Tasaki-type topological order. This is the first example of a frustrated spin chain in which quantum fluctuations induce gapped topological order.
Whac-a-constraint with anomaly-free dark matter models

Sonia El Hedri, Karl Nordström

SciPost Phys. 6, 020 (2019) · published 7 February 2019 | · pdf

Theories where a fermionic dark matter candidate interacts with the Standard Model through a vector mediator are often studied using minimal models, which are not necessarily anomaly-free. In fact, minimal anomaly-free simplified models are usually strongly constrained by either direct detection experiments or collider searches for dilepton resonances. In this paper, we study the phenomenology of models with a fermionic dark matter candidate that couples axially to a leptophobic vector mediator. Canceling anomalies in these models requires considerably enlarging their field content. For an example minimal scenario we show that the additional fields lead to a potentially much richer phenomenology than the one predicted by the original simplified model. In particular collider searches for pair-produced neutralinos and charginos can be more sensitive than traditional monojet searches in thermally motivated parts of the parameter space where the mediator is outside the reach of current searches.
Fast control of interactions in an ultracold two atom system: Managing correlations and irreversibility

Thomás Fogarty, Lewis Ruks, Jing Li, Thomas Busch

SciPost Phys. 6, 021 (2019) · published 8 February 2019 | · pdf

We design and explore a shortcut to adiabaticity (STA) for changing the interaction strength between two ultracold, harmonically trapped bosons. Starting from initially uncorrelated, non-interacting particles, we assume a time-dependent tuning of the inter-particle interaction through a Feshbach resonance, such that the two particles are strongly interacting at the end of the driving. The efficiency of the STA is then quantified by examining the thermodynamic properties of the system, such as the irreversible work, which is related to the out-of-equilibrium excitations in the system. We also quantify the entanglement of the two-particle state through the von Neumann entropy and show that the entanglement produced in the STA process matches that of the desired target state. Given the fundamental nature of the two-atom problem in ultracold atomic physics, the presented shortcut can be expected to have significant impact on many processes that rely on inter-particle interactions.
Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor

C. W. J. Beenakker, A. Grabsch, Y. Herasymenko

SciPost Phys. 6, 022 (2019) · published 11 February 2019 | · pdf

Majorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they may not produce an unpaired fermion with equal probability. Building on a recent proposal to inject edge vortices in a chiral mode by means of a Josephson junction, we show how the fusion rule manifests itself in an electrical measurement. A $2\pi$ phase shift at a pair of Josephson junctions creates a topological qubit in a state of even-even fermion parity, which is transformed by the chiral motion of the edge vortices into an equal-weight superposition of even-even and odd-odd fermion parity. Fusion of the edge vortices at a second pair of Josephson junctions results in a correlated charge transfer of zero or one electron per cycle, such that the current at each junction exhibits shot noise, but the difference of the currents is nearly noiseless.
Equations of state in generalized hydrodynamics

Dinh-Long Vu, Takato Yoshimura

SciPost Phys. 6, 023 (2019) · published 15 February 2019 | · pdf

We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound states such as strings.
The Global Higgs Picture at 27 TeV

Anke Biekoetter, Dorival Gonçalves, Tilman Plehn, Michihisa Takeuchi, Dirk Zerwas

SciPost Phys. 6, 024 (2019) · published 25 February 2019 | · pdf

We estimate the reach of global Higgs analyses at a 27 TeV hadron collider in terms of Higgs couplings and in terms of a gauge-invariant effective Lagrangian, including invisible Higgs decays and the Higgs self-coupling. The new collider will indirectly probe new physics in the TeV range and allow for a meaningful test of the Higgs self-coupling also embedded in a global analysis.
A classical density functional from machine learning and a convolutional neural network

Shang-Chun Lin, Martin Oettel

SciPost Phys. 6, 025 (2019) · published 26 February 2019 | · pdf

We use machine learning methods to approximate a classical density functional. As a study case, we choose the model problem of a Lennard Jones fluid in one dimension where there is no exact solution available and training data sets must be obtained from simulations. After separating the excess free energy functional into a "repulsive" and an "attractive" part, machine learning finds a functional in weighted density form for the attractive part. The density profile at a hard wall shows good agreement for thermodynamic conditions beyond the training set conditions. This also holds for the equation of state if it is evaluated near the training temperature. We discuss the applicability to problems in higher dimensions.
Dynamical signatures of topological order in the driven-dissipative Kitaev chain

Moos van Caspel, Sergio Enrique Tapias Arze, Isaac Pérez Castillo

SciPost Phys. 6, 026 (2019) · published 27 February 2019 | · pdf

We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad generator $\hat{\mathcal{L}}$ of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes -- localized eigenmodes of $\hat{\mathcal{L}}$. Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed system, which are now separated by intermediate regions where winding numbers are ill-defined and the bulk-boundary correspondence breaks down. Combining these techniques with the Floquet formalism reveals higher winding numbers and different types of edge modes under periodic driving. Finally, we link the presence of edge modes to a steady state current.